
931 F.Supp. 1167 (1996)
PENTECH INTERNATIONAL, INC., Plaintiff,
v.
Leon HAYDUCHOK, All-Mark Corporation, Inc., and Paradise Creations, Inc., Defendants.
ALL-MARK CORPORATION, INC. and Paradise Creations, Inc., Counterclaim-Plaintiffs,
v.
PENTECH INTERNATIONAL, INC. and Norman Melnick, Counterclaim-Defendants.
No. 87 CIV 7233 (KTD).
United States District Court, S.D. New York.
July 30, 1996.
*1168 Stroock & Stroock & Lavan, New York City (Steven B. Pokotilow, Matthew W. Siegal, of counsel), for Counterclaim-Plaintiff Paradise Creations, Inc.
Kalin & Banner, New York City (Robert A. Banner, Susan B. Ratner, of counsel), for Counterclaim-Defendant Pentech International, Inc.

OPINION & ORDER
KEVIN THOMAS DUFFY, District Judge:
In November 1990, Judge Pierre N. Leval, then a District Judge, determined after a bench trial that Counterclaim-Defendant Pentech International, Inc. ("Pentech") had literally infringed United States Patent Number 4,681,471 ("the patent"), which was licensed exclusively to Counterclaim-Plaintiff Paradise Creations, Inc. ("Paradise").[1] When Judge Leval assumed the bench on the Court of Appeals for the Second Circuit, the issue of damages remained to be tried. That trial was held by me on March 20, 27, and 28, 1996, and this Opinion resolves the remaining issues.[2]
The patent at issue is directed generally to a kit consisting of (a) a plurality of ink dispensers containing water-based inks, the inks containing at least red, yellow, and blue dyes, and (b) a dispenser of ink-eradicating fluid including a reducing agent which works to eradicate marks made by the water-based inks and a common carrier of defined formulation in the marker and eradicating fluid. The kit consists of the ink and eradicating dispensers in a common package. Judge Leval's Opinion explained the infringement issue as follows:
Plaintiff admits that its erasable markers are virtually identical to those patented by defendants. The only notable difference *1169 is that plaintiff's marker kit does not contain a yellow marker, plaintiff having removed that marker precisely to distinguish the product from defendant's patent. (Plaintiff continues to use yellow dyes, to create hybrid colors such as orange and green). Plaintiff contends that this difference precludes a finding of infringement....
[P]laintiff continues to use the yellow dye specified in defendant's patent, and relies on the eradicability of that dye to permit erasure of the hybrid inks containing yellow. Plaintiff's product thus uses all of the teachings of defendant's patent.
(Opinion and Order dated November 12, 1990, at p. 31-32).
Thus, Judge Leval's decision depended upon whether Pentech's marker kit, which had orange and green markers, but no yellow, could infringe the patent. Pentech argued at trial that Claim 1 covered only marker kits having a blue marker, a red marker, and a yellow marker. Paradise argued that the patent covered Pentech's product because an orange marker has a combination of dyes of the colors red and yellow. According to Paradise, the absence of a yellow marker did not preclude infringement.
Judge Leval accepted Paradise's interpretation of the patent, and the Court of Appeals for the Federal Circuit affirmed. Judge Lourie filed a dissenting opinion, arguing that the removal of the yellow marker was sufficient to avoid infringing the patent.
The issue of damages having been tried before me, I make the following findings of fact and conclusions of law.

FINDINGS OF FACT
On August 3, 1983, Leon Hayduchok and Leopold Strauss filed a patent application for an invention involving erasable marker kits. In September 1983, Hayduchok began a series of meetings with an investor group including David Melnick, Norman Melnick, and Richard Kalin, Esq., now all of Pentech. Hayduchok showed them a copy of his pending patent application and discussed with Norman Melnick the prospect of Melnick's financing the sale of erasable marker kits covered by the patent application.
David Melnick, Norman Melnick, and Richard Kalin decided not to do business with Hayduchok. Instead, they formed Pentech and made arrangements to purchase similar erasable marker kits from various Italian manufacturers. Pentech's marker kits contained markers capable of making colored marks including colors having red, yellow, and blue dyes, with water based ink and an eradicator capable of removing the marks made by the markers in the kit. Pentech marketed its kits as ERASABLES.
In September, 1984, Hayduchok assigned his patent rights to his company, All-Mark Corporation, Inc. ("All-Mark"). On April 17, 1986, All-Mark entered into an agreement with Paradise, whereby Paradise became the exclusive licensee of the suit patent.
Paradise marketed the erasable marker kits and sold to mass marketers such as Kmart. They participated in toy fairs and back-to-school shows in 1986 through 1988. (Tr. 94-95). The erasable marker kits were sold to stationery and toy buyers. (Tr. 92-93). These were Paradise's best selling items, and were affected the most by infringing products. Paradise made suspected infringers aware of its intention to enforce the patent once it issued.
By letter dated February 24, 1986, Mr. Kalin, on behalf of Pentech, filed with the U.S. Patent and Trademark Office ("PTO") a protest against Hayduchok's pending patent application. As early as March 9, 1987, Pentech became aware that Paradise had received a Notice of Allowance for the patent and would enforce its patent rights. On July 21, 1987, United States Patent Number 4,681,471 issued.
Upon the issuance of the patent, Pentech's patent counsel, John J. Kane, Esq., sent a copy of the patent to Mr. David Melnick. (Kane Tr. 309). Mr. Melnick telephoned Mr. Kane and asked him "to do an analysis of the patent." (Id. at 310). Pentech continued selling ERASABLES while awaiting the advice of counsel.
Mr. Kane analyzed the file wrapper and references, and then prepared the opinion *1170 letter dated September 4, 1987. (Id.). His letter concluded that Pentech's kit probably infringed Claims 1 through 33 of the patent. Specifically, Mr. Kane advised
if you were to omit one of the three primary colors from your kit it would be our opinion that if suit were brought a Court would hold that your kit would not infringe Claim 1 nor any claims dependent thereon. As to Claim 32 there was not a great deal of prosecution concerning that claim therefore it would be easiest to formulate a kit outside of the limits for specific components set forth in that claim. If you can formulate your product such as to avoid Claims 1 and 32 then you will be avoiding infringement of any of the claims of this patent.
In summary it could be interpreted that the kit as you now sell does indeed infringe Claims 1 through 33....
(Sept. 4, 1987 Letter) (emphasis added). The letter did not address the validity of the patent in any meaningful way.
Moreover, Mr. Kane made Pentech aware that a finding of infringement was likely, given the configuration of the product at that time. Therefore, I find that, as of September 4, 1987, Pentech knew that the ERASABLES infringed the patent. Yet, Pentech continued selling its product and never advised its customers that the product infringed the patent.
Mr. Kane testified that Mr. Melnick called him after reading the opinion letter and asked whether the removal of yellow would avoid infringement. (Tr. 311). Mr. Kane answered yes, and then sent a follow-up letter on September 29, 1987. The follow-up letter stated "a judge would hold that there is no infringement of claims 1 through 31 and 33 if the kit which you sell does not include any yellow markers." Apparently, however, Melnick failed to tell Kane that Pentech continued selling the ERASABLES containing a yellow marker. The follow-up letter stated "it is our opinion that your product as now currently sold is not an infringement of any claims in U.S. Patent No. 4,681,471." (Emphasis added). Mr. Kane's opinion apparently was based upon the assumption or misunderstanding that Pentech had ceased selling kits having a yellow marker. That clearly was not the case.
In light of all of the evidence, I find that Pentech continued to sell ERASABLES kits having yellow markers  i.e. known infringing products  as late as June 1989. Pentech argues that the change was made as early as December 1987. Melnick stated at trial that, in September 1987, he called Pentech's purchaser, Derek Harris, "and told him to pull the yellow from all the packages of ERASABLES." (Melnick Tr. at 212-13). Pentech admits that it did not immediately cease selling the kits having a yellow marker, but made a "running change" in its product. (Melnick Tr. 174). Pentech's running change means that Pentech continued selling its supply of the known infringing products until the supply was depleted, and then Pentech began selling the newly manufactured products. According to Mr. Melnick, Pentech made a running change because "it was the easiest thing for us to do." (Tr. at 193). Pentech's supply of known infringing products lasted about three months. Id. at 174. Therefore, Pentech admits selling the known infringing marker kits for at least the first five months after the patent issued.
At trial, David Melnick, one of the founders of Pentech and the president of Pentech during the course of this litigation, testified that Pentech ceased manufacturing kits having yellow markers beginning in September 1987. (Tr. 168-71). However, Pentech gave the following answer to an interrogatory: "Effective June 1989, Pentech modified product nos. 55012 (fineline markers) and 66012 (broadline markers) to delete yellow or yellow-derivative markers such as green from these sets." (Melnick Tr. 168-71). The interrogatory answer failed to state when the change was allegedly made in Pentech's other erasable marker sets (i.e. 66006, 55022, 55446, and 50612). Mr. Melnick stated at a deposition that the answer to the interrogatory was correct (i.e. that the change was made in June 1989) and that he remembered the date because he himself directed that the changes be made. (Melnick Tr. 175). Furthermore, invoices of one of Pentech's suppliers indicate that the supplier did not receive instructions to delete the yellow marker until *1171 January, 1989. (Def.Exh.BAH). Moreover, Pentech's 1988 catalog continued to display marker sets having a yellow marker, despite other changes in the catalog's artwork. (Melnick Tr. 178).
Given the contradictory statements by Melnick and in light of his demeanor, I do not credit his testimony. I find that Pentech continued selling known-infringing marker kits (i.e. those having yellow markers) until June 1989. There is no dispute that Pentech did not remove the orange and green markers from its marker kits prior to February 1991.
Sometime before October 8, 1987, Pentech contacted Lewis H. Eslinger, Esq., a patent attorney to handle the patent litigation that would ensue. On October 8, 1987, Mr. Eslinger filed, on behalf of Pentech, a declaratory judgment action against Paradise, seeking a declaration of invalidity and non-infringement. Paradise filed a counterclaim alleging that, even after Pentech removed the yellow markers from its ERASABLES kit the kits infringed the patent.
Mr. Eslinger testified before me that, at some point, he told Pentech "that if they proceeded without an opinion, ... there could be a charge of willful infringement." (Tr. 268). Pentech then allegedly requested an opinion from Mr. Eslinger. (Id.). Mr. Eslinger testified that he told Pentech orally that their marker kits would not infringe the patent if the yellow marker was removed from the kits. Mr. Eslinger testified that he believed Pentech then removed the yellow markers from their kits. (Id. at 268-69). Mr. Eslinger testified that Mr. Kalin, Pentech's Secretary and general counsel, told him Pentech did not want Eslinger's opinion to be put in writing. (Id. at 265). Mr. Eslinger submitted an invoice to Pentech for the month of December 1987, which purports to charge for a "study of the client's new product." There is no further evidence regarding the basis for, or content of, Mr. Eslinger's opinion.
After a trial on the issues of patent validity and infringement, Judge Leval issued an Opinion and Order, dated November 12, 1990, in which he upheld the validity of the patent and found that Pentech's ERASABLES marker kits infringed Claim 1 of the patent under the doctrine of equivalents. In a subsequent Memorandum and Order, Judge Leval found that there was literal infringement of the patent.[3]
After Judge Leval issued his opinion, Pentech continued selling the ERASABLES marker sets. Mr. Eslinger testified before me that he advised Pentech that they could continue selling the ERASABLES marker sets, because he would get Judge Leval's decision reversed on appeal. Mr. Eslinger's astounding testimony is set forth below:
Q. [ON DIRECT EXAMINATION] In November of '90 Judge Leval issued an order, correct?
A. That's correct, an opinion.
Q. An opinion, and did you have any discussion with Pentech on or around November of 1990 in which you directed Pentech or advised Pentech to stop selling the product at that time?
A. Well, there are several things that I advised them at that time. I first advised them 
THE COURT: He asked you specifically about that. Let me ask you, did you tell them specifically that? Did you tell them to stop selling?
THE WITNESS: I told them they did not have to stop selling, your Honor, because there was no injunction in effect at that time.
THE COURT: Judge Leval issued an opinion which was contrary to your opinion, therefore they could go ahead and sell. Interesting.
THE WITNESS: Well, at that point I was of the opinion that I would be able to reverse Judge Leval's holding of validity [and] infringement.
.   .   .   .   .
THE WITNESS: What I advised them was that if Judge Leval's opinion was affirmed that the patent was valid and infringed, that they certainly would be liable for damages.

*1172 THE COURT: Counselor, are you telling me that you generally tell your clients to ignore orders of the district court?
THE WITNESS: No, your Honor, but I considered at that time it wasn't an order from the District Court. There was no injunction. It was an opinion. I did not feel that was in any way being violated by continuing to sell because there was a damage phase.
.   .   .   .   .
THE COURT: Did you consider the question of willfulness of the violation if it was found to be an infringement?
.   .   .   .   .
THE WITNESS: Well, at that time in my opinion, I felt that by continuing to sell, there was no willfulness because we still 
THE COURT: No willfulness?
THE WITNESS: I was still of the opinion that the patent was invalid and not infringed.
Pentech continued selling the infringing marker sets until at least February 1991. In March 1991, Pentech introduced, as a replacement for ERASABLES, a non-infringing marker kit, which involved color changing, but not erasing. According to the testimony of Mr. Melnick, Pentech stopped ordering the erasable markers immediately after Judge Leval's decision and began a "running change." (Tr. at 221). Pentech sold the infringing marker kits until March 1, 1991. (Tr. at 218). The evidence supports a finding that Pentech did not tell its customers that the ERASABLES markers had been found to infringe Paradise's patent. In fact, Pentech's change in products went unnoticed by some customers, because Pentech used the same product numbers to identify the replacement product as it had used to identify the ERASABLES. There is no evidence to show when the last of the infringing products was sold by Pentech. However, Pentech's ERASABLES were on the market (i.e. in retail stores) as late as January 1993. (Tr. at 83).
On May 20, 1991, Judge Leval issued an injunction, which specifically prohibited Pentech from "importing, manufacturing, using, selling or offering for sale erasable marker kits which infringe the claims of [the patent]." (¶ 6). Paragraph seven directed Pentech to turn over its infringing items to Paradise, stating specifically
7. Within fifteen (15) days of entry of this Order, Pentech shall deliver all infringing marker kits including all Pentech Erasables marker kits in Pentech's possession to Counterclaim-plaintiffs or their counsel for storage pending the outcome of Pentech's appeal, at Pentech's expense.
Pentech failed to comply with Paragraph seven of the injunction, as they never turned over the markers to Paradise. Melnick alleges that the markers were destroyed. However, given his lack of candor, I do not believe that this was done.
Paradise spent nearly $350,000 in 1986 and more than $30,000 in 1987 to advertise erasable markers. (Tr. 73). Paradise did not advertise its product further. In 1989, Paradise stopped selling aggressively its patented product, and its sales volume dropped dramatically in 1989 and 1990. (Tr. 119-20).

Calculation of Damages
As the exclusive licensee of the patent, Paradise is entitled to sue for and collect damages as if Paradise were the patent's owner. Waterman v. Mackenzie, 138 U.S. 252, 255, 11 S.Ct. 334, 335, 34 L.Ed. 923 (1891). Because Pentech has been found to be infringing the patent, Paradise is entitled, by statute, to receive "damages adequate to compensate for the infringement, but in no event less than a reasonable royalty for the use of the invention by the infringer, together with interests and costs as fixed by the court." 35 U.S.C. § 284 (1984). Section 284 also authorizes a court to "increase the damages up to three times the amount found or assessed." Section 285 of Title 35 states that "[t]he court in exceptional cases may award reasonable attorney fees to the prevailing party."

Lost Profits
To determine the amount of patent infringement damages, "the general rule ... *1173 [for] a patentee that is itself producing the patented item is to determine the sales and profits lost to the patentee because of the infringement." Rite-Hite Corp. v. Kelley Co., 56 F.3d 1538, 1545 (Fed.Cir.), cert. denied, ___ U.S. ___, 116 S.Ct. 184, 133 L.Ed.2d 122 (1995). The patentee must show a reasonable probability that "but for" the infringement, it would have made the sales that were made by the infringer. Id. The patentee can meet this burden by establishing (1) a demand for the patented product, (2) the absence of acceptable non-infringing substitutes, (3) the manufacturing and marketing capability to exploit the demand, and (4) the amount of the profit it would have made. Id. (citing Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (6th Cir.1978).
Paradise claims that it should be compensated for profits lost as a result of Pentech's infringing sales. The claimed losses are of two types: losses caused by Pentech's making sales that could have been made by Paradise; and losses caused by Pentech's price competition which forced Paradise to lower its prices to sell its products.
Paradise argues that it had to cut prices to compete with Pentech's infringing product. Pentech does not challenge Paradise's calculation of this aspect of the lost profits. The lost profits due to price competition can be measured by comparing its pre-infringement profit margin with its profits during infringement. Paradise's pre-infringement profit margin averaged 59.1%. (Lubow Decl. ¶ 18). Paradise's profit margin during the infringement averaged 45%. Therefore, Paradise should recover the difference in profit (14.1%) for each unit of sales made during the infringement period. As Paradise sold $1,928,660 worth of product during the post-infringement period (Lubow Decl. Exh.DAAL), this aspect of Paradise's losses totaled $271,941.
Paradise also claims that it could have made all the sales that Pentech made, and therefore Paradise should recover the profit it would have made on those sales. However, Paradise has failed to prove its costs associated with the patented product, and I cannot determine the amount of Paradise's lost profits. Paradise proposes an incremental approach to proving its lost profits, which assumes that additional sales could be made without increasing Paradise's fixed costs. The proper method is to subtract both the cost per unit of product and variable costs associated with the manufacture and sale of the unit from the price per unit of product. Paradise has provided inadequate evidence of its past variable costs. Moreover, Paradise admitted that it would have incurred additional variable costs (e.g. additional warehouse and transportation costs and at least one additional employee) to make Pentech's sales. (Hockroth Tr. 98). It is probable that Paradise would also have incurred additional marketing costs. Paradise has not provided evidence of these additional costs. Therefore, Paradise has failed to prove the total amount of incremental profit that should it might have made.
The only lost profits that Paradise has proven is the amount of $271,941.

Reasonable Royalty
Paradise's minimum statutory recovery is the amount of the reasonable royalty on Pentech's sales of ERASABLES. See 35 U.S.C. § 284; Rite-Hite, 56 F.3d at 1545 ("the purpose of this alternative [i.e. reasonable royalty] is not to direct the form of compensation, but to set a floor below which damage awards may not fall"). Pentech asserts that a reasonable royalty would be three to five percent of its net sales of the marker kits. Paradise on the other hand, seeks fifty percent of Pentech's profit on the ERASABLES.[4]
The appropriate method for determining a reasonable royalty is to postulate a hypothetical negotiation between the parties as willing licensor and licensee at the time the infringement began. See Georgia-Pacific Corp. v. U.S. Plywood Corp., 318 F.Supp. 1116, 1120 (S.D.N.Y.1970), modified, 446 *1174 F.2d 295 (2d Cir.), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971). The court in Georgia-Pacific described fifteen factors to be used to determine the issue of the amount of a reasonable royalty:
1. The royalties received by the patentee for the licensing of the patent in suit, proving or tending to prove an established royalty.
2. The rates paid by the licensee for the use of other patents comparable to the patent in suit.
3. The nature and scope of the license, as exclusive or non-exclusive; or as restricted or non-restricted in terms of territory or with respect to whom the manufactured product may be sold.
4. The licensor's established policy and marketing program to maintain his patent monopoly by not licensing others to use the invention or by granting licenses under special conditions designed to preserve that monopoly.
5. The commercial relationship between the licensor and licensee, such as whether they are competitors in the same territory in the same line of business; or whether they are inventor and promoter.
6. The effect of selling the patented specialty in promoting sales of other products of the licensee; that existing value of the invention to the licensor as a generator of sales of his non-patented items; and the extent of such derivative or convoyed sales.
7. The duration of the patent and term of the license.
8. The established profitability of the product made under the patent; its commercial success; and its current popularity.
9. The utility and advantages of the patent property over the old modes or devices, if any, that had been used for working out similar results.
10. The nature of the patented invention; the character of the commercial embodiment of it as owned and produced by the licensor; and the benefits to those who have used the invention.
11. The extent to which the infringer has made use of the invention; and any evidence probative of the value of that use.
12. The portion of the profit or of the selling price that may be customary in the particular business or in comparable businesses to allow for the use of the invention or analogous inventions.
13. The portion of the realizable profit that should be credited to the invention as distinguished from non-patented elements, the manufacturing process, business risks, or significant features or improvements added by the infringer.
14. The opinion testimony of qualified experts.
15. The amount that a licensor (such as the patentee) and a licensee (such as the infringer) would have agreed upon (at the time the infringement began) if both had been reasonably and voluntarily trying to reach an agreement; that is the amount which a prudent licensee  who desired, as a business proposition, to obtain a license to manufacture and sell a particular article embodying the patented invention  would have been willing to pay as a royalty and yet be able to make a reasonable profit and which amount would have been acceptable by a prudent patentee who was willing to grant a license.
Georgia-Pacific, 318 F.Supp. at 1120 (emphasis added).
After weighing all factors, I find that a reasonable royalty would be fifty percent of Pentech's profit.
The first factor (royalties received by the patentee for the licensing of the patent in suit) favors a royalty of fifty percent of Pentech's profit on the sales of infringing kits. The license agreement between Paradise and All-Mark gives Paradise an exclusive right to make and sell the patented product and gives All-Mark fifty percent of Paradise's total profits  on all products. I realize that this is not a typical licensing arrangement. Ira Hockroth, Paradise's Vice President of Sales, described the relationship of Paradise and All-Mark as a joint venture. (Tr. at 141). Nonetheless, the agreement indicates the strong perceived value of the patented product even before the patent had issued.
*1175 Robert I. Pearlman, Esq., Pentech's expert on damages, argues against a royalty based on net profits. According to Pearlman, such a royalty would be unlikely because it "penalizes the licensor [i.e. Paradise] for the inefficiencies of the licensee and opens up disputes due to the vagaries of what constitutes net profit." (Pearlman Affid. at 11) (emphasis added). Even assuming Pearlman's objection to have merit, this would mean that Paradise would have been foolish to accede to such an agreement. There is no indication that Pentech, as licensee, would not have accepted such an agreement.
The second factor (rates paid by the licensee for the use of comparable patents) favors a higher royalty than Pentech asserts. Pentech presented evidence of licenses having royalty amounts in the five and six percent range. (Tr. at 223-25). At the time those licenses were agreed to, however, there was no patent on the products covered by the license, and the licensed product did not have the proven success that Paradise's patented product enjoyed. Id. at 242-43.
The third, fourth, and fifth factors (the nature and scope of the license, the licensor's policy to maintain a monopoly, and the commercial relationship between the parties) favor a high royalty. Pentech argues that the hypothetical license would have been non-exclusive (since Pentech and Paradise are competitors) and thus a low royalty would be reasonable. This argument is ill-conceived. Paradise and Pentech were competitors (Tr. 88-93, 96-97, 117, 143), but Pentech was protected by Paradise's attempt to maintain the monopoly offered by the patent. Although non-exclusive licenses generally result in price competition between licensees, Pentech would not have suffered from price competition. Paradise would have granted a license only if the license would increase Paradise's profits. (Hockroth Tr. 98). Moreover, Paradise maintained much higher prices than Pentech did; Pentech could have raised its prices without being affected by price competition because Paradise sought to maintain prices higher than Pentech's prices. In fact, despite the competition between Pentech and Paradise, Pentech was still able to maintain a gross-profit margin of 48 percent. This is due in large part to the monopoly protection afforded Pentech by Paradise's policy of not licensing others to make the patented product. Paradise would have been unwilling to license Pentech as a competitor, unless Paradise could profit sufficiently from Pentech's sales to overcome Paradise's competition-induced losses.
The sixth factor (known as convoyed sales) is neutral. Although ERASABLES were one of Pentech's earliest successes, at the time the patent issued no more than fifteen percent of Pentech's sales were of the ERASABLES markers. There is sufficient evidence of Pentech's sales efforts to find that, even if Pentech ceased selling ERASABLES, its sales of its non-infringing products would not have decreased.
The seventh and eighth factors (the duration of the patent, and the commercial success and popularity of the product) favor a high royalty. At the time of the hypothetical negotiation, the patent had just issued and would last for seventeen years. The patented markers were selling strong. In 1987, Pentech sold $1,196,423 in ERASABLES, which constituted 11.9% of its total sales. (Tr. 202-03). Paradise' sales were $433,106 in 1987. (Exh. AAJ). Moreover, there was no indication that the market would decline.
The ninth, tenth, and eleventh factors (the utility and advantages of the patent property, the nature of the patented invention, and the extent and value of the infringer's use of the invention) favor a high royalty. First, I note that Judge Leval found that the patented product "fulfilled a significant need for consumers." (Opinion and Order of November 12, 1990, at 25). Pentech argues that the patent has little or no value because the product was already on the market and was widely available. (Pentech Mem. at 37). The fact that the product was already on the market demonstrates the success and value of the product at the time the patent issued. Furthermore, the fact that Pentech would risk the expense of a law suit implies that the product is valuable.
Pentech also argues that the patent had little value because "infringement could be avoided simply by removing the markers containing the dye of any one of the primary *1176 colors," and "the colors of the markers in the kits were irrelevant to the kits' marketability." (Id. at 37-38). However, Pentech's own refusal to "simply remove" the markers of one of the primary colors indicates that the patented product's available spectrum of markers is an advantageous feature. When Pentech finally decided to sell a non-infringing product, they did not "simply remove" all markers having yellow dye. Instead, they stopped selling the erasable marker kits. Clearly, the proven success of the markers, and Pentech's own actions, demonstrate that the patented product was very valuable.
The twelfth factor (the customary royalty in the particular business) is neutral. There was no evidence submitted by either party as to the customary licenses granted for patents on similar or analogous products.
The thirteenth factor (the portion of the profit attributed to the invention) favors a high royalty. The patent covered the entire product as sold by Pentech  that is, the patent was for a kit of markers having the same characteristics as that sold by Pentech. The infringing item was not merely a part of a larger product, but comprised the entire product. Thus, there is no non-patented aspect of the product to which some of Pentech's profit may be attributed. Therefore, the entire profit generated by the product may be attributed to the patent.
The fourteenth factor, the opinion testimony of qualified experts, favors a high royalty. I discount the opinion testimony and affidavit of Pentech's expert, Mr. Pearlman, because I find that he lacked credibility. His conclusions are based on untenable assumptions and are often preposterous. For example, Mr. Pearlman asserts that the patented product had little value. The first flaw in this conclusion is that Mr. Pearlman is looking at the current value of the patented product, rather than the value at the time the hypothetical negotiation would have occurred. Moreover, the evidence cited above clearly belies his conclusion. Pearlman also asserts that "Pentech and Paradise were not competitors at all, much less `direct competitors.'" (Id. at 13). However, Paradise lost sales and had to lower its prices because of competition from Pentech. (Hockroth Tr. 96-97; 117; 119-20). In fact, Kenneth Ware, a stationery buyer and Pentech's expert witness, testified at trial that he had purchased ERASABLES from Pentech but rejected Paradise's sales efforts primarily because of the price. (Tr. 326-27). Also, a space-planning chart from a Woolworth department store shows the Pentech and Paradise markers on the same display. (Tr. 88-89). Mr. Pearlman's lack of candor is also apparent in his insistent effort to convince me that the patent never should have issued. It is a clear matter of patent law that when determining a reasonable royalty, the patent is presumed valid. On the issue of willfulness, Mr. Pearlman asserts that I should find that Pentech was not a willful infringer because "Mr. Kane's opinions [letters] were on their face thorough and well reasoned." (Pearlman Affid. ¶ 87). Mr. Pearlman overlooked the fact, however, that Pentech continued to sell the known infringing product during the "running change." As for the issue of lost profits, Mr. Pearlman wrongly assumed that there were "a number of substitutes for the patented product during the relevant period." (Pearlman Affid. ¶ 70). Pentech failed to prove that any of the alleged substitutes were non-infringing or that they contained the characteristics that made the patented invention profitable.
In contrast to Pearlman's opinions, Paradise's expert on the issue of a reasonable royalty, George H. Gerstman, Esq. is credible. He proposes that the best evidence of a reasonable royalty is the amount Paradise agreed to pay All-Mark. Accordingly, Mr. Gerstman proposes a royalty of one-half of Pentech's profits.
The fifteenth factor  the amount that a prudent licensee would have been willing to pay and yet be able to make a reasonable profit and the amount that would have been acceptable by a prudent patentee who was willing to grant a license  also favors a royalty of half of Pentech's net profits. According to Paradise, Pentech's profit margin on its sales was 48 percent. (Lubow Decl. ¶ 7). Pentech argues that its profit margin was only 38.4%. (Affidavit of Sheldon M. Whitman ¶ 9). At trial, however, I enforced Judge Leval's discovery order and excluded *1177 the affidavit of Pentech's expert witness as to the amount of damages, Sheldon M. Whitman, to the extent it relied on his audit work papers.[5] Accordingly, I must accept Paradise's calculation of Pentech's profit margin. At a royalty rate of one-half of Pentech's profits, Pentech would retain a profit of 24%. Thus, I find that the reasonable royalty is one-half of Pentech's profits on sales of infringing markers.[6]
To calculate Pentech's royalty amount, I need only multiply Pentech's profit margin by its net sales and then divide by two. Paradise alleges that Pentech's sales of ERASABLES totaled $4,300,000 during the period of infringement. Pentech admits that Paradise's calculation of its total sales was correct except that Paradise should have reduced the amount by the number of non-infringing sales made during July 1987. (Affid. of Whitman at ¶ 8). According to Pentech, Paradise should have pro-rated the July 1987 sales to account for the fact that sales prior to July 21, 1987, were not infringing. Paradise argues that Pentech's sales could have occurred at any point during the month of July, but Pentech failed to produce documentation showing the actual sales dates. I hold that Pentech must suffer the result of the inaccuracy caused by its lack of documentation. See Sensonics, Inc. v. Aerosonic Corp., 81 F.3d 1566, 1572-73 (Fed.Cir.1996) ("if evidentiary imprecision is due to inadequacy of the infringer's records, uncertainty is resolved against the wrongdoer."). Accordingly, Paradise's total infringing sales were $4,300,000.
Pentech also asserts that the figure used by Paradise was gross sales and not net sales. Pentech proposes a reduction for sales returns and allowances. This reduction, however, is based on the affidavit of Mr. Whitman, which I had to exclude from evidence due to Pentech's willful failure to supply documentation to Paradise. Accordingly, I must accept Paradise's calculation of net sales as $4,300,000.
The profit earned by Pentech, therefore, was 48% of $4,300,000 or $2,064,000. A royalty of fifty percent of net profits, therefore, is $1,032,000. Since this amount exceed Paradise's proven lost profits, Paradise is entitled to recover the reasonable royalty of $1,032,000.

Prejudgment Interest
An award of prejudgment interest is required to compensate Paradise "for the use of its money between the date of injury and the date of judgment." Oiness v. Walgreen Co., 88 F.3d 1025, 1034 (Fed.Cir.1996) (affirming an interest rate of eight percent); King Instruments Corp. v. Perego, 65 F.3d 941, 953 (Fed.Cir.) (affirming a rate of eleven percent), reh'g denied, 72 F.3d 855 (1995), cert. denied ___ U.S. ___, 116 S.Ct. 1675, 134 L.Ed.2d 778 (1996); Sensonics, 81 F.3d at 1574 ("prejudgment interest is the rule, not the exception.").
Pentech seeks a rate equal to the prime rate plus three percent, compounded annually. The interest rates over the relevant years would thus range from 9.00% to 13.88%. (Exh. BBX-4). I find that rate equal to the prime rate plus 1.00%, compounded annually, is appropriate to compensate Paradise for Pentech's use of its money. The prejudgment interest is to be calculated on the basis of the damages, in this case the reasonable royalty amount of $1,032,000.

Enhanced Damages
Paradise has requested enhanced damages under Section 284. The Court of Appeals for the Federal Circuit has identified several factors which should be considered by a court when deciding whether to award *1178 enhanced damages: (1) whether the infringer deliberately copied the ideas or design of another; (2) whether the infringer formed a good-faith and soundly-based belief that either the patent was invalid or the product was not infringing; (3) the infringer's behavior as a party to the litigation; (4) the infringer's size and financial condition; (5) the closeness of the case; (6) the duration of the infringer's misconduct; (7) remedial action by the infringer; (8) the infringer's motivation for harm; and (9) whether the infringer attempted to conceal its misconduct. Read Corp. v. Portec, Inc., 970 F.2d 816, 826-27 (Fed.Cir.1992).
A finding of willful infringement supports, but does not compel enhanced damages. Id. at 826; Brooktree Corp. v. Advanced Micro Devices, Inc., 977 F.2d 1555, 1581 (Fed.Cir.1993) (en banc) (affirming denial of enhanced damages); see also National Presto Indus. v. West Bend Co., 76 F.3d 1185, 1193-94 (stating that award should "reflect the interest of justice in adjusting the damages appropriate to the culpability of the acts of infringement"). Nonetheless, the circumstances are so egregious that enhanced damages are warranted.
The court in Read explained a potential infringer's duty as follows:
One who has actual notice of another's patent rights has an affirmative duty to respect those rights.... That affirmative duty normally entails obtaining advice of legal counsel.... Those cases where willful infringement is found despite the presence of an opinion of counsel generally involve situations where opinion of counsel was either ignored or found to be incompetent.
Read, 970 F.2d at 828-29 (citations omitted).
Here, there is evidence that Pentech copied Hayduchok's invention. Although Judge Leval found that Pentech did not misappropriate confidential information from Hayduchok, it is clear that Pentech sought to market the same product as covered by Hayduchok's patent. Also, Pentech had advanced notice that the patent would issue and even filed a protest with the PTO to have the patent application rejected. Thus, Pentech obviously believed the patent was a threat to its sales of ERASABLES. As soon as the patent issued, Pentech had an affirmative duty to seek competent advice of counsel.
Mr. Kane's opinion letter is not objectively competent in its infringement analysis. It does not state his understanding of the composition of Pentech's product. Nor is there any evidence that Mr. Kane had even seen or been advised of the composition of Pentech's ERASABLES kits. Thus, there is no evidence that he knew that Pentech's ERASABLES kits contained markers having inks which were combinations of the primary colors (e.g. orange = yellow + red; green = yellow + blue). According to the evidence, it is reasonable to infer that Mr. Kane believed that the ERASABLES kits contained only three markers  red, blue, and yellow  and an eradicator. If that were his understanding, the removal of a primary color would indeed have avoided infringement. The evidence does not show that Pentech ever advised Mr. Kane that the orange and green markers were also at issue.
Nonetheless, Mr. Kane's letter advised that Pentech was infringing, and Pentech had no reason to question the competence of that advice. (Melnick Tr. 154). Mr. Kane recommended removal of a "primary color." Pentech argues that it followed Mr. Kane's advice by removing the yellow marker from its kits. However, Mr. Kane's letter was vague, at best, as to whether he recommended removal of a primary color marker (as Pentech suggests) or dye of a primary color (which would have affected more than one marker).
The objective reasonableness of Mr. Kane's letter depends upon the information that was made available to him by Pentech. Since Pentech failed to produce such evidence, I must find that Pentech did not reasonably rely upon Mr. Kane's advice contained in his September 4, 1987, letter.
Moreover, despite Mr. Kane's advice to remove a primary color, Pentech did not immediately stop selling the marker kits containing yellow markers. Thus, Pentech was willfully selling a product that it knew to be infringing. There is no evidence that Pentech took any remedial action with regard to *1179 that product. Pentech did not advise its customers that they were infringing the patent, nor did Pentech seek a license from Paradise to sell the product. Rather, Pentech did what was "easiest" for them.
More important, however, is the fact that Pentech disregarded Judge Leval's finding of infringement and continued selling its ERASABLES for several months. Pentech claims that it relied on advice of Mr. Eslinger that it could continue selling the infringing items. However, such advice is not objectively competent. Pentech cannot disclaim responsibility for its own actions by saying "one of my attorneys told me it was okay." At the point when Judge Leval found Pentech to be infringing, Pentech could have no doubt that enhanced damages would result from continued infringement.
I find that Pentech willfully disregarded Paradise's patent rights and infringed the patent.
Pentech made no remedial efforts. Pentech did not change its product code for the replacement product and did not inform all of its customers that the product was changing. There is no evidence that Pentech told its customers that the products they were purchasing were infringing. Pentech did what was easiest for them, and disregarded Paradise's rights.
Pentech's size and financial condition do not dissuade me from awarding enhanced damages. Pentech's yearly sales are presently in the mid $50 million range. (Melnick Tr. 203).
In this case, the issue of whether ERASABLES infringed the patent was close. Although the appellate panel affirmed Judge Leval's decision, Judge Lourie dissented on the issue of infringement. I cannot disregard Judge Lourie's opinion about the scope of the patent claims. Nonetheless, Pentech's infringement occurred without the benefit of competent advice of counsel, and in disregard for the advice of counsel. Pentech also ignored Judge Leval's findings. Obviously, Pentech had no concern for Paradise's rights.
Pentech asserts that it had "no financial or other motive for willful infringement." Pentech also asserts that the "erasables marker kit product was relatively insignificant for Pentech." (Pentech Mem. at 43). The facts indicate otherwise. In 1987, at the time the patent issued, Pentech's sales of the erasable markers exceeded one million dollars annually and comprised 11.9% of Pentech's business. Moreover, Mr. Melnick has stated that Pentech was concerned with doing whatever was easiest for Pentech.
The facts in this case make treble damages appropriate. Accordingly, the reasonable royalty amount of $1,032,000 is trebled to $3,096,000. The prejudgment interest is to be calculated based upon the damage award  i.e. $1,032,000  and not on the trebled amount.

Attorney's Fees
Attorney's fees may be awarded in exceptional cases. 35 U.S.C. § 285. Due to Pentech's willful infringement, and especially in light of Pentech's disregard for Judge Leval's finding of infringement, this case meets the test as exceptional. Accordingly, Paradise is awarded its attorney fees.

Postjudgment Interest
Interest shall be the amount set forth in 28 U.S.C. § 1961(a) (1988).

Conclusion
Paradise is awarded a reasonable royalty, in the amount of $1,032,000. The award is trebled, and Pentech is to pay Paradise's attorneys fees. Prejudgment interest shall be paid on the reasonable royalty, at a rate equal to the prime rate plus 1.00%, compounded annually.
Paradise is to submit a judgment to the court within ten days.
SO ORDERED.
NOTES
[1]  Judge Leval held that the patent was valid and literally infringed by Pentech. 1990 WL 180579, 18 U.S.P.Q.2d 1337, 87 Civ. 7233 (PNL) (S.D.N.Y. Nov. 12, 1990) (Leval, J.), modified, 1991 WL 230377, 21 U.S.P.Q.2d 1958 (Oct. 29, 1991), reconsideration denied, 1991 WL 268633 (Dec. 3, 1991), aff'd mem., 979 F.2d 216 (Fed.Cir. 1992).
[2]  The reader is presumed to be familiar with Judge Leval's comprehensive opinion.
[3]  See note 1, supra.
[4]  According to Pentech, this is just slightly more than the amount advocated by Pentech. (Pentech Mem. at 5) ("50% of Pentech's net profit ... [would yield] effective royalty ranges from 5.6 percent to 6.6 percent of net sales.").
[5]  Paradise had filed a motion to compel production of documents regarding Pentech's deductions for specific costs for ERASABLES markers. Judge Leval's order stated that "Pentech agrees, and the Court orders that, if Pentech will offer matter covered by those exhibits at trial, it will disclose those to Paradise within two weeks of receipt of Paradise's pretrial order and allow ample time for Paradise to prepare to defend as to those documents." Pentech failed to turn over those documents to Paradise until days before the damages phase of the trial. Therefore, Pentech was precluded from relying on the content of those documents.
[6]  After weighing all the factors above, I would have thought reasonable a royalty of 30% of Pentech's net sales. Even after paying the thirty percent to Paradise, Pentech would have retained a profit of 18%.
