718 F.2d 1056
219 U.S.P.Q. 670
LAM, INC., Plaintiff-Appellee,v.JOHNS-MANVILLE CORPORATION and Johns-Manville SalesCorporation, Defendants-Appellants.
Appeal No. 83-776.
United States Court of Appeals,Federal Circuit.
Sept. 30, 1983.

Charles F. Brega, Denver, Colo., argued for appellants.  With him on the brief was J. Stephen McGuire, Denver, Colo.
Charles E. Pfund, Boston, Mass., argued for appellee.  With him on the brief were Richard W. Daily and Donald E. Phillipson, Denver, Colo.
Before KASHIWA, BENNETT and MILLER, Circuit Judges.
KASHIWA, Circuit Judge.


1
This is an appeal from a judgment of the United States District Court for the District of Colorado (Civil Action No. 76-W-1216), entered December 3, 1982, and amended December 13, 1982.  The judgment is on the accounting phase of a similarly-captioned case (Lam, Inc. v. Johns-Manville Corp., 668 F.2d 462, 213 USPQ 1061 (10th Cir.), cert. denied, 456 U.S. 1007, 102 S.Ct. 2298, 73 L.Ed.2d 1302 (1982)) that decided defendants-appellants' liability.  The district court awarded plaintiff-appellee trebled damages of $1,334,769.00 and attorneys' fees and expenses of $436,365.21 for a total sum of $1,771,134.21.  We affirm in part and reverse in part.

Prior Decision

2
The defendants-appellants, Johns-Manville Corporation and Johns-Manville Sales Corporation (hereinafter "J-M"), infringed plaintiff-appellee's U.S. Patent No. 3,950,638, issued April 13, 1976, for a high intensity discharge lamp.  The lamp is an interior, indirect lighting fixture.  The infringing activities took place between 1976 and 1979.  The district court found that J-M's CLASSPAK lamps infringed Lam's patent in suit the embodiment of the claimed invention being Lam's LUXXtra lamps.  The district court also found willful infringement and assessed treble damages.  Last, the district court awarded attorneys' fees and expenses.  Accordingly, the district court issued an injunction against J-M on October 23, 1979.

Background

3
During the trial of the instant case, Lam sought, inter alia, three types of damages.  They are (1) profits from potential sales of its LUXXtra fixtures which were lost to J-M's actual sales of CLASSPAKs (hereinafter "lost profits");  (2) profits lost on its sales of LUXXtra fixtures the prices for which were reduced to meet J-M's competitive CLASSPAK prices (hereinafter "reduced profits");  and (3) profits from projected lost sales of its LUXXtra fixtures as a result of J-M's infringement (hereinafter "projected lost profits").  The projected lost profits claim did not include the lost profits claim.


4
In support of its claims, Lam calculated the incremental profit or "gross margin" for each LUXXtra lamp sold between 1976 and 1979.  The gross margin equals the value of all the LUXXtra fixtures sold during the infringement period minus the direct cost of material, labor, commissions, and freight, with the resulting difference divided by the total number of LUXXtras sold.  It then multiplied the gross margin for each year times the number of J-M units actually sold to arrive at the damage figure for the first type of losses.  The number of J-M units actually sold, 944, was based on an estimate presented by J-M during a settlement hearing in 1979.  The breakdown of Lam's lost profits is as follows:


5
       LAM'S GROSS  NUMBER OF
       MARGIN PER   J--M INFRINGING
YEARS  UNIT         UNITS SOLD       TOTAL MARGIN
-----  -----------  ---------------  ------------
1976      $107            536           $57,352
1977       103              6               618
1978       101            182            18,382
1979       104            220            22,880
                          ---            ------
TOTAL                     944           $99,232


6
J-M, however, presented evidence showing that it sold 536 CLASSPAKs in 1976, 23 in 1977, 29 in 1978, and 231 in 1979 for a total of 819 units.1   In addition, J-M attempted to show that Lam failed to deduct variable costs from its gross margin calculation.


7
In its calculation of prejudgment interest on the lost profits claim, Lam multiplied the "average prime rate" of each of the years 1977-1982 times the total margin for that year to produce an interest calculation of $67,999.  The breakdown of the interest calculation is as follows:


8
        Average Prime
Year    Interest Rate  $57,352  $618  $18,382  $22,880
------  -------------  -------  ----  -------  -------
1977            7.82%   $4,485
1978           10.05%    5,764    62
1979           13.66%    7,834    84    2,511
1980           17.72%   10,163   110    3,257    4,054
1981           21.21%   12,164   131    3,899    4,853
1982           17.39%    4,987    54    1,598    1,989
                       -------  ----  -------  -------
TOTALS                 $45,397  $441  $11,265  $10,896  $67,999


9
As for the reduced profits claim, Lam presented evidence showing a total of $4,584 that was lost in four sales.2   J-M, however, stated that two of these sales (Hollybrook and Newberg) occurred after the December, 1979 injunction and the competitor in those sales was a different company.  In addition, Lam claimed prejudgment interest of $2,330 on the reduced profits claim.3


10
Last, Lam submitted Exhibit PX-6 to illustrate its projected lost profits claim.  It is a graph showing (1) the number of LUXXtra lamps actually sold by Lam between 1973 and 1982;  and (2) Lam's growth rate before infringement, i.e., before 1976, and after infringement, i.e., after 1979.  PX-6 is reproduced below:


11
NOTE: OPINION CONTAINS TABLE OR OTHER DATA THAT IS NOT VIEWABLE


12
The post-1979 growth rate is perceptively greater than that for the pre-1976 rate.  The dotted line, extending from the lower left-hand corner of the graph to the upper right-hand corner, represents the amount of projected lost sales from 1976 to 1981.  The solid line, extending from 1979 to 1982, represents Lam's growth rate after the infringement.  The numerals at the right margin of the graph represent Lam's losses per year, from 1976 to 1981.  The losses are computed by comparing the projected pre-1976 growth rate with actual sales.  The total loss is $1.4 million.  Mr. John Kluse, the vice president and treasurer of Lam, testified that the profit margin for the LUXXtra product line was at least 26%.  To arrive at the projected lost profits, he first multiplied the number of CLASSPAKs sold by J-M (944) times Lam's average selling price for each unit of the comparable LUXXtra lamps to arrive at a figure of $246,784.  This figure is then subtracted from the projected lost sales of $1.4 million to arrive at the amount of $1,153,220.  Multiplying the 26% figure times $1,153,220 produced the projected lost profits claim figure of $299,837.


13
At trial, J-M, claimed that the projected lost sales figure included lamps manufactured by Lam which were not comparable to its infringing CLASSPAKs.  In addition, J-M argued that Lam's decline in sales was caused by factors other than its infringement;  factors such as Lam's own poor financial management and the severe industry-wide cost-price squeeze in 1978.  Moreover, the amount of Lam's legal fees, about $30,000, was not a factor in diminishing its growth, especially in light of its gross sales exceeding $10 million in the first three years of the infringement.

District Court Proceeding

14
The district court found that the actual damages suffered by Lam were $444,923.00.  This amount is a summation of damages which were classified into three categories:  (1) Lam's lost profits and the prejudgment interest on these lost profits;  (2) Lam's reduced profits and the prejudgment interest on these reduced profits;  and (3) Lam's projected lost profits.  The breakdown of the actual damages is as follows:


15
NOTE: OPINION CONTAINS TABLE OR OTHER DATA THAT IS NOT VIEWABLE


16
(1)  Lost profits  $89,309.00
(1) Lost profits                    $89,309.00
         Interest on lost profits    61,200.00
(2) Reduced profits & interest        6,914.00
(3) Projected lost profits          287,500.00
                                   -----------
                                   $444,923.00


17
In finding the Category One damages, the district court stated:


18
For a company the size of defendant to be unable to establish with exactness the number of units it manufactured or sold defies belief, but the number changed with the person vouching for it and with the records allegedly relied upon.  * * *    [W]hen an infringer can't come up with positive records, the punishment for the inaccuracies lies on the infringer, and that's the rule I apply here.  At one stage of the proceedings defendant told plaintiff it had produced 944 CLASSPAK fixtures [a statement made under oath in a desposition [sic] of a responsible person employed by defendant] and plaintiff relied heavily on this testimony in the course of its preparation for the damage hearing.  * * *    I hold defendant to the sworn testimony of its own witness, and for the purposes of awarding damages, I find that 944 CLASSPAK fixtures is the number of units to be considered.  [I do this with full recognition that at time of trial defendant had some testimony on other figures, including a low total of 843 fixtures testified to by one witness.]


19
In addition, the district court held that, in a two-supplier market as it existed in this case, the patent owner may recover lost profits he would have made but for the infringement.  He need not be limited to recovering only the reasonable royalty.  After accepting the figure of 944 units sold which produced a total margin of $99,232, the district court said:


20
Giving the defendant the benefit of the doubt, I reduce by 10% the units sold and the dollars lost on sales made by Manville.  I make no effort to allocate between years and I find that over the 4 year period, had it not been for defendant's wrongful conduct, plaintiff would have sold 850 fixtures, the margin on which would have been $89,309.  Defendants vigorously disputs [sic] that there would have been a profit, but I accept the margin figures shown by Lam's witnesses.  They were the more credible and the more convincing to me.


21
Regarding the assessment of prejudgment interest on the Category One damages, the district court accepted the $67,999 figure proposed by Lam.  The district court then commented:


22
Statutory rates don't get the job done because of the high rates of interest paid in the marketplace during the years in question, and prime rates are really unfair because of rates charged Lam because of its impoverishment resulting from the expenses of the lawsuit.  Using prime rates is surely not unfair to defendant, although it may be unfair to plaintiff, but plaintiff is happy with the use of prime rates.


23
* * *


24
* * *


25
Applying the rule * * * that when the fact of damage is certain, the amount of damage need not be precisely proved, and again using the 90% average figure used in arriving at the 850 units, I find that for the sales in question, defendant owes plaintiff $61,200 interest.


26
Next, in finding the Category Two damages, the district court stated:


27
I have already found that the market was supplied by only two suppliers, and if plaintiff hadn't reduced its prices, defendant would have made these sales.  If that be true, logic requires the award of these damages resulting from plaintiff's inability to make the sales unless it cut prices.  The damage calculation is the same as that applied to the 850 units.  * * *


28
[T]he total damages claimed for these cut price sales is * * * $20,742.  I think that plaintiff is entitled to recover the $20,742, because I am satisfied that were it not for defendant's wrongful competition, plaintiff would have made the sales at full price and would have made its full profit.


29
In the amended judgment of December 13, 1982, the $20,742 figure was reduced to $6,914.  This figure includes both the actual damage portion and its prejudgment interest.


30
As for the last category of damages, projected lost profits, the district court said:


31
It is certain beyond doubt that Lam's growth was impaired because of the cash drain resulting from the litigation.


32
* * *


33
* * *


34
Lam was hurt and it was hurt badly by the litigation.  Its ability to compete against a giant was almost destroyed because of the trade's belief that Lam had nothing to sell which wasn't available from defendant.  This was just a little bit of the injury Lam sustained.  The real injury was the drain on Lam's resources resulting from the expensive litigation.  Lam was drained of its cash and came under the control of its bankers--a situation which rarely leads to growth and success.  Its limited human resources had to be devoted to the lawsuit instead of to business.  On top of all of this, the record shows that the hastily developed CLASSPAK didn't work very well, and the entire concept of the fixture received a bad name.  The market reasoned that if the giant couldn't make a good product, the pygmy surely couldn't.


35
Sales projections are seldom accurate, but the record shows two important things, (1) before the infringement sales increased rapidly, and (2) after the injunction they increased again.  The slow sales were during the time of the unlawful competition, and, had it not been for defendant's wrongful acts, I think that sales would have steadily increased.  Plaintiff has approximated a reasonable sales growth based on the prior sales increase between 1974 and 1976.  This is graphically portrayed in Exhibit 6, and I think that defendant's attack on the projection falls short.


36
* * *


37
* * *


38
I accept plaintiff's projection as to sales and I think that the 26% profit margin is fair and reasonable.  Realizing that the figures are necessarily imprecise, I round them a bit for ease of calculation of this phase of the damage award, and I find that had it not been for the infringement, sales would have grown at about the same prior rate to a sales figure of $1,150,000 and that plaintiff's profit thereon would be 25%.  In making this finding I do not ignore the claim of defendant that increased sales would increase variable expenses which plaintiff says are not variable.  This is a judgment call, and I don't think that defendant has met its burden on this point.  I award $287,500.00 as damages for sales which would have been made had the company been permitted to grow the way it would have grown absent the lawsuit.


39
Last, the district court awarded $436,365.21 in attorneys' fees and expenses.4   The district court commented:


40
Hourly time records have been submitted by counsel and full expense statements have been received.  There is no real challenge made to the amount of fees claimed.  Defendant could have called plaintiff's counsel for cross-examination, but, instead, accepted affidavits.  Defendant could have made an in depth examination of the time records, but the records were not fully audited and they were accepted.  Defendant could have called expert witnesses had there been any serious dispute as to the amounts claimed.  No expert witness was called.  The amounts were paid by plaintiff or plaintiff is obligated to pay them, and there is no suggestion that the time was not spent nor that it should not have been spent.  The same can be said as to the expenses.

Appellants' Arguments

41
Regarding the Category One damage award, the appellants argue that the district court erred in its failure to accept the best, most compelling evidence as to (1) the actual number of infringing units and when these infringing sales occurred;  and (2) Lam's profit margin for the units covered by the patent in suit.


42
Regarding the prejudgment interest assessed on the Category One damages, the appellants argue that the district court erred in (1) trebling the prejudgment interest award, and (2) awarding "broadened" interest, i.e., interest above or at the prime rate.


43
Regarding the Category Two damage award, the appellants argue that the district court erred in awarding damages since two of the reduced price sales were not reduced in order to meet J-M's competition.


44
Regarding the Category Three damage award, the appellants argue that the award of damages based on projected lost sales is remote and speculative.


45
Last, the appellants argue that the district court erred (1) in not requiring Lam to demonstrate the reasonableness of its attorneys' fees, and (2) in awarding all alleged disbursements.

OPINION

46
* Pursuant to 35 U.S.C. Sec. 284,5 a patent owner is entitled to damages that are adequate to compensate for the infringement.   General Motors Corp. v. Devex Corp., --- U.S. ----, ----, 103 S.Ct. 2058, 2062, 76 L.Ed.2d 211, 217 USPQ 1185, 1188 (1983).  Such damages "constitute 'the difference between his pecuniary condition after the infringement, and what his condition would have been if the infringement had not occurred.'  * * *    The question to be asked in determining damages is 'how much had the Patent Holder * * * suffered by the infringement.  And that question [is] primarily:  had the Infringer not infringed, what would Patent Holder * * * have made?' "    [Citations omitted.]  Aro Manufacturing Co. v. Convertible Top Replacement Co., 377 U.S. 476, 507, 84 S.Ct. 1526, 1543, 12 L.Ed.2d 457, 141 USPQ 681, 694 (1964) (generally referred to and hereinafter cited as Aro II ).


47
In determining such damages, the profits lost by the patent owner in a two-supplier market is a proper ground for granting relief.   See Livesay Window Co. v. Livesay Industries, Inc., 251 F.2d 469, 471, 116 USPQ 167, 168-69 (5th Cir.1958).  Lost profits may be in the form of diverted sales, eroded prices, or increased expenses.  The patent owner must establish a causation between his lost profits and the infringement.  A factual basis for the causation is that "but for" the infringement, the patent owner would have made the sales that the infringer made, charged higher prices, or incurred lower expenses.   See Milgo Electronic Corp. v. United Business Communications, Inc., 623 F.2d 645, 663, 206 USPQ 481, 495 (10th Cir.), cert. denied, 449 U.S. 1066, 101 S.Ct. 794, 66 L.Ed.2d 611 (1980).  In proving his damages, the patent owner's burden of proof is not an absolute one, but rather a burden of reasonable probability.  The Fifth Circuit, in Livesay, stated:


48
If in all reasonable probability, the Patent Owner would have made the sales, which the Infringer had made, what the Patent Owner in reasonable probability would have netted from the sales denied to him is the measure of his loss, and the Infringer is liable for that.


49
251 F.2d at 471-72, 116 USPQ at 169.


50
Where, as here, the patent owner and the infringer were the only suppliers of the product, causation may be inferred.   See Livesay, 251 F.2d at 473, 116 USPQ at 170.  Moreover, when the amount of the damages cannot be ascertained with precision, any doubts regarding the amount must be resolved against the infringer.  The Court, in Story Parchment Co. v. Paterson Parchment Paper Co., 282 U.S. 555, 563, 51 S.Ct. 248, 250-51, 75 L.Ed. 544 (1931), stated:


51
Where the tort itself is of such a nature as to preclude the ascertainment of the amount of damages with certainty, it would be a perversion of fundamental principles of justice to deny all relief to the injured person, and thereby relieve the wrongdoer from making any amend for his acts.  In such case, while the damages may not be determined by mere speculation or guess, it will be enough if the evidence show [sic] the extent of the damages as a matter of just and reasonable inference, although the result be only approximate.  The wrongdoer is not entitled to complain that they cannot be measured with the exactness and prevision that would be possible if the case, which he alone is responsible for making, were otherwise.  * * *    [T]he risk of the uncertainty should be thrown upon the wrongdoer instead of upon the injured party.  [Citations omitted.]


52
In addition, any adverse consequences must rest on the infringer when the inability to ascertain lost profits is due to the infringer's own failure to keep accurate or complete records.   See Milgo, 623 F.2d at 665, 206 USPQ at 496.


53
In the instant case, the appellants argue that the district court erred in its failure to accept the best, most compelling evidence for determining the Category One damages.  We disagree.


54
As to the actual number of CLASSPAKs sold, any uncertainty must be resolved against J-M since it failed to keep accurate records.  See Milgo, id.    J-M advanced different numbers at different stages of this litigation--944 at the 1979 settlement hearing, and 843 and 819 at trial.  It was therefore within the district court's province to accept the more credible evidence after it had heard testimony and reviewed documentary evidence from both sides.  Moreover, the district court discounted the 944 figure by 10% to 850 in order to compensate for any uncertainties.


55
As to J-M's contention that the district court erred in not deducting variable costs from Lam's incremental profit, thereby miscalculating Lam's profit margin, we also disagree.  J-M presents a litany of variable costs that it contends were ignored by the district court.  The district court, however, heard testimony from both sides regarding these variable costs before it found Lam's profit margin figure.


56
Accordingly, J-M has failed to show that these findings of fact were clearly erroneous.  F.R.Civ.P. 52(a).

II

57
Prejudgment interest may be assessed by the district court after damages have been found.   General Motors, --- U.S. at ----, 103 S.Ct. at 2062, 217 USPQ at 1188.  Contrary to Lam's contention, where, as here, the damages were increased to punish J-M for its willful infringement, prejudgment interest cannot be assessed on the increased or punitive portion of the damage award.   Underwater Devices, Inc. v. Morrison-Knudsen Co., 717 F.2d 1380, (Fed.Cir.1983), aff'g Underwater Devices, Inc. v. Morrison-Knudsen Co., 217 USPQ 1039 (D.Hawaii 1982).   Accord Trio Process Corp. v. L. Goldstein's Sons, Inc., 638 F.2d 661 (3d Cir.1981);  H.K. Porter Co. v. Goodyear Tire & Rubber Co., 536 F.2d 1115, 191 USPQ 486 (6th Cir.1976).  Prejudgment interest is awarded to compensate for the delay in payment of the damages, and not to punish the infringer.    Underwater, at 1389.  We therefore reverse the award of prejudgment interest on the increased portion of the Category One damage award.6


58
As to J-M's contention that the district court erred in awarding "broadened" interest, i.e., interest above or at the prime rate, we disagree.  Under section 284, the district court has discretion to award prejudgment interest and the amount of that award.7   General Motors, --- U.S. at ----, 103 S.Ct. at 2063, 217 USPQ at 1189.  The district court may "fix" the interest and select an award above the statutory rate,8 see Underwater Devices, 217 USPQ at 1065, or select an award at the prime rate.   Cf. General Facilities, Inc. v. National Marine Service, Inc., 664 F.2d 672, 674 (8th Cir.1981) (discretionary award of prejudgment interest at the prime rate in an admiralty action).  Once the claimant has affirmatively demonstrated that a higher rate should be used, cf. Decca, Ltd. v. United States, 640 F.2d 1156, 1168, 225 Ct.Cl. 326, 335, 209 USPQ 52, 61 (1980), cert. denied, 454 U.S. 819, 102 S.Ct. 99, 70 L.Ed.2d 89 (1981) (8% interest rate in a 28 U.S.C. Sec. 1498 action), the district court may fix the interest at that higher rate.  In the instant appeal, Lam affirmatively demonstrated and the district court found that Lam borrowed money at or above the prime rate in order to continue its operations.  Since the appellants have failed to show that the district court abused its discretion in awarding prejudgment interest at the prime rate, we agree with the district court's decision.III


59
Regarding the Category Two damage award, an award based on reduced profits is proper.   Yale Lock Manufacturing Co. v. Sargent, 117 U.S. 536, 6 S.Ct. 934, 29 L.Ed. 954 (1886).  J-M argues that Lam did not reduce its prices solely to meet J-M's competition.  The district court, however, found that the market had only two suppliers, and that Lam reduced its prices to meet J-M's competition.  Although there were other competitors in this market, as evidenced by the 1980 reduced-price sales, they were insignificant.   See Photo Electronics Corp. v. England, 581 F.2d 772, 784, 199 USPQ 710, 721 (9th Cir.1978);  Ingersoll-Rand Co. v. Brunner & Luy, Inc., 182 USPQ 257 (S.D.Fla.1974).  Again, J-M has failed to show that the district court's finding was clearly erroneous.


60
Since the Category Two damage award includes trebled prejudgment interest, we reverse the award of such prejudgment interest on the increased portion.9

IV

61
As stated before, the question that needs to be answered in determining damages is "how much had the Patent Holder * * * suffered by the infringement.  And that question [is] primarily:  had the Infringer not infringed, what would Patent Holder * * * have made?"   Aro II, 377 U.S. at 507, 84 S.Ct. at 1543, 141 USPQ at 694.  The damages which are recoverable are "the detriments suffered by the plaintiffs [patent holders] through the infringement."   Livesay, 251 F.2d at 472, 116 USPQ at 169.  In relation to the Category Three damage award, J-M contends that this award, which is based on projected lost sales, is remote and speculative.  It cites Velo-Bind, Inc. v. Minnesota Mining & Manufacturing Co., 647 F.2d 965, 211 USPQ 926 (9th Cir.), cert. denied, 454 U.S. 1093, 102 S.Ct. 658, 70 L.Ed.2d 631 (1981) and Union Carbide Corp. v. Graver Tank and Manufacturing Co., 282 F.2d 653, 213 USPQ 3 (7th Cir.1960), cert. denied, 365 U.S. 812, 81 S.Ct. 695, 5 L.Ed.2d 691 (1961) for the proposition that Lam's projected lost profits damage award is remote and speculative.  We disagree.


62
In Velo-Bind, the Ninth Circuit held that the projected lost profits on unpatented consumable supplies--paper, plastic strips, and book and document covers, for use in the infringed bookbinding machine were unrecoverable since they were indirect consequential damages.  In Union Carbide, the master recommended, and the district court granted, an increase in the compensatory damages award "to cover the inconvenience, trouble and expense which the plaintiff has suffered by reason of the infringement and based on the fact that the plaintiff has been compelled to conduct long and expensive litigation and which the plaintiff should recover as reimbursement for what it has actually suffered * * *."    282 F.2d at 673, 127 USPQ at 18.  The Seventh Circuit rejected the award of additional compensatory damages on the ground that the master failed to find or disclose any basis for his recommendation of additional compensatory damages.


63
In contrast to Velo-Bind and Union Carbide, the district court's Category Three award was based on evidence showing Lam's injury, and not based on mere speculation or conjecture.  See Carter v. Baker (Case No. 2,472), 5 Fed.Cas. 195, 201 (C.C.D.Cal.1871);  Cargill, Inc. v. Taylor Towing Service, Inc., 642 F.2d 239, 241 (8th Cir.1981).  Although J-M contends that it was impossible for Lam to reach the pre-infringement growth rate during the infringing years, that Lam's sales decline was related to general business problems, and that there was no causal effect between Lam's legal fees and its sales decline, we are not persuaded that the district court's finding was clearly erroneous.  The district court found, after evaluating testimonial and documentary evidence, that Lam was badly hurt by this litigation.  There is no doubt that its growth was seriously impaired by J-M's infringement.  The litigation not only interfered with Lam's financial resources, but also with its human resources.  Lam's cash resources were drained and its employees devoted valuable time to the lawsuit.  Moreover, J-M's hastily-developed CLASSPAKs seriously damaged Lam's goodwill.  Since these fixtures didn't work very well, the customers developed doubts concerning the entire concept.


64
Lam's impaired growth was clearly shown in Exhibit PX-6.  A high rate of growth is evident from 1974 to 1976.  Following years of decreased growth due to J-M's infringement, Lam has since enjoyed an even greater growth rate.  Such post-infringement growth rate is certainly admissible evidence to form a basis for inferring that Lam would have grown at the pre-infringement rate had J-M not infringed.   Cf. Sinclair Refining Co. v. Jenkins Petroleum Process Co., 289 U.S. 689, 697-99, 53 S.Ct. 736, 738-39, 77 L.Ed. 1449 (1933).  Such growth would have given Lam a profit margin of 25%.


65
J-M contends that PX-6 contained inaccurate information.  For example, the data for plotting the graph included sales of other types of lamps manufactured by Lam with respect to which J-M did not compete, the pre-infringement growth rate included "start-up" sales which distorted the growth rate, and if a growth rate projection is to be drawn from 1977 to 1978, at the middle of the infringement period, it would even exceed the post-infringement growth rate.  The district court, however, considered both testimonial and documentary evidence before it and found the profit margin to be 25%.  Although J-M contends that it offered "no practical competition" with respect to two types of lamps manufactured by Lam, the "1000 watts" and "HPS LUXXtra", there is no evidence showing that it did not produce the "1000 watts" and there is evidence showing that it did manufacture counterparts to Lam's "HPS LUXXtra."


66
Where, as here, a two-supplier market existed, an award based on projected lost sales is neither remote nor speculative when there is evidence of actual pre-infringement and post-infringement growth rates.  Such evidence illustrates the proven detriments suffered by the patent owner.  These damages were not picked out by mere speculation or guess, but rather, found by the district court as the result of an extrapolation of actual data.  The district court found that Lam would have grown at the pre-infringement rate during 1976-79 but for J-M's infringement.    See Milgo, supra.


67
In the instant case, J-M has failed to show that the district court's finding on the Category Three damages was clearly erroneous.

V

68
Last, the appellants argue that the district court erred (1) in not requiring Lam to demonstrate the "reasonableness" of its attorneys' fees, and (2) in awarding all alleged disbursements.  We disagree.


69
35 U.S.C. Sec. 28510 permits a district court to award reasonable attorneys' fees in an exceptional case.   See American Safety Table Co. v. Schreiber, 415 F.2d 373, 380, 163 USPQ 129, 133-34 (2d Cir.1969), cert. denied, 396 U.S. 1038, 90 S.Ct. 683, 24 L.Ed.2d 682 (1970).  The amount of the award is assessed at the discretion of the district court.  See American Safety, id., Purer & Co. v. Aktiebolaget Addo, 410 F.2d 871, 880, 161 USPQ 270, 275-76 (9th Cir.), cert. denied, 396 U.S. 834, 90 S.Ct. 90, 24 L.Ed.2d 84 (1969).  In determining the reasonableness of the award, there must be some evidence to support the reasonableness of, inter alia, the billing rate charged and the number of hours expended.   See Codex Corp. v. Milgo Electronic Corp., 717 F.2d 622 at 631-632 (1st Cir.1983), aff'g Codex Corp. v. Milgo Electronic Corp., 541 F.Supp. 1198 (D.Mass.1982);  Loctite Corp.


70
v. Fel-Pro, Inc., 667 F.2d 577, 585, 213 USPQ 905, 912 (7th Cir.1981).


71
In the instant appeal, Lam's attorneys submitted hourly time records and full expense statements, along with documentation in support of their billing rates.   Compare Codex, 541 F.Supp. at 1202-03 (documentation of community billing rates) with Loctite, 667 F.2d at 585, 213 USPQ at 912 (no documentation of community billing rates).  Lam's attorneys, however, failed to organize their hourly time records in such a fashion as to permit the district court to review the reasonableness of the hours expended.    See Codex, at 632.  Despite such an omission, we will not remand this case for this purpose alone since J-M made no real challenge at trial concerning the amount of the fees claimed by Lam.   See Milgo, 623 F.2d at 667, 206 USPQ at 499.


72
Contrary to J-M's contention that Lam's disbursements were improperly granted, section 285 also permits the prevailing party to recover disbursements that were necessary for the case.   See Codex, 541 F.Supp. at 1201;  Arbrook, Inc. v. American Hospital Supply Corp., 202 USPQ 685, 690 (N.D.Tex.1979), rev'd on other grounds, 645 F.2d 273, 210 USPQ 84 (5th Cir.1981);  Kaehni v. Diffraction Co., 342 F.Supp. 523, 538, 173 USPQ 705, 715 (D.Md.1972), aff'd, 473 F.2d 908 (4th Cir.), cert. denied, 414 U.S. 854, 94 S.Ct. 151, 38 L.Ed.2d 103 (1973);  and Brian Jackson Associates, Inc. v. San Manuel Copper Corp., 305 F.Supp. 66, 75, 163 USPQ 198, 204 (D.Ariz.1969).  In addition, the district court found that J-M did not seriously dispute Lam's expense statements.


73
Accordingly, J-M has failed to show that the district court abused its discretion in awarding attorneys' fees and expenses to Lam.

VI

74
In conclusion, we affirm the award of lost profits, prejudgment interest on the lost profits, reduced profits, prejudgment interest on the reduced profits, projected lost profits, and attorneys' fees and expenses.  We also affirm the trebling of the lost profits, reduced profits and projected lost profits awards.  We reverse the award of prejudgment interest on the punitive portions of the lost profits and reduced profits awards.  The breakdown of the damage award is as follows:


75
Lost profits (trebled)              $267,927.00
  Prejudgment interest                61,200.00
Reduced profits (trebled)             13,752.00
  Prejudgment interest                 2,330.00
Projected lost profits (trebled)     862,500.00
Attorneys' fees and expenses         432,115.2111
                                  --------------------
                                  $1,639,824.21


76
AFFIRMED-IN-PART.


77
REVERSED-IN-PART.



1
 J-M also presented testimony at trial that it sold 843 CLASSPAKs


2
 The claimed profits for the four instances of reduced-price sales were:
1978    Coastal Gerrard School        Phila., PA    --      $1,458
1979    Taholah Education Center      Aberdeen, WA  --      $2,835
1980    Hollybrook Elementary School  Gresham, OR   --  Negligible
1980    Newberg Middle School         Newburg, OR   --      $  291
                                                        ----------
TOTALS                                                      $4,584


3
 The breakdown of the interest calculation is as follows:
        Average Prime
Year    Interest Rate  $1,458  $2,835  $291
------  -------------  ------  ------  ----
1979       13.66%        $199
1980       17.72%         258     502
1981       21.21%         309     601    62
1982       17.39%         127     247    25
                       ------  ------  ----
TOTALS                   $893  $1,350   $87  $2,330


4
 The breakdown of Lam's attorneys' fees and expenses is as follows:
Fees of patent counsel            $325,576.68
Fees of local counsel               73,848.46
Fees of professional consultants    29,533.46
Travel and $281 of miscellaneous
  expenses                          11,606.61
                                  -----------
                                  $436,365.21


5
 35 U.S.C. Sec. 284 states:
Upon finding for the claimant the court shall award the claimant damages adequate to compensate for the infringement but in no event less than a reasonable royalty for the use made of the invention by the infringer, together with interest and costs as fixed by the court.
When the damages are not found by a jury, the court shall assess them.  In either event the court may increase the damages up to three times the amount found or assessed.
The court may receive expert testimony as an aid to the determination of damages or of what royalty would be reasonable under the circumstances.


6
 The prejudgment interest on the increased portion of the Category One damage award is $122,400.00


7
 Even where statutes do not explicitly permit the award of prejudgment interest, the district court has discretion to award prejudgment interest.   See Moore-McCormack Lines v. Richardson, 295 F.2d 583, 592-95 (2d Cir.1961) (admiralty law);  Lodges 743 and 1746, Int'l Ass'n of Machinists and Aerospace Workers, AFL-CIO v. United Aircraft Corp., 534 F.2d 422, 446-47 (2d Cir.1975), cert. denied, 429 U.S. 825, 97 S.Ct. 79, 50 L.Ed.2d 87 (1976) (labor law);  and Occidental Life Ins. Co. v. Pat Ryan & Assocs., Inc., 496 F.2d 1255, 1268-69 (4th Cir.), cert. denied, 419 U.S. 1023, 95 S.Ct. 499, 42 L.Ed.2d 297 (1974) (securities law).   See also Blau v. Lehman, 368 U.S. 403, 414, 82 S.Ct. 451, 457, 7 L.Ed.2d 403 (1962) (securities law)


8
 Discretionary award of prejudgment interest above the statutory rate in admiralty actions include In re M/V Vulcan, 553 F.2d 489, 491 (5th Cir.), cert. denied, 434 U.S. 855, 98 S.Ct. 175, 54 L.Ed.2d 127 (1977) (commercial borrowing rate of 12%);  Fisher v. Agios Nicolaos V, 628 F.2d 308, 319 (5th Cir.1980), cert. denied, 454 U.S. 816, 102 S.Ct. 92, 70 L.Ed.2d 84 (1981) (commercial rate of 9%);  United States v. Motor Vessel Gopher State, 614 F.2d 1186, 1190 (8th Cir.1980) (commercial rate of 8%);  and Sauers v. Alaska Barge and Transp., Inc., 600 F.2d 238, 248 (9th Cir.1979) (commercial rate of 8%)
It is interesting to note that post-judgment interest pursuant to 28 U.S.C. Sec. 1961 (1982) is set at a rate equal to the coupon issue yield of U.S. Treasury bills.


9
 The amount of the prejudgment interest on the increased or punitive portion of the Category Two damage award is $4,660.00


10
 35 U.S.C. Sec. 285 states:
The court in exceptional cases may award reasonable attorney fees to the prevailing party.


11
 Lam inadvertently included $4,250.00 in the attorneys' fee category for services not performed for the patent infringement case.  That amount is accordingly subtracted from the amount granted by the district court


