RICH, Circuit Judge.

These are cross-appeals from the May 15, 1987, judgment of the District Court for the District of Nebraska, as amended May 22, 1987, holding that the claims of patent No. 4,337,805 for “Agricultural Bag Loading Apparatus” (’805 patent), assigned to Ag-Bag Corporation, are not invalid, and that Ryco, Inc., Kelly P. Ryan, and Blair Manufacturing Company had infringed claims 1-10, 12-16, and 32-35 of the ’805 patent. The district court awarded Ag-Bag $83,100.73 in damages as a reasonable royalty and denied Ag-Bag’s claims for increased damages and attorney fees. We affirm in part, reverse in part, vacate in part, and remand.

BACKGROUND

A. The Silopress k01 Machine

In the 1970’s, the Gebruder Eberhardt Company of Germany developed an in-the-field agricultural bagging machine for compressing silage into large air-tight plastic bags one hundred feet or more in length and eight feet in diameter. Eberhardt obtained two U.S. patents on its bagging machine, Nos. 3,687,061 (’061 patent) and 4,046,068 (’068 patent), both issued to Eg-genmueller, et. al. Eberhardt then granted Midwest Silopress, Inc., of Sioux City, Iowa, a license under the patents.

Pursuant to its license, Midwest Silo-press sold a bagging machine known as the “Silopress 401.” The Silopress 401 (see Appendix) is powered by attaching a power takeoff (16) to a tractor. An oscillating feed table (2) at the intake forces silage toward a rotor (3) located in a stripper basket (6) between the intake and the discharge chamber. The rotor teeth (5) are arranged in a helical pattern similar to an opposed flight auger which when rotated causes the silage to move from the sides of the intake toward the center. The rotor then forces the silage through the discharge chamber and compresses it into a large plastic bag (9).

Both the bagging machine and the tractor move away from a backstop (10) placed at the back end of the bag as silage is

forced into it. To control the silage compression, the backstop is connected to the bagging machine by two cables (12) which run to two drums (13) on the machine. The cable drums are mounted on a shaft (14) and an adjustable band brake (18) is secured to one of the drums. The brake resists the movement of the machine and thus controls the silage pressure within the bag.

The Silopress 401 had several design problems which became apparent after long-term use. For example, the helical arrangement of the rotor teeth caused power surges which resulted in uneven compression of the silage. The oscillating feed table contributed to the problem by causing the silage to surge into the rotor. The placement of the rotor within the stripping basket limited contact of silage with the rotor teeth and reduced the flow of silage through the machine. Also, the band brake was difficult to set accurately and would often cause the machine to skip, jump, or buck.

B. The ’805 Patent

The ’805 patent is directed to an improved agricultural bagging machine which eliminates the problems of the Silopress machine. The patent application was filed December 3, 1980, and the patent issued July 6, 1982, to David Rasmussen, Richard Lee, and William Johnson. Rasmussen, Lee, and Larry Inman were dealers for Midwest Silopress who later founded Ag-Bag.

Although the inventors made many changes to the Silopress machine, the bagging machine of the ’805 patent differs from the Silopress in four primary respects:

*1.Teeth* — The rotor teeth are evenly distributed on the rotor shaft in groups of three or four in a “random pattern” instead of the helical arrangement of the Silopress. In Figure 5 of the patent (reproduced in the Appendix) the surface of the rotor shaft (52) is shown flat, illustrating the placement of the teeth (46) in groups (92) on the shaft in the preferred embodiment. This tooth arrangement, in which the leading edge of each group of teeth does not coincide with the leading edge of any other group, eliminates the power surges and uneven flow of silage associated with the Silopress. The even distribution of the teeth, albeit random, further insures that the movement of silage is approximately the same along the length of the shaft.

2. Stripper — The stripper basket of the Silopress is replaced by a comb (48) of curved prongs or “J-bars” (90) positioned on the discharge side of the rotor in such a way as to allow the rotor teeth (46) to pass between them. (See Figures 3 and 4 in the Appendix.) The improved stripper comb admits more feed to the rotor and thus increases the capacity of the bagging machine over the Silopress.

3. Feeder — A “beater bar” feeder turning in the same direction as the rotor is mounted in the intake instead of an oscillating feed table. The beater bar feeder shown in Figure 3 of the patent includes a horizontally mounted shaft (60) and a plurality of prongs or tines (62) made of angle iron and mounted generally perpendicular to the shaft. The beater bar feeder pre-compresses the silage to a slight degree and insures that an adequate supply of silage is always presented to the rotor teeth.

4. Brake — The band brake of the Silo-press is replaced by a conventional automobile disc brake actuated by a manually operated hydraulic pump with a pressure sensor and dial. The disc brake eliminates the jerking and bucking which plagued the Sil-opress.

Independent claims 1, 15, 32, and 35 (see Appendix) are each directed to a bagging machine having one of the specific improvements. Dependent claims 2-10, 12-14, 16, 33, and 34 describe the features in more detail and in combination with the other improvements. No single claim of the ’805 patent incorporates all four improvements.

Ryco filed a request for reexamination of the ’805 patent in the Patent and Trademark Office on January 8, 1985. In the certificate of reexamination issued October 26, 1987, the patentability of all of the

claims asserted against Ryco (claims 1-10, 12-16, and 32-35) was confirmed. Of the remaining claims, one was cancelled and the rest were found patentable either in their original form or as amended.

C. The “Ag-Bagger”

Ag-Bag was formed in 1978 for the purpose of building the improved bagging machines of the ’805 patent. Ag-Bag had no manufacturing facilities so Rasmussen contacted Kelly Ryan, president of Blair Manufacturing, who agreed to make the machines for Ag-Bag. Blair Manufacturing built the improved bagging machine, known as the “Ag-Bagger,” from 1978 until 1984.

After the termination of the parties’ relationship in 1984, Blair Manufacturing still had a number of bagging machines it had manufactured for Ag-Bag in its inventory. Blair Manufacturing repainted these machines and sold them under a different name.

D. Ryco’s “Big-Bagger”

Kelly Ryan formed Ryco, Inc., in 1984 to compete with Ag-Bag. From its inception, Ryco manufactured machines with parts and labor supplied by Blair Manufacturing. Ryco also leased its manufacturing facilities from Blair Manufacturing. The manufacturing facilities and employees of both Ryco and Blair Manufacturing were transferred to Kelly Ryan Equipment Company (not a party in this case) in 1986.

Ryco made both two-wheel and four-wheel bagging machines which it sold under the name “Big Bagger.” Like the bagging machine of the ’805 patent, Ryco’s four-wheel machine has both a beater bar feeder and a hydraulic disc brake. The projections on the beater bar, however, are not perpendicular but are set at an angle to the shaft. The rotor teeth are arranged in groups of two in a helical pattern so that at least two groups of teeth engage the silage at the same time and the stripper bars are straight instead of curved.

The principal difference between Ryco’s two-wheel and four-wheel bagging machines is that in its two-wheel machine, the beater bar is omitted. In its place, the two-wheel machine uses a reverse-flighted auger made of strips of metal welded to a shaft to distribute the silage and feed it to the rotor.

THE DISTRICT COURT DECISION

Ryco sued Ag-Bag for a declaratory judgment that the '805 patent and two related U.S. patents, Re. No. 31,810 (’810 patent) and No. 4,320,036 (’036 patent) are invalid. Ag-Bag counterclaimed against Ryco, Kelly Ryan, and Blair Manufacturing for direct infringement and inducing infringement of the ’805 and '810 patents.

The district court held, inter alia, that Ryco had failed to establish by clear and convincing evidence that the claims of the '805 patent (except 17, 18, and 22 which were not considered) are invalid for obviousness under 35 U.S.C. § 103. The court held, however, that all claims of the ’810 patent are invalid under § 103. The court did not address the validity of the ’036 patent because the evidence presented no case or controversy on this issue.

On Ag-Bag’s counterclaim for infringement, the district court found that Ryco’s two-wheel and four-wheel bagging machines do not literally infringe the asserted claims of the ’805 patent (claims 1-10, 12-16, and 32-35), but infringe under the doctrine of equivalents. The court found that Blair Manufacturing had literally infringed the claims of the ’805 patent, however, by selling the machines it had manufactured for Ag-Bag and held in inventory after the termination of their relationship. While the court could not hold Kelly Ryan liable for direct infringement under 35 U.S.C. § 271(a), it held that he actively induced infringement of the ’805 patent in violation of § 271(b). The court also held that Blair Manufacturing induced infringement of the patent by providing materials, parts, plant space, and labor required by Ryco to manufacture its bagging machines.

In awarding damages under 35 U.S.C. § 284, the district court found that there was insufficient evidence to award lost profits to Ag-Bag. The court instead

awarded Ag-Bag a reasonable royalty of 5% on Ryco’s gross sales of the infringing bagging machines for a total award of $83,-100.73. The court found that Blair Manufacturing’s sale of the machines originally manufactured for Ag-Bag constituted willful infringement, but because there was no evidence showing the number of machines sold or the price at which they were sold, the court declined to treble those damages or to award attorney fees on this portion of Ag-Bag’s claim. The court also denied Ag-Bag’s claims for increased damages and attorney fees on the remaining infringing sales because Ryco reasonably believed that the ’805 patent was invalid, and if valid, that their bagging machines did not infringe.

Appellants Ryco, Kelly Ryan, and Blair Manufacturing (collectively Ryco) appeal from the portion of the judgment holding that claims 1-10, 12-16, and 32-35 of the ’805 patent are not invalid for obviousness under 35 U.S.C. 103 and that Ryco infringed these claims. Consequently, we need not consider the other claims of the ’805 patent. Ag-Bag cross-appeals from the judgment with respect to the finding that Ryco’s infringement was not willful, the denial of increased damages and attorney fees, and the award of damages of a reasonable royalty instead of lost profits. Neither party has appealed any issue regarding either the ’810 patent or the ’036 patent.

OPINION

Under 35 U.S.C. § 282, a patent is presumed valid, and the party attacking validity has the burden of proving facts supporting a conclusion of invalidity by clear and convincing evidence. See, e.g., American Hoist & Derrick Co. v. Sowa & Sons, Inc., 725 F.2d 1350, 1360, 220 USPQ 763, 770 (Fed.Cir.), cert. denied, 469 U.S. 821, 105 S.Ct. 95, 83 L.Ed.2d 41 (1984). Although this burden remains on the challenger, it may be more easily met where the challenger produces prior art that is more pertinent than that considered by the Patent and Trademark Office (PTO). See Connell v. Sears, Roebuck & Co., 722 F.2d 1542, 1549, 220 USPQ 193, 199 (Fed.Cir.1983).

A determination that an invention would have been obvious under § 103 is a conclusion of law based on fact. Panduit Corp. v. Dennison Mfg. Co., 810 F.2d 1561, 1568, 1 USPQ 2d 1593, 1597 (Fed.Cir.), cert. denied, — U.S. -, 107 S.Ct. 2187, 95 L.Ed.2d 843 (1987). The degree to which the determination involves facts, and is thus subject to the “clearly erroneous” standard of Fed.R.Civ.P. 52(a) is that degree required to erect a foundation of facts sufficient to support the legal conclusion. Id.

a. Scope of the Prior Art

At trial, Ryco submitted a great deal of prior art in its effort to establish the invalidity of the ’805 patent, some of which was not previously considered by the PTO. The district court found that the most significant prior art was the Silopress 401 machine, the Silopress parts list, and the Eg-genmueller ’061 and ’068 patents under which the Silopress was licensed. Ryco had previously cited the Eggenmueller patents and the Silopress parts list to the PTO in its request for reexamination.

One category of prior art which the PTO did not consider was art classified in U.S. Class 242 which relates to cable drums and brakes for cable drums. The district court found that the scope of the prior art should not be limited to just agricultural machinery because one of ordinary skill in the art would also look to the art of cable drums and brakes for cable drums in solving the problems of the Silopress machine. See Shatterproof Glass Corp. v. Libbey-Owens Ford Co., 758 F.2d 613, 620, 225 USPQ 634, 638 (Fed.Cir.1985) (“If the reference is not within the field of the inventor’s endeavor, one looks at whether the field of the reference is reasonably pertinent to the problem the inventor is trying to solve.”). Thus, the district court also considered patents to Pendleton, U.S. No. 3,964,692, Stum, U.S. No. 3,650,492, and Conti, U.S. No. 4,127,241, which disclose brake mechanisms in combination with ca

ble reels or drums, as pertaining to the subject matter of the ’805 patent.

b. The Teeth Claims (1-10, 12-14)

The only difference between the subject matter of claim 1 of the '805 patent and the Silopress machine is the arrangement of the rotor teeth on the shaft. In addition to reciting the basic structure of the bagging machine, claim 1 includes the limitation of “a plurality of teeth mounted along said primary shaft in a random pattern with said teeth being evenly distributed on the surface of said shaft.”

We agree with the district court that the invention of claim 1 would not have been obvious to one of ordinary skill in the art. Nothing in the prior art suggests the claimed agricultural bagging machine with the rotor teeth evenly distributed in a “random pattern.” This arrangement is contrary to the teaching of the Eggenmuel-ler ’068 patent in which the helical tooth arrangement causes the silage to move from the sides of the intake chamber toward the center. In the bagging machine of claim 1, the movement of silage is approximately the same along the length of the rotor shaft.

Ryco disputes Ag-Bag’s assertion that mounting the teeth on the rotor shaft as in claim 1 actually works better than the helical arrangement of the Silopress. Of course, this is irrelevant to the question of obviousness. Nothing in the patent statute requires that an invention be superior to the prior art to be patentable. Custom Accessories, Inc. v. Jeffrey-Allan Indus., Inc., 807 F.2d 955, 960 n. 12, 1 USPQ 2d 1196, 1199 n. 12 (Fed.Cir.1986); G. Rich, Principles of Patentability, 28 Geo.Wash. L.Rev. 393 reprinted in 42 J.Pat.Off.Soc’y 75 (1960).

Claims 2-10 and 12-14 are dependent on claim 1. Accordingly, we affirm the district court’s determination that these claims are not invalid under § 103 as well.

c. The Feeder Claims (15 and 16)

Claim 15 claims the improvement of the beater bar feeder mounted in the intake of the agricultural bagging machine comprising:

Ryco argues that it would have been obvious to substitute a beater bar feeder of the type in claim 15 for the oscillating feed table of the Silopress.

Beater bars as such were certainly old in the agricultural art, having been used on agricultural machines such as manure spreaders and balers. Ryco relies on the Nikkei patent, No. 2,917,993, for example, which shows a baler having a beater bar type pick-up unit mounted on the front. The pick-up unit has a rotating shaft with a series of spring wire projections to pick up hay from the field and feed it to a rotor.

Ryco has shown nothing in the prior art, however, which would suggest the use of a beater bar as a feeder in a bagging machine as in claim 15. Ag-Bag’s expert, Mr. Bryan, testified that where beater bars are used as feeders on other types of machines, they generally perform a different function. Instead of breaking up and dispersing the material as in other machines, the beater bar feeder in claim 15 compresses the material as it is fed to the rotor.

Thus, we agree with the district court that Ryco has not established that the improvement of claim 15 would have been obvious to one of ordinary skill in the art. Claim 16 is dependent on claim 15 and its subject matter is therefore unobvious as well.

d. The Comb Claim (35)

Claim 35 reads on the Silopress machine except for the limitation of a stripper comb mounted in the housing comprising a plurality of curved prongs with the convex surfaces facing the output chamber. Ryco

argues that it would have been obvious to replace the curved stripper basket of the Silopress with the stripper bars of the Nikkei patent to produce the claimed invention. The Nikkei patent, which the PTO did not consider, shows a plurality of curved stripper bars for stripping hay from a toothed rotor in the same manner as the ’805 patent. The convex surfaces of the bars also face the discharge side of the rotor.

This teaching of the Nikkei patent, when considered with the Silopress machine, clearly suggests the substitution of the curved stripper bars for the stripper basket. The function performed is identical. Thus, we conclude that Ryco satisfied its burden of proving invalidity of claim 35 and that the claimed invention would have been obvious as a matter of law. The district court made no erroneous findings of fact (there being very few discernible findings on this issue at all) but clearly arrived at the wrong legal conclusion. Accordingly, the district court’s holding that claim 35 was not invalid under § 103 is reversed.

e. The Brake Claims (32-34)

Claim 32 is directed to the improved brake means of the agricultural bagging machine. Specifically, claim 32 requires a “manually operated pump for pressuring said brake.” The only difference between the brake means of claim 32 and the Silo-press is that the brake is hydraulically operated rather than mechanically operated.

In holding the claims of the ’810 patent invalid, the district court found that the patents to Pendleton, Conti, and Stum all disclose disc brakes actuated by hydraulic pressure in combination with cable reels or drums. The court also found that Conti and Stum disclose manually operated pumps for supplying the hydraulic pressure as well. Although the district court found these references to be pertinent pri- or art to the ’805 patent, it apparently ignored them in its analysis of the claims.

Counsel for Ag-Bag conceded at oral argument that the improved brake means alone was not patentable over the Silopress and we certainly agree. There is ample suggestion in the references for replacing the band brake of the Silopress with a hydraulic brake. The brake performs the same function as in the references, albeit in a different environment. We conclude that the invention of claim 32 would have been obvious under § 103 as a matter of law and therefore reverse the district court’s holding that claim 32 is not invalid.

Ag-Bag has not separately argued claims 33 and 34 apart from claim 32 from which they depend, and we cannot see any independent basis for their validity. Accordingly, we hold that claims 33 and 34 are invalid under § 103 as well. See Gardner v. TEC Sys., Inc., 725 F.2d 1338, 1350, 220 USPQ 777, 786 (Fed.Cir.) (in banc) (dependent claim not separately argued is invalid along with independent claim), cert. denied, 469 U.S. 830, 105 S.Ct. 116, 83 L.Ed.2d 60 (1984).

a. Inventory

Ryco argues that there is no evidence to support the district court’s finding that Blair Manufacturing literally infringed the claims of the ’805 patent by selling the machines it had manufactured for Ag-Bag and held in inventory. We disagree.

First, there is no dispute that the bagging machines Blair Manufacturing built for Ag-Bag were made according to the ’805 patent. Second, Kelly Ryan admitted that while Blair Manufacturing modified some of the machines it had built for Ag-Bag, others were simply repainted and sold unchanged. Although the actual number is unknown, the district court had sufficient evidence from which to conclude that Blair Manufacturing sold some bagging machines that literally infringed one or more of the asserted claims.

b. Two-Wheel and Four-Wheel Machines

The district court held that Ag-Bag failed to prove Ryco’s two-wheel and four-wheel bagging machines literally infringe any of the asserted claims of the ’805 pat

ent, but that Ag-Bag had established infringement under the doctrine of equivalents. The court found that “the modifications found on the accused devices sold by Ryco performed substantially the same function in substantially the same way to obtain the same result” and that Ryco had “incorporated into the accused’s [sic] devices substitutes which, although literally can be distinguished from the patent’s claim [sic], nonetheless appropriate the invention’s benefits.”

Ryco argues that the district court misapplied the doctrine of equivalents with respect to claims 1-10 and 12-14. Ryco contends that its bagging machines are in fact not infringements of the claimed bagging machine because they do not achieve the result in substantially the same way. Ryco also argues that the district court improperly expanded the claim language to encompass the prior art.

Infringement under the doctrine of equivalents is a factual determination which we review under the clearly erroneous standard. See, e.g., Under Sea Indus., Inc. v. Dacor Corp., 833 F.2d 1551, 1557, 4 USPQ2d 1772, 1776 (Fed.Cir.1987). The district court found that the rotor teeth of Ryco’s two-wheel and four-wheel machines, while distributed on the shaft in a “helical” pattern, provide the same advantages of the rotor in claim 1 by allowing for more even compaction and distribution of the silage. Like the rotor in claim 1, the teeth are evenly distributed across the rotor and are arranged in groups. The silage does not move from the sides of the intake to the center but is evenly distributed along the rotor shaft. Thus, we cannot say that the district court’s finding of equivalence of this element of the claim is clearly erroneous. See Pennwalt Corp. v. Durand-Wayland Inc., 833 F.2d 931, 936, 4 USPQ2d 1737, 1740-41 (Fed.Cir.1987).

There are limits to the doctrine of equivalents, however. Specifically, the doctrine will not be used to extend a patent claim to cover a device in the public domain, i.e., found in the prior art applicable to the patent. Loctite Corp. v. Ultraseal Ltd., 781 F.2d 861, 870, 228 USPQ 90, 96 (Fed.Cir.1985). Ryco argues that the district court improperly extended the scope of claim 1 to cover the Silopress.

The “helical” arrangement of the teeth on Ryco’s rotors superficially resembles that of the Silopress—they are both helical and not “random.” Looking closer, however, it is apparent that the two are similar in name only and not in function. Unlike the Silopress rotor, adjacent groups of teeth on Ryco’s rotors are separated by 60° on the rotor shaft compared to about 8° between individual teeth on the Silopress. By successively contacting the silage, the teeth on the Silopress rotor cooperate to move the silage toward the center. Adjacent groups of teeth on Ryco’s rotors, however, act independently and do not cooperate as they do in the Silopress. Instead, the teeth are evenly distributed in groups so that only four teeth contact the silage at a time.

To say that Ryco is practicing the prior art and therefore does not infringe is to put form over function. Ryco’s rotor works like the one in claim 1, not like the Silo-press. Ryco's placement of the groups of teeth in a helix does not change the way the rotor works as compared to the claimed invention. It merely serves to take Ryco’s machines out of the literal language of claim 1. The district court correctly recognized that by using this tooth arrangement, Ryco had substituted an equivalent of the required element of the claim thereby appropriating the benefits of the invention while technically escaping the claim language.

Ryco argues that dependent claims 2-10 and 12-14 are not infringed for the same reason. Accordingly, we affirm the district court’s finding that Ryco's two-wheel and four-wheel bagging machines infringe claims 1-10 and 12-14.

Ryco also argues that its two-wheel and four-wheel machines do not infringe claims 15 and 16. On the four-wheel machine, the angle iron projections on the beater bar feeder are slanted at an angle of 60° to 67° instead of generally perpendicular to the shaft. Ryco contends that this is an improvement because each projection makes a

5- to 6-inch sweep through the silage and, thus, moves a greater amount of silage towards the rotor.

Even so, Ryco has not shown any error in the district court’s finding that Ryco’s four-wheel machine is an infringement of the claimed invention. That the accused device is an improvement on the claimed subject matter does not avoid infringement even under the doctrine of equivalents. See Datascope Corp. v. SMEC, Inc., 776 F.2d 320, 326, 227 USPQ 838, 842 (Fed. Cir.1985).

Likewise, with respect to the two-wheel machine, Ryco points out only what is known in the record and was found by the district court—that the feeder bar on the two-wheel machine does not have “projections” within the literal language of claim 15. The court also found, however, that instead of projections, the two-wheel machine has plates welded to the shaft to form an auger and that the auger performs the same function as the projections of forcing silage to the rotor. Again, Ryco has not shown any error in the court's finding that the two-wheel machine infringes the claim under the doctrine of equivalents.

Ryco has not separately argued that dependent claim 16 is not infringed. Accordingly, we affirm the district court’s finding that Ryco’s two-wheel and four-wheel bagging machines infringe claims 15 and 16.

In determining whether Ag-Bag is entitled to its lost profits under 35 U.S.C. § 284 as damages for Ryco’s infringing sales, the district court followed the four-part test outlined in Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152, 1156, 197 USPQ 726, 729-30 (6th Cir.1978), which this court has approved as one method of calculating lost profits. See e.g., Gyromat Corp. v. Champion Spark Plug Co., 735 F.2d 549, 552, 222 USPQ 4, 6 (Fed.Cir.1984). The guidelines set forth in Panduit generally provide that to obtain lost profits, the patent owner must prove: (1) a demand for the patented product during the period of infringing sales; (2) an absence of acceptable noninfringing substitutes; (3) the patent owner had the ability to meet the demand for the products covered by the patent; and (4) the amount of profit the patent owner would have made. The court held that Ag-Bag had clearly established the first three parts of the Panduit formulation, but not the fourth, i.e., Ag-Bag had not proved with reasonable certainty the profit it would have made.

Ag-Bag’s sales dropped from 168 machines in 1984 to seventy-two in 1985 and fifty-three in 1986. Based on the testimony of Ag-Bag’s expert, the court found that this decrease in sales was in uncertain part due to a slump in agricultural economy. This seems to us to be irrelevant to Ag-Bag’s lost profit due to Ryco’s infringing sales. During the relevant time period, Ryco had $1,662,014.52 in gross sales on the infringing bagging machines. To whatever degree the agricultural economy affected Ag-Bag’s sales, it affected the market as a whole, including Ryco’s sales. Having established the first three elements of the Panduit test, Ag-Bag had already shown a reasonable probability that it would have made the infringing sales made by Ryco. All that remained was to show what profit it would have made on those sales. The effect of the agricultural economy, being common to both Ag-Bag’s and Ryco’s sales, simply factors out.

The district court also found the proof of Ag-Bag’s profits insufficient because there was no indication that Ag-Bag’s expert considered the fact that Ryco’s machines sold for less than Ag-Bag’s. If anything, this fact favors Ag-Bag, not Ryco. See Livesay Window Co. v. Livesay Indus., Inc., 251 F.2d 469, 473-74, 116 USPQ 167, 170-71 (5th Cir.1958) (demonstrating that profit calculation based on infringer’s sales at lower price “if erroneous is so in favor of, not adverse to, infringer”). Ag-Bag’s disregard of this fact could only reduce the profit which it might have proved.

Ag-Bag sells three different models of the “Ag-Bagger” each of which has

a different profit margin. The court found, however, that the profit margin for these three models is roughly twenty-five percent of the dealer price. “The amount of lost profits awarded cannot be speculative but the amount need not be proven with unerring precision.” Bio-Rad, Laboratories, Inc. v. Nicolet Instrument Corp., 739 F.2d 604, 616, 222 USPQ 654, 664 (Fed.Cir.), cert. denied, 469 U.S. 1038, 105 S.Ct. 516, 83 L.Ed.2d 405 (1984). Ryco has not challenged this figure and there is nothing to indicate that it is not a valid approximation. Furthermore, “when the amount of the damages cannot be ascertained with precision, any doubts regarding the amount must be resolved against the infringer.” Lam, Inc. v. Johns Manville Corp., 718 F.2d 1056, 1065, 219 USPQ 670, 675 (Fed.Cir.1983).

We conclude that the district court's finding that Ag-Bag failed to prove with reasonable certainty the profit it would have made is clearly erroneous.

The district court denied Ag-Bag's claim for increased damages under 35 U.S.C. § 284 and attorney fees under 35 U.S.C. § 285 even though the court found that the infringement was in part willful. The court found that “wilfull infringement occurred when machines originally manufactured for Ag-Bag were painted and sold by Blair.” The court declined to treble those damages, however, or to award Ag-Bag its attorney fees, because there was no evidence delineating the sale of the literally infringing bagging machines from the sale of Ryco’s other infringing machines. The court also declined to award Ag-Bag increased damages or attorney fees on the remaining sales. The court found that Ryco reasonably believed that the '805 patent was invalid, and if valid, that their bagging machines did not infringe.

The question of whether infringement is willful, justifying increased damages, is one of fact. Shatterproof Glass Corp. v. Libbey-Owens Ford. Co., 758 F.2d 613, 628, 225 USPQ 634, 644 (Fed.Cir.1985). Ag-Bag argues that the district court’s finding that infringement was not willful as to all sales is clearly erroneous. We agree.

There is no dispute that Kelly Ryan, who was both the president of Blair Manufacturing and the founder of Ryco, knew of Ag-Bag’s patents. “[WJhere a potential infringer has actual notice of another’s patent rights he has an affirmative duty of due care.” Rolls-Royce, Ltd. v. GTE Valeron Corp., 800 F.2d 1101, 1109, 231 USPQ 185, 191 (Fed.Cir.1986). The test is whether, under all the circumstances, a reasonable person would prudently conduct himself with any confidence that a court might hold the patent invalid or not infringed. See Central Soya Co. v. Geo. A. Hormel & Co., 723 F.2d 1573, 1577, 220 USPQ 490, 492 (Fed.Cir.1983). The court found that Ryco “reasonably believed” that the ’805 patent was invalid or that its bagging machines did not infringe. This finding, however, is simply unsupportable on the facts and the law.

The duty of due care normally requires that a potential infringer obtain competent legal advice before infringing or continuing to infringe. Rolls-Royce, 800 F.2d at 1109, 231 USPQ at 191. Kelly Ryan and Ryco, however, never consulted an attorney about the changes made to the Ag-Bag design or apparently at any other time until Ryco decided to challenge the patents, first by reexamination and then by this declaratory judgment action. Although the failure to obtain legal advice is not determinative, it is one of the factors supporting a finding of willfulness. See Kloster Speedsteel AB v. Crucible Inc., 793 F.2d 1565, 1579, 230 USPQ 81, 90 (Fed.Cir.1986), modified in part, 231 USPQ 160, cert. denied, 479 U.S. 1034, 107 S.Ct. 882, 93 L.Ed.2d 836 (1987). More importantly, in this case, it points to the complete absence of any possible basis for the court’s finding that Ryco “reasonably believed” that the patent was invalid or that it did not infringe.

The court’s description in Kloster Speed-steel, supra, is particularly apt with respect to Ryco’s conduct:

An “aggressive strategy” unsupported by any competent advice of counsel, thorough investigation of validity and infringement, discovery of more pertinent uncited prior art, or similar factors, is the type of activity the reference in the patent law to increased damages seeks to prevent. An alleged infringer who intentionally blinds himself to the facts and law, continues to infringe, and employs the judicial process with no solidly based expectation of success, can hardly be surprised when his infringement is found to have been willful.

Id. at 1580 n. 11, 230 USPQ at 91 n. 11. Because we conclude that the finding that Ryco did not act willfully is clearly erroneous, we hold that Ryco willfully infringed the ’805 patent. Id. at 1577, 230 USPQ at 88-89.

Although we reverse the district court’s finding that Ryco’s infringement was not willful, we do not decide whether the district court should or should not award increased damages under 35 U.S.C. § 284 or attorney fees under 35 U.S.C. § 285. Instead, we vacate the portion of the district court’s judgment deciding not to award increased damages or attorney fees and remand.

If infringement is willful, increased damages may be awarded at the discretion of the district court, and the amount of the increase, up to three times, may be set in the exercise of that same discretion. Id. at 1580, 230 USPQ at 91. We remand to the district court so it may exercise its discretion.

Willful infringement may also be a sufficient basis for finding a case “exceptional” for purposes of awarding, attorney fees under 35 U.S.C. § 285. See, e.g., Bott v. Four Star Corp., 807 F.2d 1567, 1574, 1 USPQ2d 1210, 1215 (Fed.Cir.1986). A finding that a case is exceptional is one of fact, and must be made in the first instance by the district court. S.C. Johnson & Son, Inc. v. Carter-Wallace, Inc., 781 F.2d 198, 201, 228 USPQ 367, 369 (Fed.Cir.1986). Accordingly, on remand the court may make an appropriate finding and exercise its discretion as to an award of attorney fees. Id.

CONCLUSION

The judgment of the district court that the claims of the ’805 patent are not invalid is affirmed as to claims 1-10 and 12-16 and reversed as to claims 32-35.

The judgment of the district court that claims 1-10 and 12-16 are infringed is affirmed.

The award of damages of $83,100.73 as a reasonable royalty is reversed and the case is remanded for determination of Ag-Bag’s lost profits.

The district court’s finding that infringement was not willful is reversed. The court’s decision to deny Ag-Bag increased damages and attorney fees is vacated. The case is remanded for decision whether to award increased damages or attorney fees.

COSTS

Costs on appeal to cross-appellant Ag-Bag Corporation.

AFFIRMED IN PART, REVERSED IN PART, VACATED IN PART, AND REMANDED.

APPENDIX

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Silopress 401

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U.S. Patent No. 4,337,805

1. An agricultural bag loading apparatus for loading material into agricultural bags, said apparatus comprising:

15. In an agricultural bag loading apparatus for loading silage and the like into an agricultural bag including a housing having an intake for receiving silage and an output for discharging silage into an agricultural bag, and a silage moving device for forcing silage from the intake into the output and into the agricultural bag, the improvement comprising;

32. In an agricultural bag loading apparatus having a primary shaft rotatably mounted therein in which silage and the like is forced into an agricultural bag by a plurality of teeth mounted along the primary shaft when the shaft is rotated, the improvement comprising:

35. An agricultural bag loading apparatus for loading silage and the like into an agricultural bag, said loading apparatus comprising:

a driven sprocket on one end of said shaft for rotating said shaft;

NIES, Circuit Judge,

dissenting in part.

I agree with parts 1, 2, and 3 of the majority’s opinion. I cannot join part 4 of the opinion, however, because the district court’s finding that Ryco did not willfully infringe Ag-Bag’s patent by sales of its redesigned machine must be upheld under the constraints of Federal Rules of Civil Procedure 52(a). There are two possible views of the evidence so that the district court’s finding that willfulness was not proved cannot be found “clearly erroneous.” Without a reversal of that finding, there is no foundation for holding that this case either is exceptional under 35 U.S.C. § 285 (1982), thereby permitting an attorney fee award, or warrants increased damages under 35 U.S.C. § 284 (1982). I would, accordingly, affirm those portions of the court’s judgment.

I

The question of whether infringement is willful is one of fact and, therefore, is subject to Rule 52(a)’s clearly erroneous standard of appellate review. See, e.g., Underwater Devices Inc. v. Morrison-Knudsen Co., 717 F.2d 1380, 1389, 219 USPQ 569, 576 (Fed.Cir.1983). That standard is defined in United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746 (1948):

See also SSIH Equip. S.A. v. United States Int’l Trade Comm’n, 718 F.2d 365, 381, 218 USPQ 678, 692 (Fed.Cir.1983) (Nies, J., additional views). Further, the patentee has the burden to prove willfulness by clear and convincing evidence. See Shatterproof Glass Corp. v. Libbey-Owens Ford Co., 758 F.2d 613, 628, 225 USPQ 634, 644 (Fed.Cir.), cert. denied, 474 U.S. 976, 106 S.Ct. 340, 88 L.Ed.2d 326 (1985). We may not, of course, merely substitute our view of the weight of the evidence. See Anderson v. City of Bessemer City, N.C., 470 U.S. 564, 573-74, 105 S.Ct. 1504, 1511-12, 84 L.Ed.2d 518 (1985) (“[T]he court of appeals may not reverse ... even though convinced that had it been sitting as the trier of fact, it would have weighed the evidence differently. Where there are two permissible views of the evidence, the factfinder’s choice between them cannot be clearly erroneous.”). Thus, the precise

question is whether the district court clearly erred in ruling that the evidence that the infringers acted willfully was not clear and convincing.

The district court found Kelly Ryan’s and Ryco’s (hereinafter, collectively, Ryco’s) infringement had not been proved willful, finding instead that they “reasonably believed the ’805 patent was invalid. Moreover, they reasonably felt the modifications they made to the agricultural bag loading devices sold by Ryco did not infringe the ’805 patent, if it was valid.” A review of the entire record fails to leave one “with the definite and firm conviction” that the district court committed a mistake in those findings or in the ultimate finding that willfulness was not established.

The applicable test for determining willfulness is whether the infringer possessed a culpable intent to infringe. “[Ijnfringement may range from unknowing, or accidental, to deliberate, or reckless, disregard of a patentee’s rights.” Rite-Hite Corp. v. Kelley Co., 819 F.2d 1120, 1125-26, 2 USPQ2d 1915, 1918-19 (Fed.Cir.1987). There is no “rigorous rule” under that test; rather, all of the circumstances are considered. Id. Under all the circumstances here, the district court’s finding that Ag-Bag failed to prove willfulness with respect to all of Ryco’s infringing sales is not clearly erroneous.

II

To establish that the court’s findings are clearly erroneous, Ag-Bag’s principal argument is that Ryco knew of Ag-Bag’s patents yet failed to consult an attorney before infringing. Contrary to Ag-Bag’s view, however, that failure alone is not conclusive. See, e.g., Rolls-Royce Ltd. v. GTE Valeron Corp., 800 F.2d 1101, 1109-10, 231 USPQ 185, 191 (Fed.Cir.1986) (no per se rules in respect of willfulness and “not every failure to seek an opinion of competent counsel will mandate an ultimate finding of wilfulness”); Machinery Corp. of Am. v. Gullfiber AB, 774 F.2d 467, 472, 227 USPQ 368, 372 (Fed.Cir.1985) (same). It is, of course, a factor to be considered. Ag-Bag also asserts willfulness is shown by Ryco’s continued infringement after the validity of the patent was recognized, albeit by consent decrees, in other litigation. Ag-Bag’s other evidence is that Ryco used a trademark similar to Ag-Bag’s and that Ryco used the same manufacturing facilities as previously used to manufacture machines for Ag-Bag. In addition, Ag-Bag argues that because Ryco had sold machines which it had made for Ag-Bag, and which were in inventory when their relationship ended, the “willfulness” of that infringement taints all of Ryco’s sales.*

On the other side of the scale, the district court’s disposition of, and this court’s holding on, Ryco’s validity challenges in themselves support a finding that Ryco could reasonably believe the ’805 and ’810 patents were invalid. The district court held the ’810 patent, claiming an improved brake mechanism, was invalid as obvious under 35 U.S.C. § 103 (1982). That portion of the court’s judgment was not appealed. Although the district court upheld the validity of the ’805 patent against Ryco’s challenge, this court reverses with respect to claims 32-35, finding those claims invalid as obvious. Moreover, the close nature of the obviousness challenge to the remaining ’805 claims required both courts to perform a thorough analysis; it supports the reasonableness of Ryco’s belief that the ’805 patent was invalid.

Turning to infringement, the district court found that Ag-Bag failed to prove Ryco’s redesigned machines literally infringed the ’805 patent. Nevertheless, it found infringement under the doctrine of equivalents, and this court affirms that judgment. The infringement question under the doctrine was reasonably contested and far from being a foregone conclusion.

Ryco’s litigation conduct is another factor to weigh in determining whether Ryco’s infringement was willful. Bott v.

Four Star Corp., 807 F.2d 1567, 1572, 1 USPQ2d 1210, 1213 (Fed.Cir.1986). It was Ryco that initiated this action by requesting a declaratory judgment invalidating Ag-Bag’s patents. Although that fact alone is insufficient to show a reasonable belief of a right to continue allegedly infringing acts, Kaufman Co. v. Lantech, Inc., 807 F.2d 970, 979, 1 USPQ2d 1202, 1209 (Fed.Cir.1986) (“mere fact [alleged in-fringer] brought suit is not evidence that there was such a reasonable basis” for belief), it is a factor. In addition, Ryco’s counsel did provide an opinion before Ryco brought suit. Moreover, Ryco has not resorted to meritless defenses or dilatory tactics in litigating before the district court or this court. Such conduct further supports the finding that Ryco acted in good faith. See, e.g., Bott, 807 F.2d at 1572, 1 USPQ2d at 1213; Yarway Corp. v. Eur-Control USA, Inc., 775 F.2d 268, 277, 227 USPQ 352, 358 (Fed.Cir.1985); accord Lam, Inc. v. Johns-Manville Corp., 668 F.2d 462, 474-75, 213 USPQ 1061, 1071 (10th Cir.), cert. denied, 456 U.S. 1007, 102 S.Ct. 2298, 73 L.Ed.2d 1302 (1982).

Another circumstance to consider is whether Ryco deliberately copied Ag-Bag’s patented device. Bott, 807 F.2d at 1572, 1 USPQ2d at 1213. As Ag-Bag acknowledges, Ryco “undertook to change the design which [Ryco] had previously made for Ag-Bag to something else.” That attempt to “design around” the ’805 patent included a series of design alterations in which Ryco (1) separated the teeth on the rotor shaft axially and arranged them helically, (2) angled the projections on the feeder bar, (3) flattened the stripper bars to avoid a convex shape, (4) attached the disc brake to the same shaft as the cable drums, and (5) provided an auger, instead of a feeder bar with projections, on its two-wheeled device. This court has stated that the incentive to design around a patent is a positive result of the patent system:

State Indus., Inc. v. A.O. Smith Corp., 751 F.2d 1226, 1236, 224 USPQ 418, 424 (Fed.Cir.1985) (quoted in Yarway, 775 F.2d at 277, 227 USPQ at 359). Ryco’s nonfrivo-lous attempt to avoid infringement by changed design undermines Ag-Bag’s charge of “deliberate copying.”

In sum, given the evidence on both sides of the willfulness issue, the district court’s finding of no willful infringement cannot be held clearly erroneous under the standard of Anderson and United States Gypsum Co. The evidence of willfulness is not so overwhelmingly in Ag-Bag’s favor that only one conclusion can be reached. Accordingly, I would affirm those portions of the district court’s judgment denying Ag-Bag increased damages and attorney fees.