PER CURIAM.
In the liability phase this court affirmed the district court’s judgment, reported at Beatrice Foods Co. v. New England Printing and Lithographing Co., 224 USPQ 982, 1984 WL 1493 (D.Conn.1984), of infringement by New England Printing and Lithographing Co. (“New England”) of three United States patents owned by Beatrice Foods (hereinafter “Webcraft”, now the independent company Webcraft Technologies, Inc. and the real party in interest). Beatrice Foods Co. v. New England Printing and Lithographing Co., 758 F.2d 668 (Fed.Cir.1984) (unpublished). On remand the district court determined that this case had not been proven to be “exceptional” within the meaning of 35 U.S.C. § 285 (1982), and declined to reinstate its earlier award of attorney fees. Order, June 5, 1985. An accounting of damages was ordered.
After extensive discovery and other procedures, a trial of damages was held in March 1988. The district court awarded Webcraft damages for patent infringement in the amount of $22,107,837.69, and prejudgment interest. Beatrice Foods Co. v. New England Printing and Lithographing Co., No. B-80-335 (D.Conn. July 14, 1988). The district court imposed a personal sanction on New England’s attorneys under 28 U.S.C. § 1927 (1982) for “multiplying the proceedings unreasonably and vexatiously”, Order, filed November 19, 1987, and assessed costs, expenses, and attorney fees incurred by Webcraft, in the amount of $17,754.99. Order, July 20, [1173]*11731988. New England appeals the damages award and the sanction.
DAMAGES
A
Damages “adequate to compensate for the infringement”, in the words of 35 U.S.C. § 284 (1982), are usually measured, depending on the circumstances and the proof, as the patent owner’s lost profits or as a reasonable royalty. Del Mar Avionics, Inc. v. Quinton Instrument Co., 836 F.2d 1320, 1326, 5 USPQ2d 1255, 1260 (Fed.Cir.1987). Kori Corp. v. Wilco Marsh Buggies & Draglines, Inc., 761 F.2d 649, 653-54, 225 USPQ 985, 987 (Fed.Cir.), cert. denied, 474 U.S. 902, 106 S.Ct. 230, 88 L.Ed.2d 229 (1985).
Citing Panduit Corp. v. Stahlin Bros. Fibre Works, 575 F.2d 1152, 1156, 197 USPQ 726, 729 (6th Cir.1978) and Bio-Rad Laboratories, Inc. v. Nicolet Instrument Corp., 739 F.2d 604, 616, 222 USPQ 654, 663 (Fed.Cir.), cert. denied, 469 U.S. 1038, 105 S.Ct. 516, 83 L.Ed.2d 405 (1984), the district court, in applying Webcraft’s lost profits as the measure of damages, found that there was demand for the patented product, that Webcraft had the capability to meet that demand, and that there were no acceptable noninfringing substitutes. The patent owner’s burden of proof regarding these elements is one of “reasonable probability.” Kori, 761 F.2d at 653, 225 USPQ at 987 (citing Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1065, 219 USPQ 670, 675 (Fed.Cir.1983)). When the patent holder would reasonably have made the sale, but for the infringement, the award of lost profits is proper. Kori, 761 F.2d at 653, 225 USPQ at 987 (citing Paper Converting Machine Co. v. Magna-Grafhics Corp., 745 F.2d 11 at 21, 223 USPQ 591 at 598, (Fed.Cir.1984) and Bio-Rad, 739 F.2d at 616, 222 USPQ at 663).
New England argues that damages should be measured as a reasonable royalty, not lost profits. At the time Webcraft first gave notice of infringement, Webcraft had offered New England a license at an apparently modest royalty rate or a paid-up license, and has since offered and granted royalty-bearing licenses to others. New England argues that Webcraft’s offers to license others “where no actual dispute has arisen” is probative of the damages that should be assessed against New England.
New England states that the district court refused to receive evidence of licenses offered to and royalties paid by others, that such evidence is admissible, and therefore that the court committed reversible error. However, the question is not whether such evidence is admissible under Rule 408, Federal Rules of Evidence, as New England argues, but whether it was required to be admitted. A trial judge has broad authority to manage the trial and to exclude irrelevant evidence. Further, it appears that New England’s expert testified without restraint on the subject of royalties offered to or paid by others.
The district court was not required to receive evidence pertinent to a determination of what royalty would be reasonable, when a royalty was correctly held not to be the measure of damages. Accord, e.g., Greenwood Ranches, Inc. v. Skie Constr. Co., 629 F.2d 518, 523 (8th Cir. 1980) (district court’s exclusion of testimony on “actual” loss from failure of irrigation system upheld because such proof was not relevant under district court’s interpretation of state law).
The court held that the appropriate measure of damages was Webcraft’s lost profits due to New England’s infringing activity. Although New England argues that Webcraft failed to carry its burden of proof, reversible error has not been shown. We affirm the district court’s holding that damages were properly measured by Web-craft’s lost profits.
B
The accounting period covered July 7, 1974 (six years before the commencement of litigation in 1980) through February 1983, when New England ceased infringing activity. The liability phase came to trial in 1983, after éxtensive pre-trial procedures. In 1983 New England destroyed all of its [1174]*1174manufacturing “job tickets”. The job ticket folders” contained a sample of the job and the press specification sheet which listed the press number, amounts and press counts. This was the primary and for many jobs the only source of information as to what had been manufactured and in what quantity. In response to interrogatories in 1980, New England stated that the job tickets “appear[ed] to be available”. In 1981 New England’s vice-president of manufacturing averred that by company policy these tickets were maintained for six years. New England also destroyed all invoices for sales prior to 1978, and some for later sales. A “job order” book remained that had entries from 1975. The parties agree that this book, and other remaining records, did not provide complete information either as to the product that was manufactured in each job, or the quantities sold.
Webcraft, carrying the burden of proving damages, attempted to fill the gaps that were due to these incomplete records. Webcraft undertook third party discovery of customers that Webcraft identified, it appears, from accounts that it had lost to New England. Based bn purchase orders from such customers’ files, Webcraft tried to identify which of the entries in the “job order” book were for infringing goods, and to correlate these entries with invoices or purchase orders.
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PER CURIAM.
In the liability phase this court affirmed the district court’s judgment, reported at Beatrice Foods Co. v. New England Printing and Lithographing Co., 224 USPQ 982, 1984 WL 1493 (D.Conn.1984), of infringement by New England Printing and Lithographing Co. (“New England”) of three United States patents owned by Beatrice Foods (hereinafter “Webcraft”, now the independent company Webcraft Technologies, Inc. and the real party in interest). Beatrice Foods Co. v. New England Printing and Lithographing Co., 758 F.2d 668 (Fed.Cir.1984) (unpublished). On remand the district court determined that this case had not been proven to be “exceptional” within the meaning of 35 U.S.C. § 285 (1982), and declined to reinstate its earlier award of attorney fees. Order, June 5, 1985. An accounting of damages was ordered.
After extensive discovery and other procedures, a trial of damages was held in March 1988. The district court awarded Webcraft damages for patent infringement in the amount of $22,107,837.69, and prejudgment interest. Beatrice Foods Co. v. New England Printing and Lithographing Co., No. B-80-335 (D.Conn. July 14, 1988). The district court imposed a personal sanction on New England’s attorneys under 28 U.S.C. § 1927 (1982) for “multiplying the proceedings unreasonably and vexatiously”, Order, filed November 19, 1987, and assessed costs, expenses, and attorney fees incurred by Webcraft, in the amount of $17,754.99. Order, July 20, [1173]*11731988. New England appeals the damages award and the sanction.
DAMAGES
A
Damages “adequate to compensate for the infringement”, in the words of 35 U.S.C. § 284 (1982), are usually measured, depending on the circumstances and the proof, as the patent owner’s lost profits or as a reasonable royalty. Del Mar Avionics, Inc. v. Quinton Instrument Co., 836 F.2d 1320, 1326, 5 USPQ2d 1255, 1260 (Fed.Cir.1987). Kori Corp. v. Wilco Marsh Buggies & Draglines, Inc., 761 F.2d 649, 653-54, 225 USPQ 985, 987 (Fed.Cir.), cert. denied, 474 U.S. 902, 106 S.Ct. 230, 88 L.Ed.2d 229 (1985).
Citing Panduit Corp. v. Stahlin Bros. Fibre Works, 575 F.2d 1152, 1156, 197 USPQ 726, 729 (6th Cir.1978) and Bio-Rad Laboratories, Inc. v. Nicolet Instrument Corp., 739 F.2d 604, 616, 222 USPQ 654, 663 (Fed.Cir.), cert. denied, 469 U.S. 1038, 105 S.Ct. 516, 83 L.Ed.2d 405 (1984), the district court, in applying Webcraft’s lost profits as the measure of damages, found that there was demand for the patented product, that Webcraft had the capability to meet that demand, and that there were no acceptable noninfringing substitutes. The patent owner’s burden of proof regarding these elements is one of “reasonable probability.” Kori, 761 F.2d at 653, 225 USPQ at 987 (citing Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1065, 219 USPQ 670, 675 (Fed.Cir.1983)). When the patent holder would reasonably have made the sale, but for the infringement, the award of lost profits is proper. Kori, 761 F.2d at 653, 225 USPQ at 987 (citing Paper Converting Machine Co. v. Magna-Grafhics Corp., 745 F.2d 11 at 21, 223 USPQ 591 at 598, (Fed.Cir.1984) and Bio-Rad, 739 F.2d at 616, 222 USPQ at 663).
New England argues that damages should be measured as a reasonable royalty, not lost profits. At the time Webcraft first gave notice of infringement, Webcraft had offered New England a license at an apparently modest royalty rate or a paid-up license, and has since offered and granted royalty-bearing licenses to others. New England argues that Webcraft’s offers to license others “where no actual dispute has arisen” is probative of the damages that should be assessed against New England.
New England states that the district court refused to receive evidence of licenses offered to and royalties paid by others, that such evidence is admissible, and therefore that the court committed reversible error. However, the question is not whether such evidence is admissible under Rule 408, Federal Rules of Evidence, as New England argues, but whether it was required to be admitted. A trial judge has broad authority to manage the trial and to exclude irrelevant evidence. Further, it appears that New England’s expert testified without restraint on the subject of royalties offered to or paid by others.
The district court was not required to receive evidence pertinent to a determination of what royalty would be reasonable, when a royalty was correctly held not to be the measure of damages. Accord, e.g., Greenwood Ranches, Inc. v. Skie Constr. Co., 629 F.2d 518, 523 (8th Cir. 1980) (district court’s exclusion of testimony on “actual” loss from failure of irrigation system upheld because such proof was not relevant under district court’s interpretation of state law).
The court held that the appropriate measure of damages was Webcraft’s lost profits due to New England’s infringing activity. Although New England argues that Webcraft failed to carry its burden of proof, reversible error has not been shown. We affirm the district court’s holding that damages were properly measured by Web-craft’s lost profits.
B
The accounting period covered July 7, 1974 (six years before the commencement of litigation in 1980) through February 1983, when New England ceased infringing activity. The liability phase came to trial in 1983, after éxtensive pre-trial procedures. In 1983 New England destroyed all of its [1174]*1174manufacturing “job tickets”. The job ticket folders” contained a sample of the job and the press specification sheet which listed the press number, amounts and press counts. This was the primary and for many jobs the only source of information as to what had been manufactured and in what quantity. In response to interrogatories in 1980, New England stated that the job tickets “appear[ed] to be available”. In 1981 New England’s vice-president of manufacturing averred that by company policy these tickets were maintained for six years. New England also destroyed all invoices for sales prior to 1978, and some for later sales. A “job order” book remained that had entries from 1975. The parties agree that this book, and other remaining records, did not provide complete information either as to the product that was manufactured in each job, or the quantities sold.
Webcraft, carrying the burden of proving damages, attempted to fill the gaps that were due to these incomplete records. Webcraft undertook third party discovery of customers that Webcraft identified, it appears, from accounts that it had lost to New England. Based bn purchase orders from such customers’ files, Webcraft tried to identify which of the entries in the “job order” book were for infringing goods, and to correlate these entries with invoices or purchase orders.
Before the district court, New England disputed the adequacy of the evidence compiled by Webcraft to show what New England had manufactured, in what quantities, and whether the items manufactured were of infringing structure. Webcraft reports, without contradiction, that New England refused to admit that it “maintained a record of production in job book entries.” New England also stated that it was unable to identify its nomenclature in the job book and on its invoices, or which product descriptions applied to infringing products.
New England argued at the accounting trial that the purchase orders that Web-craft had obtained from New England’s customers, even those with New England’s invoice numbers, were not a correct or probative measure of what had been manufactured and sold by New England. New England argued, and repeats on this appeal, that Webcraft’s attempts to reconstruct New England’s infringing activities were inadequate to meet Webcraft’s burden of proving damages for infringement.
New England also argues on this appeal that the parties “reduced the level of their disagreement to about 3 million out of more than 950 million products sold,” and that infringement damages must be limited accordingly. Webcraft replies that there was no agreement as to the total amount of infringement, and that “any threshold agreement reached was only as to the absolute minimum infringing quantities.” The record supports Webcraft’s position. In response to a request for admissions, New England had replied: “For each request that asks the defendant to admit that a copy of an invoice ‘establishes a sale,’ the request is denied. An invoice only establishes that an invoice was prepared, it does not establish that the goods were actually made, or shipped, or that any payment was made or received.” In response to an interrogatory concerning sales to specific identified customers, New England answered: “Defendant has not yet completed the calculation by which it will formulate a contention in this regard. When and if such a contention has been formulated, this answer will be supplemented”. Webcraft states that New England never responded further, despite repeated requests.
This evidence clearly showed that the incompleteness of Webcraft’s proof was due to New England’s destruction of its job tickets and other records, New England’s refusal to admit that its own invoices established a sale or that its customers’ purchase orders established a sale, and New England’s lack of cooperation and refusals to respond in discovery and other procedures. New England stated before the district court that it had not deliberately destroyed its manufacturing records, that the destruction had been done routinely. The district court received testimony on the issue from New England’s witnesses. The court did not believe New England’s explanations. We have no basis for disturbing [1175]*1175the district court’s credibility determinations, and the court’s view that this evidence was deliberately destroyed. See, Inwood Laboratories, Inc. v. Ives Laboratories, Inc., 456 U.S. 844, 856, 102 S.Ct. 2182, 2189, 72 L.Ed.2d 606 (1982) (“Determining the weight and credibility of the evidence is the special province of the trier of fact”); Litton Sys., Inc. v. Whirlpool Corp., 728 F.2d 1423, 1445, 221 USPQ 97, 111 (Fed.Cir. 1984).
New England’s procedures were not well received by the district court. In its opinion the court wrote: “The most outrageous is, of course, defendant’s intentional destruction of its job tickets, the only yardstick to measure accurately defendant’s guilt in dollars, thus hindering plaintiff in proving defendant’s illegal use of its patents [sic, inventions].”
C
The district court held that Webcraft had proved its damages without the need for drawing adverse inferences against New England. The court measured damages by the amount of New England’s sales that Webcraft had proven to be infringing, plus certain “convoyed” sales. The court then used this sales figure as Webcraft’s lost profits, stating that since New England’s sales were illicit, New England was not entitled to deductions from this total. Damages were thus awarded of $22,107,-837.69.
Webcraft states that the district court made an equitable determination of the amount of damages suffered by Webcraft and that, in the absence of hard data due to New England’s misfeasances, this discretionary judgment should not be disturbed. Webcraft states that the figure of $22 million in sales was a conservative minimum, in that the job book showed billions of units produced, and that only those jobs that could be compared with invoices or with purchase orders obtained from third persons, and that could reasonably be presumed to be infringements based on the available product descriptions, were counted by Webcraft.
Webcraft cites the example of jobs listed in the job book for National Liberty Insurance, an ex-customer of Webcraft, where no quantities or product descriptions were shown in the job book and the invoices were destroyed by New England, but New England’s ledger showed sales for these job numbers of over $281,000. Webcraft calls this an example of “infringing production which escaped the accounting” due to destruction of the probative documents, and argues that the district court was entitled to take such factors into account in reaching an equitable measure of damages.
New England argues that Webcraft is not entitled to the inclusion of “convoyed” sales. Webcraft had identified as “convoyed” certain sales, including sales to ex-customers of Webcraft, for which it lacked proof of infringing structure. The law does not bar the inclusion of convoyed sales, Paper Converting, 745 F.2d at 23, 223 USPQ at 599-600, and the district court did not clearly err in including these sales under these circumstances.
New England continues to challenge the probative value of Webcraft’s figures; pointing out, for example, that one of the ostensible customers approached by Web-craft turned out to have bought its pamphlets not from New England but from Webcraft’s licensee. New England’s position appears to be that, absent the possibility of precise measure of actual infringement, damages must be limited to that minimum production as to which there was not substantial disagreement. This was not adopted by the district court. Such an outcome would simply reward New England’s actions.
An infringer can not destroy the evidence of the extent of its wrongdoing, and limit its liability to that which it failed to destroy. The uncertainty in the damages calculation is the direct result of New England’s procedures. “Fundamental principles of justice require us to throw any risk of uncertainty upon the wrongdoer rather than upon the injured party.” Kori, 761 F.2d at 655, 225 USPQ at 989 (citing Story Parchment Co. v. Paterson Parchment Co., 282 U.S. 555, 563, 51 S.Ct. 248, [1176]*1176251, 75 L.Ed. 544 (1931)). See also Westinghouse Elec. & Mfg. Co. v. Wagner Elec. & Mfg. Co., 225 U.S. 604, 620, 32 S.Ct. 691, 696, 56 L.Ed. 1222 (1912) (infringer bears the risk where precise calculation impossible); Computing Scale Co. v. Toledo Computing Scale Co., 279 F. 648, 673 (7th Cir.1921), cert. denied, 257 U.S. 657, 42 S.Ct. 184, 66 L.Ed. 420 (1922) (a knowing infringer “should be held to the duty of keeping separate and accurate records of all his infringing acts; and, on his failure to keep such records, the court, in measuring the damages on account of his trespasses, should resolve all doubts against him”); Yesbera v. Hardesty Mfg. Co., 166 F. 120, 122 (6th Cir.1908), cert. denied, 214 U.S. 513, 29 S.Ct. 696, 53 L.Ed. 1063 (1909) (“failure or refusal to produce the most satisfactory evidence” creates presumption that such evidence is damaging).
Substantial discretion is reposed in the trial court when reaching a judgment following lack of cooperation of a party. The trial court may increase damages up to treble the amount of actual damages. See, e.g., Fox v. Knickerbocker Engraving Co., 165 F. 442, 444 (2d Cir.1908) (treble damages upheld where the defendant destroyed its files showing use of the infringing process before the commencement of the accounting, “although this was not done maliciously or for the purposes of concealment”). In Fox, the court found that where the defendant’s conduct had “subjected the complainants to a long and expensive litigation which might easily have been avoided if a license had been taken, [the lower court, in awarding increased damages] may well have thought that the damages which it was possible to prove were inadequate.” Id. at 444.
New England provided no actual amounts of infringing sales, offered no estimates of infringing sales, did not assist in their reconstruction, and consistently denied the accuracy of Webcraft’s evidence. While New England argues that the figure chosen by the court is clearly erroneous, it has not shown that there is better support for any other figure. Lindemann Maschinenfabrik GmbH v. American Hoist & Derrick Co., 895 F.2d 1403 at 1406 (Fed. Cir.1990). We affirm the district court’s selection of $22,107,837.69 as New England’s infringing sales.
However, we can not agree with Webcraft that the district court had equitable discretion to equate New England’s gross sales with Webcraft’s lost profit damages. The court’s stated reason for so doing — that New England as a tortfeasor had no manufacturing costs, does not implement the standard of Webcraft’s lost profits that the court had correctly adopted. We vacate the judgment that damages shall be $22,107,837.69, and remand to the district court for the purpose of determining Webcraft’s damages on the basis of lost profits. In so doing, the court may give consideration to Webcraft’s request that its actual damages be multiplied, as authorized by 35 U.S.C. § 284, and may in its equitable discretion grant said request, whether or not such an award exceeds $22,107,837.69.
Further, we do not decide whether Web-craft is entitled to the elements or quantum of damages asserted in its brief, viz. a 35% profit margin, 3% overage on job book entry sales, or loss of freight profits. These aspects are appropriately subject to consideration by the district court on remand.
SANCTIONS UNDER SECTION 1927
The district court imposed sanctions under 28 U.S.C. § 1927 against New England’s attorneys, for “multiplying the proceedings unreasonably and vexatiously.” Specifically, the court found that New England’s weighty four motions and memoran-da filed on August 28, 1987, along with the oppositions and replies generated by the motions, were made for the purpose of delay.
New England protests that these motions were filed concurrently with several motions by Webcraft, in a time frame that had been approved by the court; that the subject matter of the motions was relevant and material because Webcraft filed three motions on the same issues; and that the imposition of a monetary sanction without [1177]*1177prior notice and an opportunity to be heard violates due process.
A trial court has broad discretionary authority in managing the litigation before it, and the deterrence of intentional and unnecessary delay in the proceedings, the ground here cited by the district court, is a principal purpose of 28 U.S.C. § 1927. However, in Roadway Express, Inc. v. Piper, 447 U.S. 752, 767, 100 S.Ct. 2455, 2465, 65 L.Ed.2d 488 (1980), the Supreme Court stated that “[l]ike other sanctions, attorney’s fees certainly should not be assessed ... without fair notice and an opportunity for a hearing on the record.” See generally Oliveri v. Thompson, 808 F.2d 1265, 1280 (2d Cir.1986), cert. denied, 480 U.S. 918, 107 S.Ct. 1373, 94 L.Ed.2d 689 (1987) (requiring “[a]t a minimum, ... notice and an opportunity to be heard”). In the present case there was no opportunity for a hearing on the sanction.
Weberaft suggests that New England could have moved under Rule 59(e) for reconsideration of the court’s order imposing the sanction, thus obtaining a hearing. Such motions are to be favored under circumstances like the present. They can result in either a withdrawal of the order or a more detailed explication of the district court’s reasons for adhering to it. Thus they may eliminate either an appeal from the sanction order or the need for a remand. Nonetheless, reconsideration after a decision is rendered is not a substitute for a pre-decision hearing, when such hearing is otherwise required. Cleveland Bd. of Ed. v. Loudermill, 470 U.S. 532, 542, 105 S.Ct. 1487, 1493, 84 L.Ed.2d 494 (1985); Boddie v. Connecticut, 401 U.S. 371, 379, 91 S.Ct. 780, 787, 28 L.Ed.2d 113 (1971).
In the absence of a hearing or justification for its absence, see Boddie, 401 U.S. at 379 & n. 6, 91 S.Ct. at 787 & n. 6, the order imposing sanctions under 28 U.S.C. § 1927 is vacated and the matter is remanded for the conduct of an appropriate hearing.
OTHER ISSUES
We have reviewed the issues raised in New England’s counter-claim with respect to claim 10 of the ’817 patent, including Webcraft’s assertion that New England did not press the issue at the liability trial. The district court correctly held that the issue of validity was precluded at the accounting trial, and that the parchment products were properly included in the total infringing sales.
With respect to patent marking and the other issues and arguments raised on appeal, we discern no reversible error.1
COSTS
Each side shall bear its costs.
AFFIRMED IN PART, VACATED IN PART, AND REMANDED.