
    ANDREW CORPORATION, Plaintiff, v. GABRIEL ELECTRONICS, INC., Defendant.
    Civ. No. 83-0372 P.
    United States District Court, D. Maine.
    March 2, 1992.
    
      John Paterson, Bernstein, Shur, Sawyer, & Nelson, Portland, Me., Stephen Rudisill, Arnold, White & Durkee, Chicago, Ill., for Andrew Corp.
    Peter Murray, Murray, Plumb & Murray, John Rich, Perkins, Thompson, Hinckley & Keddy, Portland, Me., Charles Pfund, Boston, Mass., for Gabriel Electronics, Inc.
    
      
      . Ms. Kone’s testimony puts AFC's sales at 27 for fiscal 1986, which would result in an even smaller market share. Tr. 174.
    
   OPINION

GENE CARTER, Chief Judge.

This case, which is the damages phase of a trial conducted in this Court in 1986, was tried to the Court between July 8 and July 16, 1991. Defendant Gabriel’s liability for infringement of Plaintiff’s Knop patent was established by the Court of Appeals for the Federal Circuit in Andrew Corp. v. Gabriel Electronics, Inc., 847 F.2d 819 (Fed.Cir.1988). The Knop patent, U.S. Patent No. 4,410,892, was issued on October 18, 1983 for a horn reflector antenna lined with absorber. The period of infringement for which damages must be calculated runs from October 18, 1983 through 1989.

Under 35 U.S.C. § 284 a patent owner may recover damages that are adequate to compensate for an infringement. General Motors v. Devex Corp., 461 U.S. 648, 654-55, 103 S.Ct. 2058, 2061-62, 76 L.Ed.2d 211 (1983). Plaintiff here seeks its lost profits caused by Defendant’s infringement of the Knop patent. As the Court of Appeals for the Federal Circuit has recently stated: “A lost profits award requires (1) showing that the patent owner would have made the sales but for the infringement, i.e., causation existed, and (2) proper evidence for the computation of the loss of profits.” Standard Havens Products, Inc. v. Gencor Industries, Inc., 953 F.2d 1360, 21 U.S.P.Q.2d 1321 (Fed.Cir.1991). The patent owner’s burden in proving causation is one of reasonable probability. Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1065 (Fed.Cir.1983).

There are two primary ways of establishing causation in a cáse seeking lost profits. One way is to show that Plaintiff was one of two suppliers in a two-supplier market. Id. The other is to meet the requirements of the four part test set forth in Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152, 1156 (6th Cir.1978). Under the Panduit test the patent owner must prove (1) a demand for the patented product, (2) an absence of acceptable noninfringing substitutes, (3) the manufacturing and marketing capability to exploit the demand, and (4) the amount of profit the patent owner would have made. Id.; see also Kaufman Co., Inc. v. Lantech, Inc., 926 F.2d 1136, 1140-41 (Fed.Cir.1991). Plaintiff argues that it has presented evidence sufficient to show causation under either test.

I. LOST PROFITS

A. Two-Supplier Market

The evidence shows that in 1980 when Plaintiff entered the horn reflector antenna market both Defendant and Antennas for Communication, Inc. (AFC) were selling similar antennas with 10 foot horns. Tr. 625. Defendant’s antenna, like Plaintiff’s, was made with a metal horn, while AFC’s antenna had a fiberglass horn. Tr. 625. While Plaintiff extended the absorber lining of its SHX10 antenna to arrive at the patented antenna embodied in the Andrew SHX10A, Gabriel also experimented with the absorber lining in its UHR series of antennas. This experimentation arrived at the TH-10 antenna, which was introduced in late 1983, Tr. 691, 774-77, and which, in its absorber configuration, has been found to infringe the Knop patent. The Gabriel UHR antennas and the AFC antennas are non-infringing antennas. See Andrew Corp. v. Gabriel Electronics, Inc., Civ. No. 83-372 P, slip op. at 3 (D.Me. Aug. 1,1986). Gabriel withdrew its UHR antennas from the market in. 1985. Tr. 700-01, PX 291. AFC antennas remained on the market at least through 1988. PX 291, at DO 0012907; DX 1A. The Court finds, therefore, that there was clearly a third supplier of horn reflector antennas in the market during the period of infringement. The Court of Appeals for the Federal Circuit has made plain, however, that even in the presence of a third supplier, a market will still be considered a two-supplier market if the third supplier offered only products which were not acceptable substitutes for the patented product or if the third supplier’s sales were insignificant in proportion to those of the two main suppliers. Micro Motion, Inc. v. Kane Steel Co., Inc., 894 F.2d 1318, 1322 (Fed.Cir.1990).

In fiscal year 1984, which included the last quarter of calendar year 1983, AFC sold 101 ten foot horn antennas of a total 614 antennas sold by AFC, Gabriel and Andrew for that period, giving AFC a market share of 16.4%. PX 291, at DO 0012907. During AFC’s fiscal 1985, it sold 61 antennas of a total of 623 sold by the three producers during that period, for a market share of 9.8%. Id. The Court finds that these percentages represent a significant portion of the market compared to the portion occupied by the two main suppliers in the fiscal years 1984 and 1985.

The Court also finds, however, that AFC was not a significant figure in the horn reflector antenna market after 1985. By the most advantageous calculation, its market share in fiscal 1986 had dropped to 6.8%, reflecting its sale of 30 antennas of a total of 442 sold during the period. Id. Moreover, although Defendant now argues that AFC’s sales were significant throughout the period of infringement, its own Vice-President of Sales and Marketing, Donald Crisman, testified at the liability trial in 1986 that AFC’s sales were insignificant: “It’s basically a market between us and Andrew at this stage. Fiberglass product has fallen out of favor with many of the users. They still garner a small share of the market but it’s not significant. It’s basically Andrew and us at this point.” 1986 Tr. 467. The Court is satisfied that AFC made only 10 sales in fiscal 1987 and 15 or fewer in fiscal 1988, reflecting a further reduction in its market share. See PX 291 and Tr. 174.

As the Court of Appeals for the Federal Circuit has stated: “[M]ere existence of a competing device ... does not make the device an acceptable substitute." Uniroyal, Inc. v. Rudkin-Wiley Corp., 939 F.2d 1540 (Fed.Cir.1991) (citing TWM Mfg. Co. v. Dura Corp., 789 F.2d 895, 901 (Fed.Cir.1986)). In determining whether the AFC antenna was an acceptable substitute for the patented antenna in fiscal years 1984 and 1985, an important inquiry is whether “purchasers are motivated to purchase because of particular features of a product available only from the patent owner and infringers.” Smithkline Diagnostics, Inc. v. Helena Laboratories Corp., 926 F.2d 1161, 1166 (Fed.Cir.1991). If they are, then products without such features “would obviously not be acceptable noninfringing substitutes.” Id.

The Knop invention is a horn reflector antenna with absorber placed deep in the conical feed horn for the purpose of reducing interference with other antennas, by improving the antenna’s radiation patterns, without significant loss of gain. The absorber acts by reducing the width of the radiation pattern envelope (RPE) in the E-plane (the horizontal plane in which radiation patterns are measured) without significantly increasing the width of the H-plane (the vertical plane of such measurement). Andrew Corp. v. Gabriel Electronics, Inc., 847 F.2d 819, 820 (Fed.Cir.1988); Andrew Corp. v. Gabriel Electronics, Inc., Civ. No. 83-372 P, slip op. at 2-3. In its opinion on the liability phase of this case, this Court specifically found that “there had existed a long-felt need for an antenna with substantially equal E- and H-planes and good gain that could operate in relatively wide band widths.” Id. at 27.

The sales data presented at trial demonstrate dramatically that the long-felt need was not merely an academic one but reflected a commercial desire for better patterns. The graph in PX 326M shows that after introduction of antennas with the patented features, sales of those types of antenna soared while sales of horn antennas without the patented features plummeted. The Court infers from these data that although there were other horn reflector antennas on the market, they were not considered acceptable alternatives by the purchasers, who consistently chose antennas with the patented feature.

Eric Brooker, Andrew’s Vice-President of Engineering at the time of development of the patented antenna, was qualified at trial as an expert in terrestrial microwave systems and antennas. Tr. 357-58. After analyzing the radiation patterns of the AFC antennas now proffered by Defendant as acceptable substitutes for the patented antenna, Mr. Brooker stated: “The AFC antenna has clearly a very much inferior pattern to the SHX10A, when we compare [Ex.] HOG with Exhibit 110E. And so, I consider that it is clearly not as good an antenna as the SHX10A and therefore, would not he considered as a substitute.” Tr. 364-65. Although Mr. Brooker might have reason to be biased, the appearance of the patterns confirms his opinion.

Mr. Brooker’s opinion was corroborated indirectly by Mr. Joe Echols, a former AT & T employee called by Defendant. While Mr. Echols testified that patterns were not the only factor in antenna selection, Tr. 872, he admitted under cross-examination that pattern “is an important element to consider” when there is route congestion or when it is necessary to add additional paths into an antenna site. Tr. 876, 877. Echols also testified that the infringing TH-10 had more applications than the AFC antenna; i.e., that the patterns of the infringing antenna were better in more angles than were those of the proposed alternative AFC model. Tr. 860. Based on a random survey of AT & T sites, Echols testified that other antennas could have performed adequately at these sites, and that patterns were not the only consideration. His testimony concerning the importance of patterns, however, coupled with the buying patterns of AT & T and other purchasers, indicates clearly that purchasers wanted the better patterns provided by the patented feature in Plaintiffs and Defendant’s antennas and that the AFC antenna was not considered an acceptable alternative. Since the AFC antenna was not an acceptable alternative to the patented antenna, the Court finds that Plaintiff and Defendant comprised a two-supplier market of horn reflector antennas. Plaintiff has demonstrated, therefore, that it is entitled under that test to a presumption that its lost profits were caused by the Defendant’s infringement.

B. The Panduit Test

1. Demand

The first inquiry to be made when applying the Panduit test for causation is whether there is a demand for the patented product. In the liability trial this Court found “that there was a market for such a product because of the increasingly congested routes to be traversed from one microwave horn antenna to the next.” Andrew Corp. v. Gabriel Electronics, Inc., slip op. at 28. Here Plaintiffs graph, PX 326M, demonstrates that sales of the patented (or infringing) product accounted for the bulk of sales of horn reflector antennas during the period of infringement. Moreover, just the absolute number of sales of the patented antenna and Defendant’s infringing version, over 2000 during the period of infringement, PX 326S, shows that there was a demand for the patented invention. As Ms. Kone testified, AT & T was a significant customer for horn reflector antennas and it bought significant quantities of the patented device from both Plaintiff and Defendant. Tr. 185. Demand, therefore, is established.

2. Acceptable Noninfringing Substitutes

The second Panduit factor, whether there exist acceptable noninfringing substitutes, is virtually identical to the factor considered in the inquiry concerning the two-supplier market. See supra, at 1044-46. There, the Court considered and rejected the AFC antennas as acceptable, nonin-fringing alternatives to the patented antenna. Defendant has proffered various other purportedly acceptable alternatives. First, Defendant suggests that its UHR antennas would have been satisfactory substitutes. The Court rejects this proposal. Defendant’s own witnesses testified that the radiation patterns filed for Andrew’s subsequently patented antenna were considerably better than the patterns for the UHR antennas Defendant was then producing. Tr. 797, 745. Dan Allen, one of Defendant’s engineers, stated explicitly that Andrew’s SHX10A was far better than Gabriel’s UHR horn antennas, and made the telling statement that comparing the infringing TH-10 antennas to the UHR antennas was “like comparing a Cadillac to a Ford.” Tr. 615. An internal Gabriel memorandum recognized serious deficiencies in the UHR patterns which were felt to put it at a severe competitive disadvantage. PX 67. The most persuasive evidence of all, however, is that Gabriel abandoned production of the UHR series antennas shortly after it introduced its infringing TH-10. Tr. 700-01. As the court stated in TWM Mfg. Co., v. Dura Corp., 789 F.2d at 902, an acceptable substitute argument must be viewed of limited influence when the company “ignored those substitutes while it sold the patented invention.”

Defendant also suggests that its TH-10C and TH-10X are noninfringing alternatives for the patented invention. Sale of the TH-10C and TH-10X would violate the injunction issued by this Court after the decision of the Court of Appeals for the Federal Circuit. The TH-10C has 64 inches of absorber lining below the shelf, which is greater than the 55 inches prescribed by the injunction, and has an E- to H- plane ratio of 1.3, which was the upper limit set by the injunction. Tr. 383, 391-393. The TH-10X has 73 inches of absorber below the shelf and an E- to H-plane ratio of 1.3 also. Id. The Court ruled at trial that an antenna which violated the injunction would be held to be an infringing antenna. Tr. 379. Plaintiff, therefore, has shown satisfactorily that the TH-10C and TH-10X are not acceptable noninfringing alternatives.

Plaintiff also argues that Defendant’s ATH-10 antenna is not an acceptable non-infringing alternative. The ATH-10 is a horn reflector antenna which has a short corrugated feed horn attached to a smooth-walled absorber-lined horn. Because the patent calls for a smooth-walled conical feed horn, the Court stated explicitly in the injunction that corrugated horn antennas were not covered by the order. Order Granting Permanent Injunction, at 6 (Nov. 2, 1989). The Court is satisfied that the ATH-10 is not covered by the injunction and does not infringe the patent. The walls of the ATH-10 are partially corrugated. As the Court pointed out in the injunction, the patent claims require a smooth-walled conical feed horn. This is a limitation in the claims, and is not, by the Court’s interpretation, met by an antenna in which only a portion of the conical feed horn wall is smooth. Moreover, the Court is satisfied from the testimony at both trials that in a corrugated antenna like the ATH-10, the taper of the main beam is achieved by the corrugations and not by the absorber lining as is required by the patent. Tr. 476; Tr. 824-45; see Andrew Corp. v. Gabriel Electronics, Inc., slip op. at 9, 25. The ATH-10 would, therefore, not infringe the patent either literally or under the doctrine of equivalents.

The ATH-10, however, was not available in the market until the end of 1988. In Panduit, the court explained that the inquiry concerning available substitutes must focus on the date of first infringement. Panduit, 575 F.2d at 1162. In Kaufman Co., Inc. v. Lantech, Inc., 926 F.2d at 1142, the court found that a proffered noninfringing alternative was not an acceptable substitute:

The powered prestretch machines were not fully developed or accepted in the market until certain improvements were added to the machine. These improvements were not made until 1982, which is at the end of the infringement period. Thus, powered prestretch was not an acceptable purchase option during the infringement period.

Similarly, in this case, the ATH-10 was not fully developed or accepted in the market until the very end of the infringement period. Although Defendant has tried to argue that it could easily have developed the ATH-10 in 1983 had it known it was necessary, it has cited no authority for the proposition that an acceptable noninfringing substitute is what might have been available under other circumstances. The Court finds, therefore, that the ATH-10 was not an acceptable noninfringing substitute during the period of infringement between 1983 and the end of 1988. The ATH-10 was an acceptable noninfringing substitute in 1989, the last year of the period of infringement.

3. Sales and Marketing Capability-

In order to meet the third Panduit requirement, the patentee must show that it had the marketing and manufacturing capability to exploit demand. Plaintiffs manufacturing manager, Thomas Fencken, testified very credibly about the size of Plaintiffs manufacturing facility and operations. The Court is satisfied from the record that Andrew could easily produce at least one antenna per shift, and that it had the capability of running up to three shifts per day, six days per week, for 48 weeks per year. Tr. 97-99. The record shows that Plaintiff and Defendant together never produced more than 569 horns in a given year, PX 326S, PX 291, and that Defendant sold about 1200 infringing TH-10 series antennas during the period of infringement. PX 291. The Court finds, therefore, that Plaintiff had the manufacturing capacity to meet the demand if Defendant had not infringed.

The record also shows satisfactorily that marketing and sales of horn reflector antennas is not particularly intensive, Tr. 548, and that Plaintiff, which was a large company with a large sales force, would have had the sales and marketing capability to handle the orders generated by extra sales. Tr. 547-48. Plaintiff's marketing manager testified that if Plaintiff had suddenly acquired all of Defendant’s southern region sales, it might have had to add a part of a technical sales person in that region. Tr. 554. The Court finds, therefore, that Plaintiff had the requisite marketing and sales capability to meet the demand if Defendant had not been in the market with its infringing products.

4. Lost Profits

In establishing lost profits, the Federal Circuit has endorsed the incremental income method of calculating lost profits:

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 Machine 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 on horn antennas and convoyed sales during the period of infringement to-talled $9,673,892. PX 291. Plaintiff also presented evidence seeking to prove a further loss through price erosion of more than $4,000,000. For a number of reasons the Court finds the presentation by Ms. Kone, Plaintiff’s accounting expert, flawed, and therefore unpersuasive.

Mr. Hoffman, Defendant’s accounting expert, attacked some of the basic assumptions underlying Ms. Kone’s testimony. While Mr. Hoffman and Ms. Kone were both well-qualified, the Court found Mr. Hoffman to be the more impressive expert. His experience, which was slightly more extensive than that of Ms. Kone, includes overall responsibility for Price Wa-terhouse’s Boston management consulting practice, which in turn includes marketing studies, strategic planning activities, cost accounting and a wide variety of other activities. Tr. 963-64. The Court found Mr. Hoffman’s perspective to be broader and more helpful than that of Ms. Kone, who has been primarily involved in the audit field for Arthur Anderson Company, and whose testimony was very detailed but at times gave the impression of not having the larger picture in mind. In most instances, Mr. Hoffman’s presentation was logical, cogent and very persuasive.

At the outset the Court notes that it rejects, for the most part, Mr. Hoffman’s first critique of Ms. Kone’s testimony, specifically that she assumed that Plaintiff would have made all of the sales of horn antennas made by Defendant during the period of infringement. In Kaufman, the Court said that “when the patentee establishes the reasonableness of the inference [that the infringing sales caused the loss of profits], the patentee has sustained the burden of proving his entitlement to lost profits for all infringing sales.” Kaufman Co. v. Lantech, Inc., 926 F.2d at 1141. As discussed above, Plaintiff has successfully shown that it is entitled to assume it would have made most of the infringing sales for the period through 1988, because demand existed, there were no acceptable substitutes for the patented antenna in the market, and Plaintiff had the capability to make the sales. Defendant did not successfully rebut Plaintiff’s showing on the Panduit factors for the period of infringement through 1988.

However, because of the existence of the noninfringing ATH-10 in 1989, Defendant did successfully show that “it is unreasonable to infer that some or all of the infringing sales probably caused the patentee to suffer the loss of profits” in that year. Id. at 1141-42. Ms. Kone’s testimony and exhibit PX-291 show the number of infringing antennas sold by Gabriel from fiscal 1983 through fiscal 1989 as 1216. If the Gabriel antennas sold in 1989 are excluded from this calculation, as they must be, according to PX-291, the number of infringing antennas for which Plaintiff would be entitled to lost profits, if proved adequately, is 1188.

Mr. Hoffman’s second criticism of Ms. Kone’s analysis concerns the means by which she calculated Plaintiff’s expected profit. In order to establish lost profits, it is necessary to subtract the cost of producing the goods that would have been sold but for the infringement from the price that would have been charged for the goods. In determining the costs of goods, it is necessary to include not only direct labor and materials costs, but material and labor overhead including engineering and operating expenses. Ms. Kone had determined the profit margin in part by analyzing which costs associated with production of horn antennas by Plaintiff would be fixed despite increases in volume production and which costs vary with volume changes. The methodology used by Ms. Kone and her team to do this was

to look at and interview and observe the process in the AOP (Andrew Orland Park) plant facility and discuss in detail with the managers responsible for those labor and overhead support departments what major [sic] of cost and activities are represented by what those departments support, and whether or not increased activity represents an increase in the amount of people, supplies or expenses that would be necessary to support that production.
... In looking at the departments we focus on what this amount of additional or incremental sales would represent in terms of activity for these departments, whether just activity in general or specifically related to horn antennas. And, again, it’s important as our premise for doing that because these departments support all of the production for Andrew Orland Park facility, to keep in mind in our terms, the amount of incremental production that this represented which would only have been less than 5 percent increase in production during the period as measured by sales.

Tr. 203-04. Cost records for various departments, therefore, were assessed in light of information gained from interviews and observation. Tr. 290. This method of analysis led Ms. Kone to establish as entirely fixed certain cost categories such as depreciation and occupancy charges and to establish rates of variability for others that were generally in the range of 25 to 50%. Tr. 291.

In Polaroid Corp. v. Eastman Kodak Co., 16 U.S.P.Q.2d 1481, 1526-27, 1990 WL 324105 (D.Mass.1990), the court criticized this general method of cost analysis, finding it imprecise and subject to bias. The same criticisms were presented persuasively at trial by Mr. Hoffman. Tr. 1007-08. Moreover, Ms. Kone did not have any documentation of the interviews which provided a partial basis for her cost assessments, Tr. 295, so the Court is unable to determine their thoroughness or to examine them for signs of bias. Mr. Hoffman also testified that the analysis performed by Ms. Kone is commonly used to set standards for annual or short-term internal cost accounting purposes. Tr. 1007-08. Both Mr. Hoffman and the court in Polaroid found more appropriate for assessing the nature of costs over a long period of time a cost accounting method which determines fixed and variable costs by “lookpng] at hard data ... to see what in fact changed over a 4 to 5 year period. To the extent that it can be shown that some cost in fact changed, and changed significantly, they are by definition not fixed, regardless of how compelling the account caption might sound.” Tr. 1007.

Mr. Hoffman performed an analysis of Plaintiff’s costs and testified that “looking empirically at the data over a 5 year period, we find in fact that it does change and changes substantially and that in fact was the case with many of the products cost identified as fixed in the claim.” Tr. 1008. The Court found convincing Mr. Hoffman’s demonstration, using hard data, that on the macro level, i.e., at the level of Plaintiff corporation in its entirety, selling and administrative costs varied with the level of sales. Tr. 1009. Similarly, on the micro level, i.e., the level of specific departments involved in horn antenna production, Mr. Hoffman found that costs treated as fixed by Plaintiff did in fact vary over time:

When we get down to the specifics, as to what happened to the often mentioned tool crib, for example, we find during the
5 year period the tool crib, as well as many departments which sound fixed on their face and may well be fixed for 3 to
6 month periods in fact changed and changed substantially during the period of the damage claim, and thereby we can conclude because they changed and changed substantially they’re not fixed.

Id. Although Ms. Kone had found that depreciation was a fixed cost that did not need to be subtracted from the cost of the product in order to determine incremental profits, Mr. Hoffman’s analysis, again using hard data, determined that “depreciation moves very much together with sales, and that’s what is normally to be expected.” Tr. 1010.

Mr. Hoffman testified based on his observation of “many many businesses” that there exists a pattern of depreciation expenses rising in proportion to revenue over a period of time. Tr. 1041. He also testified that an analysis of Gabriel’s financial data also showed that as its sales increased, the general and administrative overhead costs of the company also increased. Tr. 1015. Moreover, using Plaintiff’s own business plan generated about the time it introduced horn antennas, DX 11D, Mr. Hoffman also showed that Plaintiff itself had expected its costs to increase proportionately with the increase in the volume of sales of horn antennas. Tr. 1012. This evidence provides a basis for believing that generally costs do not remain fixed as sales increase over a long period of time. In light of this general proposition, Mr. Hoffman’s analysis showing that, as could be predicted, many of Plaintiff’s costs actually rose over time as its sales increased casts serious doubt on Ms. Kone’s lost profits analysis which, based on the less desirable interview method, described many of Plaintiff’s costs as fixed or primarily fixed despite the increase in sales over the period of infringement. In addition, Mr. Hoffman testified that Plaintiff had not included in its analysis costs for certain departments, such as accounting and personnel, which would be expected to increase as sales volume increased. Tr. 1016. The Court does not find Ms. Kone’s analysis of costs reliable, and it therefore cannot accept her lost profits calculations, which are necessarily based in significant part on the cost assessments.

Plaintiff also seeks recovery for profits lost on accessory items sold by Defendant that are normally sold along with the horn reflector antenna (“convoyed” sales). If Plaintiff can show that in all reasonable probability it would have made the sales made by the infringer, what it would have netted from the sales is the measure of the loss. Paper Converting Machine Co. v. Magna-Graphics Corp., 745 F.2d 11, 23 (Fed.Cir.1984). Plaintiff presented the testimony of Ms. Kone with supporting documentation claiming that it had lost $2,891,792 on lost convoyed sales. Tr. 218-20; PX 291. On the record before it, the Court. is satisfied that the items listed as accessories of the horn antenna on Schedule II of PX 291 are normally sold with the antennas and would have been sold by Plaintiff but for the infringement. Tr. 576, 954-55, 218-20. The Court cannot, however, find it reasonably probable that Plaintiff would have made all of the sales of 281 waveguide which Defendant made during the period of infringement. The record shows quite plainly that the 281 waveguide, which accounts for the bulk of the lost profits claim for convoyed sales, was not always sold together with the antennas. Tr. 601-04, 632-35, 941-42. The Court finds, therefore, that Plaintiff has not met its burden of showing its entitlement to the lost profits it claims for convoyed sales of 281 waveguide.

More important, however, Ms. Kone testified that she used the same methodology to arrive at cost of goods sold for convoyed sales as she had used for the antennas themselves. Tr. 219. Since the Court found Ms. Kone’s analysis flawed for determining the costs of producing an increasing number of horn reflector antennas over time, it also finds unreliable the figures presented by Ms. Kone as lost profits on convoyed sales, which were generated in part by the same method.

Ms. Kone also testified that Plaintiff had suffered price erosion for its horn antennas of 15% because it had to compete with Gabriel and that there was a corresponding price erosion of 13.46% on Gabriel’s infringing antennas. Tr. 223-24. Plaintiff therefore seeks $4,088,835 for price erosion for all antenna sales during the period of infringement. Ms. Kone based the percentage figure for price erosion on a memo from Plaintiffs business manager, written after the Federal Circuit’s decision in this case, in which the discounted price for horn antennas is increased 15%. Tr. 221.

The Court cannot accept Plaintiffs price erosion figure for it fails to acknowledge what Mr. Hoffman convincingly described as “a fact well recognized by management and well recognized by every economist,” Tr. at 1038, i.e., that if the price of a product is increased, there is generally an associated cost of a reduction in number of units sold. Id. This premise is good common sense and indeed was part of the basis of the projections in Plaintiffs business plan. The plan noted that a 10% price increase in the horn antenna “will reduce sales from 420 units to 310 units FY 1982. Any additional increases would drastically reduce market share.” DX 11D at 5. An exhibit to the business plan is a “price/demand curve indicating the impact on sales volume as a function of the selling price of the current high quality product.” Id. Since Ms. Kone’s figures fail to account for a likely decrease in sales volume if the product price is increased 15%, the Court does not have confidence in Plaintiffs calculation of the amount it lost due to price erosion during the period of infringement. In sum, in a variety of respects, Plaintiff

has not presented “proper evidence for computation of the loss of profits;” it is, therefore, not entitled to a damages award for lost profits. Standard Havens Products, Inc., 953 F.2d 1360, 21 U.S.P.Q.2d 1321; Panduit, 575 F.2d at 1156.

II. REASONABLE ROYALTY

When, as here, lost profits cannot be proved, the patent owner is entitled to a reasonable royalty. 35 U.S.C. § 284; see also Panduit Corp. v. Stahlin Brothers Fibre Works, 575 F.2d at 1157. As the court stated in Panduit:

The setting of a reasonable royalty after infringement cannot be treated ... as the equivalent of ordinary royalty negotiations among truly “willing” patent owners and licensees. That view would constitute a pretense that the infringement never happened. It would also make an election to infringe a handy means for competitors to impose a “compulsory license” policy upon every patent owner.
Determination of a “reasonable royalty” after infringement, like many devices in the law, rests on a legal fiction.... There is, of course, no actual willingness on either side, and no license to do anything, the infringer being normally enjoined, ... from further manufacture, use, or sale of the patented product.
The amount of a reasonable royalty after infringement turns on the facts of each case, as best they may be determined. Among the relevant facts are: “what plaintiffs property was, to what extent defendant has taken it, its usefulness and commercial value as shown by its advantages over other things and by the extent of its use,” ... and the commercial situation.

Id. at 1158-59; see also Georgia-Pacific Corp. v. United States Plywood Corp., 318 F.Supp. 1116, 1120 (S.D.N.Y.1970) (providing a more detailed list of factors to be considered).

The record here shows that at the beginning of the period of infringement, which is the first pertinent reference point for calculation of a reasonable royalty, Panduit, at 1158, Plaintiff had the rights to a horn antenna which was a significant improvement over previous horn antennas. Andrew Corp. v. Gabriel Electronics, Inc., slip op. at 27. Plaintiff also had a corporate policy of refusing to license its patents to competitors in order to protect its investment in research and development. Tr. 414-15. Defendant submitted evidence showing that in 1968 and throughout the period of infringement patents for certain microwave technology had been licensed by AT & T at a royalty of about 4%, and that that rate was reduced by 30% in some instances. Tr. 918-927. In 1981, before the infringement began and before sales of the patented antenna were underway, Plaintiffs business plan predicted that the company could make a profit of 4.8% on the sale of the SHX10A antenna. DX 11D. By the beginning of the period of infringement, the SHX10A was already a commercial success. PX 326S, Tr. 174-75. Since there were no real noninfringing alternatives, any sales which Plaintiff licensed would have cut into its own sales. The record is clear that Defendant felt it needed an antenna with patterns as good as those produced by the SHX10A. Tr. 757-58, 615-16; DX 23; PX 67.

Given the fact that Plaintiff had a demonstrably effective and desirable product and that Defendant had reason to want to produce a similar product, the Court finds that 10% would have been a reasonable royalty. Such a royalty takes into account the fact that Plaintiff would have had very little, if any, incentive for licensing its product. The Court also recognizes that at such a rate Defendant would risk having little or no profit. Defendant, however, was a much smaller company than Plaintiff, and it needed to remain competitive in the antenna field. Defendant’s customers had been dissatisfied with Defendant’s horn reflector antennas, Tr. 758, and had expressed a desire for an antenna with improved patterns. Tr. 757. At the time the Knop patent issued, Defendant had been engaged in a lengthy research and development effort, which had resulted in part in its decision to add absorber deep in the cone. Tr. 757-777. Therefore, in order to remain a viable competitor in the market, Defendant might well have been willing to forsake the possibility of large profits on antennas and to get on with production of the unit it had been developing and which had been preempted in part by the Knop patent. Moreover, if Defendant had agreed to pay a royalty of 10%, it would still have been able to anticipate significant profits on unpatented accessories which are generally sold with the patented antenna, and which have relatively high profitability compared with that of the horn antenna. Tr. 578.

The Court rejects Defendant’s proposal that a reasonable royalty for its infringement be set at 2.8%. This figure, which Defendant asserts is based on the industry rate, ignores the realities of the commercial situation as set forth above. Even though the reasonable royalty is a legal fiction, the Court cannot countenance a rate which would never have been negotiated by a willing patent holder and a willing license seeker.

The Court also rejects Plaintiff’s proposal of a reasonable royalty of 34.36%, which reflects Plaintiff’s calculation of the average of its lost incremental profit on the patented product. Given Plaintiff’s projections of the profitability of the SHX10A and Defendant’s actual profits from the sale of the TH10, it is inconceivable that the hypothetical willing parties would ever have agreed to á figure so vastly inconsistent with any reasonable prediction of profitability.

As the Federal Circuit has made plain [t]he entire market value rule allows for the recovery of damages based on the value of an entire apparatus containing several features, when the feature patented constitutes the basis for customer demand_ Where a hypothetical licensee would have anticipated an increase in sales of collateral unpatented items because of the patented device, the pat-entee should be compensated accordingly-

TWM Mfg. Co., Inc. v. Dura Corp., 789 F.2d at 901. What have previously been referred to here as convoyed sales are, therefore, correctly included in the royalty base. As discussed previously, Plaintiff proved satisfactorily that Defendant regularly sold the accessories listed in PX 291, Schedule II with its horn reflector antennas. Tr. 954-55, 576, 218-220. Although Defendant most probably sold some waveguide with its horn reflector antennas, the evidence shows that the waveguide was not always sold with antennas. Tr. 601-04, 632-35, 941-42. There is no way for the Court to determine from the evidence before it what part of the waveguide sales were really lost convoyed sales that would have gone to Plaintiff had Defendant not infringed. Therefore, the figures provided for sales of waveguide in PX 291, Schedule II cannot be included as part of the base for computation of a reasonable royalty.

III. PREJUDGMENT INTEREST

Prejudgment interest should ordinarily be awarded on patent damage awards of a reasonable royalty. General Motors Corp. v. Devex Corp., 461 U.S. at 655-56, 103 S.Ct. at 2062-63. Under the statute the amount of interest is to be determined by the Court. In General Motors, the Supreme Court stated that interest may be denied in certain circumstances, and it gave as an example a situation in which undue delay in prosecution was caused by the patentee. General Motors, 461 U.S. at 656-57, 103 S.Ct. at 2062-63. Defendant here suggests that Plaintiff is not entitled to any prejudgment interest because the lengthy proceedings are attributable to the vagueness of the Knop patent.

Without doubt these proceedings have gone on far too long. The Court is unwilling, however, to place the blame for that on one party, arid it is certainly not willing to deny interest to Plaintiff on the basis of the nature of a patent which has been adjudged by the Court of Appeals to be valid. The Court finds that Plaintiff here is entitled to an award of prejudgment interest calculated at the prime rate and compounded monthly. This rate and method of calculation will adequately compensate Plaintiff for the loss of the use of its money over the lengthy period of this litigation. Schedule IV of PX 291 sets forth the average rate of interest during the period of infringement. Schedule IV obviously does not contain an accurate calculation of the interest since the base to which the percentage is applied is inaccurate.

IV. WILLFULNESS

Under 35 U.S.C. § 284 a patent damage award may be enhanced if the Court finds that the infringement was willful. In its initial opinion the Court stated that it had been left with the impression that Defendant had probably copied Plaintiffs antenna when it designed its TH-10. Andrew Corp. v. Gabriel Electronics, slip op. at 28. After hearing the new evidence in this case and reviewing the record in the liability trial the Court is satisfied that Defendant did not copy Plaintiffs design in the early 1980’s. The Court found Mr. Whiting, Defendant’s Vice-President of Engineering to be convincingly sincere in his testimony concerning the development of the absorber-lined horn reflector antenna. Tr. 757-793. The Court finds, based on Mr. Whiting’s testimony and the equally persuasive testimony of Mr. Gemme, Tr. 649, that Defendant initially did not copy Plaintiff’s horn antenna design and that subsequent to the various proceedings in this case Defendant acted appropriately in its attempts not to infringe Plaintiff’s patent while remaining competitive in the market. Having faced the task initially of assessing the validity of the patent and later of attempting to define the limits of the invention for purposes of an injunction, the Court realizes how difficult it was to ascertain the precise point of infringement. Defendant sought and received the advice of counsel, Tr. 663, 784, DX 13B, which was based in part on evaluations of materials provided in the course of litigation. Id. The Court finds that Defendant justifiably and in good faith relied on what seemed like competent, soundly based advice. The record here provides no basis for a finding of willful infringement. The Court also finds that this is not an exceptional case meriting the award of attorneys fees under 35 U.S.C. § 285.

Accordingly, Defendant is hereby ORDERED to pay to Plaintiff a royalty of 10% of its receipts on sales of its infringing horn reflector antennas (not to include the ATH-10) and accompanying accessories (as set out in PX 291, Schedule II, but excluding sales of 281 waveguide) from October 18,1983 through 1989. Interest to the date of judgment will be payable at the prime rate, compounded monthly. The parties are hereby ORDERED to confer and try to agree on the exact dollar amount of this award and to submit within 15 days of the date of this order a proposed judgment incorporating the specific amount of the award. If the parties cannot agree on the proposed judgment, each shall submit a proposed judgment with supporting written argument within 15 days of the date of this order, and the Court will resolve the issues so generated on the papers.

SO ORDERED. 
      
      . Carol Kone, Plaintiffs accounting expert, testified that PX 291 was prepared with reference to fiscal quarters and that yearly totals referred to a fiscal year that included the fourth quarter of one calendar year and the first three quarters of the succeeding calendar year. Tr. 301-02.
     
      
      . The Court notes that while the figures given for AFC sales in PX 291, which was prepared by Ms. Kone, do not always correspond to the figures provided in her testimony, they do correspond for fiscal 1984 and 1985. Tr. 174. Although the transcript refers to a total of 61 antennas being sold by AFC in 1987, the Court’s notes show that she said 1985. The context of the quotation confirms the Court’s recollection. Ms. Kone describes sales figures in chronological order beginning with 1983 and 1984, so that 1985 is the next logical year. Moreover, PX 291 does not provide data for AFC sales for three years after 1987, although the quote as transcribed indicates that such data exist. On this point the Court accepts PX 291 and its accompanying testimony rather than DX 1A, which provides similar data, because PX 291 is more detailed and better explained.
     
      
      . PX 291 shows 48 antennas sold by AFC in fiscal 1987. After hearing the detailed examination of Ms. Kone on this figure, the Court is satisfied that 38 of those antennas were sold to a United States company for installation overseas and are therefore irrelevant for purposes of establishing domestic market sales. Tr. 336-37.
     
      
      . The horn of the AFC antenna proposed as an acceptable noninfringing substitute is made of fiberglass. Mr. Crisman's testimony, quoted above, made clear that by 1986 fiberglass had fallen out of favor. Testimony by Mr. Brooker and Mr. Leming explained fiberglass was less desirable because it cracks more easily than metal, making it less reliable for antenna performance. Tr. 369-71, 1105. While a metal horn is not one of the patented features, the absence of fiberglass in the non AFC horns was a desirable feature found in the patented and infringing horns. That the market wanted horns made of materials other than fiberglass is another reason the AFC antenna was not an acceptable substitute for the patented antenna.
     
      
      . Defendant has repeatedly urged the Court to evaluate whether the TH-10C infringes the patent without reference to the injunction. Although Defendant has tried to argue that the TH-10C does not infringe because the type of absorber used is different from and serves a different function from that used in the patented invention, the Court remains unpersuaded. Although, as Defendant suggests, there can be no literal infringement of the patent by the TH-10C since there has been no proof of the existence of hybrid modes, the Court must examine whether the TH-10C infringes the patent under the doctrine of equivalents. Under this doctrine an antenna infringes the Knop patent if it performs substantially the same function in substantially the same way to give substantially the same result. Atlas Powder Co. v. E.I. Du Pont De Nemours & Co., 750 F.2d 1569, 1579 (Fed.Cir.1984). The Court determined with its injunction order that placing absorber 54 inches or deeper below the shelf was substantially the same method used in the patented invention and that an E- to H-plane ratio of 1.3 was substantially the same result achieved by the patented invention. Defendant argues here that the effect is not achieved in substantially the same way because pyramidal absorber rather than flat absorber was placed in the cone. While the patent mentions that one type of absorber that may be used has a flat surface, as the Court stated in its prior opinion, the flat surfaced, 3/s" absorber “is only one example of the type of absorber necessary for the invention, PX-1, [DTX-1] Col. 3, and [the patent] particularly disclaims limitation of the invention to any one embodiment.” Andrew Corp. v. Gabriel Electronics, Inc., slip op. at 14-15.
      Defendant also argues that the absorber is not performing the same function as the absorber in the patented device. It argues that the pyramidal absorber is performing the traditional mopping up function of the prior art. Although the Court learned at the prior trial that pyramidal absorber was used in the shield of the patented antenna to mop up stray radiation, the Court is not persuaded that the pyramidal absorber in the TH-10C is used for that function. In its . prior opinion the Court accepted the testimony of Dr. Love that the use of absorber in the lower portion of the cone "is now fundamentally different from the use of the blue absorber in the top region of the cone. The absorber here has a definite purpose, namely to create a boundary condition which is frequency independent, in substance supports the HE11, a physical phenomena [sic ] totally different from the mopping up.” Id. at 26. The Court, therefore, infers from the fact that the pyramidal absorber was placed deep in the cone in the TH-10C rather than just in the shield that it was being used to try to shape the main beam by reducing the E-plane pattern. See id. Since the TH-10C is performing substantially the same function in substantially the same way to give substantially the same result as the patented antenna, it infringes the patent under the doctrine of equivalents.
     
      
      . Plaintiff moved to exclude the testimony of Mr. Hoffman on the grounds that adequate discovery of his opinions had not been provided prior to trial. The Court admitted the testimony de bene esse and has now had the benefit of hearing both the testimony and the cross-examination and of the submissions of counsel on the issue of admissibility. The Court is fully satisfied that Mr. Hoffman’s testimony should not be excluded. The substance of his testimony, including his critique of the assumptions made by Ms. Kone, was disclosed in his deposition. It was plain from Mr. Hoffman’s deposition that he had and would use the regression analysis which the Court has found persuasive here in assessing Plaintiffs damages claim. Moreover, he specifically stated that he would challenge Ms. Kone’s determination that the tool crib represented a fixed cost area and her assumptions relating to price erosion. Although Plaintiffs counsel argued that many of the details of the testimony had not been provided, he was able to engage in a vigorous cross-examination of Mr. Hoffman, which was demonstrably effective in certain respects. Ms. Kone was in the courtroom during Mr. Hoffman's testimony and as a professional accountant would have been able to aid Plaintiffs counsel in preparing his cross-examination. Mr. Brooker also presented rebuttal testimony directed at some of Mr. Hoffman’s assertions. The Court, therefore, cannot find that there was either the surprise or prejudice to Plaintiff which would warrant the drastic discovery sanction of exclusion of Mr. Hoffman’s testimony. See Stacey v. Bangor Punta Corp., 107 F.R.D. 786, 789 (D.Me.1985).
     
      
      . At trial the Court reserved decision on a relevancy objection to the regression analyses performed by Mr. Hoffman. Plaintiff argued that the analyses were being used to try to prove a cause and effect relationship between volume of sales and various costs and that Mr. Hoffman had said at his deposition that regression analysis cannot determine that effect. Mr. Hoffman indeed testified that regression analysis alone cannot prove cause and effect. Tr. 1041. It can be and is successfully used to demonstrate correlations between variables and inferences can be made from these correlations. See Polaroid Corp. v. Eastman Kodak Co., 16 U.S.P.Q.2d at 1527. For example, as Mr. Hoffman testified when a cause and effect relationship between two variables exists, the data representing those two variables will move together. Tr. 1030. It seems clear that lots of pairs of data could move together without any relationship existing between them. Therefore, to infer a cause and effect relationship from correlations between variables, there must be other evidence making such an inference reasonable.
      The Court finds that the regression analyses presented by Mr. Hoffman are useful, with the other evidence presented, in evaluating Defendant’s hypothesis that a business’s costs go up as the volume of its production goes up. Rule 401 of the Federal Rules of Evidence defines "relevant evidence” as evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence." The regression analyses presented at trial meet this standard. The Court notes, too, that in Polaroid, Judge Mazzone not only allowed introduction of regression analy-ses to prove costs but found them "much more accurate, credible, and appropriate” than the interview method used by Plaintiff here. Polaroid Corp. v. Eastman Kodak Co., 16 U.S.P.Q.2d at 1527.
     
      
      . Plaintiff urges that the business plan is not relevant because it was prepared before the patent issued and before the commercial success of the product and reflects projections rather than what actually happened. The Court, however, finds the business plan useful not for its specific projections but for the general economic and business principles upon which those projections were based. In this situation, the business plan illustrates precisely what Mr. Hoffman testified: that volume reduction due to price increase is a phenomenon "well-recognized by management.” Tr. at 1038. Similarly, in the discussion of cost analysis, the Court found the business plan useful because it expressed the general expectation, subsequently illustrated by Mr. Hoffman’s regression and other analyses, that costs generally rise as sales increase.
     
      
      . Although Plaintiff argues that its 15% figure is conservative, there is no way for the Court to estimate whether the “conservative” nature of the price erosion figure would adequately counterbalance the likely diminution of sales over time due to a price increase.
      Although Plaintiff increased its price after July 1988, it sold more antennas in 1989 than it had in 1988. Plaintiff urges the Court to draw from this one year pattern the inference that over the entire period of infringement the market would have behaved in the same way and that no cost in sales volume would have been incurred from increased price. The Court declines to do so. First, the Court notes that Plaintiffs antenna price did not decrease because of competition from Defendant when the TH-10 entered the market. Tr. 1005. Second, the Court heard testimony about the development and commercial utilization of new technology over the period of infringement. Third, Plaintiff sold fewer antennas in 1989 than Defendant had sold in 1988. There are, therefore, many factors which cast doubt on the general inference concerning market behavior over time which Plaintiff asks the Court to make based on a one year sales pattern.
     
      
      . Defendant ultimately earned a profit of 7.2% on its sales of infringing TH10 antennas. Tr. 1026. Defendant argues vehemently that the royalty awarded by the Court must provide for a profit for Defendant. That is plainly not the law. Radio Steel & Mfg. Co. v. MTD Products, Inc., 788 F.2d 1554, 1557 (Fed.Cir.1986). Profit would certainly be an important consideration of a willing licensee in negotiating a license, and the Court has taken it into account here.
     
      
      . The Court infers this from the fact that the horn reflector antenna sales represented an important segment of Defendant’s business, "in the order of 20, 25 percent,” Tr. 640, and from the fact that after the Federal Circuit’s decision in this case, Plaintiff specifically sought the advice of counsel in order to modify its antenna so it could "continue to manufacture a horn in competition with the market place” without violating the patent. Tr. 663.
     
      
      . The Court also does not find persuasive Defendant’s suggestion that the reasonable royalty rate should be half the difference between the cost of producing the ATH-10 and the TH-10. The corrugated horn had well-known disadvantages. Tr. 657. Moreover, there was clearly the serious possibility that if Defendant did not market the successful patented device, it would incur a serious competitive disadvantage in a very competitive market during what was then an unknown development period for the corrugated horn. The Court finds it unlikely that Defendant would have risked losing its competitive position by banking on a new product with some known disadvantages, if it could have chosen to license and market the successful patented technology while developing its own new antenna.
     
      
      . The Court takes judicial notice that the period during which Plaintiff was deprived of its funds was one in which the investment climate was favorable; thus, the prime rate is a conservative measure for compensating Plaintiff.
     
      
      . The Court notes too that the evidence presented in another case between these parties relating to horn reflector antennas, Andrew Corp. v. Gabriel Electronics, 782 F.Supp. 149 (D.Me.1992), has also provided a broader perspective on the development of the horn reflector antennas by Defendant.
     