
    MILGO ELECTRONIC CORPORATION, a Florida Corporation, Plaintiff-Appellee, v. UNITED BUSINESS COMMUNICATIONS, INC., a Kansas Corporation, Defendant-Appellant.
    No. 78-1624.
    United States Court of Appeals, Tenth Circuit.
    Argued Jan. 23, 1980.
    Decided May 29, 1980.
    
      Stanley R. Jones, Tustin, Cal. (Harold L. Jackson, Tustin, Cal., with him on the brief), of Jackson, Jones & Price, Tustin, Cal. (J. Donald Lysaught of Weeks, Thomas, Lysaught, Bingham & Mustain, Overland Park, Kan., with him on the brief), for plaintiff-appellee.
    William H. Curtis, Kansas City, Mo. (Michael C. Manning, Kansas City, Mo., with him on the brief), of Morrison, Hecker, Curtis, Kuder & Parrish, Kansas City, Mo., Carter H. Kokjer of Lowe, Kokjer, Kircher, Wharton & Bowman, Kansas City, Mo. (John F. Dodd, Shawnee Mission, Kan., and Robert D. Benham of McAnany, Van Cleave & Phillips, Kansas City, Kan., with them on the brief), for defendant-appellant.
    Before BARRETT, DOYLE and LOGAN, Circuit Judges.
   PER CURIAM.

United Business Communications, Inc. (UBC) appeals from an adverse judgment in a patent infringement action initiated by Milgo Electronics Corporation (Milgo). Bifurcated trials to the Court on the issues of liability and damages were held in September 1975 and December 1977, respectively, after which the Court found, inter alia, that: Each of the Milgo patents in question were valid; certain claims of each patent were infringed by the manufacture, use and sale of the accused modems; Rixon II was a mere instrumentality, alter ego, or agency of UBC; the infringement was flagrant and willful; and Milgo was entitled to a total judgment, including taxable costs, of $2,340,726.23.

Concurrent with its judgment upholding the validity of the Milgo patents and awarding damages, the Court rendered detailed findings of fact and conclusions of law encompassing in excess of one hundred pages of the record on appeal. We will therefore limit our development of the factual background to those issues we deem dispositive on appeal, i. e., the validity of the patents in question, the existence of an agency relationship between UBC and Rix-on II; and the damages awarded.

I.

Patent Validity

Milgo is a Florida corporation engaged in the manufacture and sale of data communication equipment, including “modems”, which are used to implement communication of binary data over telephone lines. It is not possible to transmit digital information by applying it directly to the telephone lines; accordingly, modems were developed for converting digital information from its original form to a form in which it can be carried on telephone lines. Simply stated, a modem is a telephone made specifically for a computer or an information terminal to communicate with another computer or terminal over an ordinary telephone line. Modems convert output signals from a computer or terminal into electric signals suitable for transmission through a telephone line; and convert the received signal back into an information signal receivable and understood by a computer or terminal. This process of signal conversion is called mod ulation (sending) and dem odulation (receiving) and the word modem is a contraction of mod ulator-dem odulator.

Computers operate on a number system in which all numbers are represented by an array of “l’s” and “0’s”, known as the binary numbering system. In systems for the transmission of data, the speed of transmission is usually defined in “bits” (“1” or “0”) per second or “bps”.

Telephone lines designed for voice communication have a bandwidth of approximately 300 to 3000 Hertz (Hz). Such lines are classified as either “switched or dial up lines” or “leased lines”. Switched or dial up lines utilize multiple pairs of lines and diverse electronic equipment which are switched together in a random, first available basis to form a complete circuit each time a telephone call is placed. Leased lines, on the other hand, are not switched randomly with every call and such lines can therefore be specially treated or conditioned to make them more readily adaptable for data transmission. Leased lines are graded as Types 4, 4-A, 4-B, and 4-C and the cost of such lines increase in that order. Switched or dial up lines are more difficult to utilize for data transmission than leased lines, and the less expensive leased lines, e. g. Types 4 and 4-A are more difficult to utilize than the very expensive, highly conditioned Type 4-C leased lines.

By the early 1960’s high speed computers had surpassed the ability of the available modems to transmit data over ordinary switched telephone lines. Typical available modems used a two or four level modulation technique to represent data on the carrier. Proponents of the two level modulation technique felt it was preferable over the four level because the error rate was believed to be directly related to the number of levels. It was also believed that if the bandwidth of the signal was narrowed, the data rate had to be reduced accordingly. The four level modulation technique, on the other hand, required a wide energy spectrum, from 600 to 3000 Hz, which was considered “necessary to permit the recovery of a clock signal and provide a high signal to noise ratio”. As such, the four level modulation technique incorporating a wide energy spectrum required the utilization of expensive, highly conditioned leased lines.

In the late 1950’s and early 1960’s, after its own research and development group could not produce an adequate modem for the new computers, Western Union began looking for a modem which would allow its customers to connect their high speed computers to its newly constructed broadband exchange (BEX) which operated much like its switched telephone network.

Western Union specifically sought a modem which would operate satisfactorily at 2400 bps using less than a 1000 Hz bandwidth, since it had concluded that such a modem would work within its BEX network. Western Union’s own personnel, however, were skeptical that such a modem could be developed, inasmuch as it was generally believed that the utilization of a narrow band, such as 1000 Hz, would decrease the signal to noise ratio and that the error rate would be substantially increased.

In early 1965 Sang Whang, and several other Milgo employees, took part of Milgo’s missile tracking system that handled data as a stand-alone modem and met with Western Union’s personnel. Western Union, however, believed Milgo’s modem was entirely inadequate, and it reiterated what it considered to be a workable modem for its BEX network.

Upon his return to Milgo, Whang proceeded to develop a modem capable of functioning within the prescribed limitation of Western Union’s BEX network. In so doing, Whang developed a modem which, for 2400 bps operation, utilized eight level modulation within a narrow bandwidth centered at 1700 Hz. Whang’s prototype modem created considerable interest at Western Union:

Q. What was the substance of that phone call? A. Well, the phone call was to Mr. Boughtwood and he came out of his office laughing, as I recall. He had gotten a phone call from Sang Whang, I believe, of Milgo, and Sang had informed him that unfortunately they could not build a modem that used a thousand cycles of bandwidth and he was very sorry about that, Mr. Whang was, but however would we be amenable to coming and looking at one that used eight hundred cycles of bandwidth, and it tickled us considerably but that was the first contact through any of this. I think it took us about twenty minutes to get our airline tickets.
Q. I take it you were interested in seeing an eight hundred cycle bandwidth modem?
A. We were not believers at that moment.
Q. You didn’t believe they had done that?
A. No.
Q. Did Sang Whang do it?
A. He sure did.
* * * * * *
Q. Would you set forth those key features that it highlighted? A. Okay. By far the most unique feature to us at that point in time was the narrow bandwidth that it required to operate. The second one was the compression technique used to get that narrow band. It was essentially the eight-phase modulation, because this was the first time that we had ever seen or heard of anybody making a practical version of an eight-phase modem. Four phases was considered the state of the art at that point in time.
Q. What do you mean by state of the art? A. The state of the art is pushing the art. It’s the latest version, it’s the latest technology, the latest technique, and we had gone through a development phase spearheaded by the Bell System to get to the four-phase modem and they had developed that and refined it and that was considered the state of the art in 1965 and this was a breakthrough, both in the narrow band and in the fact that they were using eight phases.
Q. And you figured the Milgo modem was a breakthrough at that point? A. To us it certainly represented a breakthrough at that point in time, yes. It satisfied a real need that we had, satisfied all our requirements.

[R. Appdx., Vol. I at pp. 282-284].

Whang subsequently was issued a patent for his modem, U.S. Patent No. 3,524,023 (Whang ’023). The Whang ’023 patent disclosed and claimed a high speed data modem system intended to operate over ordinary unconditioned switched telephone lines which would function in ordinary lines without a variable equalizer. The patent asserted that the elimination of the equalizer was achieved by limiting the bandwidth of the data transmission channel to substantially less than the 300-3000 Hz bandwidth available in the line; that a composite band limiting filter restricted the band in the modem to a width of less than 1000 Hz for a 2400 bps data rate, and that the band is centered on a frequency of around 1700 Hz with a low side of 1200 Hz and a high side of 2200 Hz. The patent asserts that the band binding of the signal to the narrow band of less than 1000 Hz resulted from Whang’s discovery that within this bandwidth, the transmission characteristics of all ordinary telephone lines in a switched network will “look” substantially alike and behave the same.

Whang’s ’023 patent, which was assigned to Milgo, was expanded upon and improved by U.S. Patent No. 3,590,381 (Ragsdale ’381) and U.S. Patent No. 3,643,023 (Payne ’023) which improved the detection techniques by relating data representing phase angles in a squared intermediate frequency at center sampling times to digital counts in high speed binary counter. These patents are follow-on patents to the Whang ’023 resulting from work done by other Milgo employees. With these patents, the analog detection circuits of the first Milgo Modem 4400/24 were replaced by digital detectors, thereby overcoming the repeatability problems associated with analog detectors.

Milgo’s patented modems were successfully marketed from the outset. Western Union successfully utilized the Milgo 2400 bps on its BEX, and the Milgo 4800 modem Model 4400/48, derived by applying the principles of a 2400 bps modem to a 4800 bps modem, was considered an “immediate commercial success”, when introduced in early 1968.

During mid 1968 Rixon, a modem manufacturer, marketing the PM24 modem which required conditioned lines and the Sebit 24 modem which was a two level amplitude modulated vestigial sideband device, arranged to test one of Milgo’s Model 4400/48 modems at one of Milgo’s customer’s locations. This test was made on a weekend without Milgo’s consent. After determining that the Milgo modem functioned efficiently, Rixon obtained a Milgo modem and embarked on a copying process, which extended over a two year period. Howard R. Andrews, a Rixon employee, deposed:

Q. Did you receive instructions from Gatfield to copy point to point the various circuit cards in the Milgo modem? A. Not precisely. At the time I was assigned to the program, the modem had been in the plant for approximately a week at least, I say at least, because it could have been sitting there for a month I suppose. But people had actively been working on it for a week according to what they told me. They had a team of technicians, not engineer actually doing the point by point analysis.
They would take the printed circuit cards, a very large piece of paper, put it up on the wall of this room, drawing the connections, label the I.C. packs with certain numbers and trace out the tracks on the board. So the actual point to point wiring was traced out by technicians. The task I was assigned to after I had been reassigned by Mr. Hollis to Mr. Gat-field was the job of interpreting these schematics and putting them into a form that is really understandable.
In other words, a schematic like this. If it were jumbled around in the fashion that it would be taken off a P.C. board, it would be incomprehensible. It requires a certain regularity of layout of the components and the connections for you to understand what it means.
That was the task I and a couple of other engineers were given. One engineer who worked for me, Mr. Ditman, came over with me from the engineering group as part of this task force.
The two of us together did I would say 95 percent of the interpretation and the redrawing of the schematics made by the technicians.
* * * % * *
Q. You mentioned that you wrote a report along with the schematics. A. It was not formal. It was handwritten. It was not typed because this whole program was handled with great secrecy. Only certain people were allowed to know what went on. You had to carefully identify yourself to people in the locked room before you would be admitted. We were all sworn never to tell anybody where this model, what it was, where it came from and how Rixon acquired it, although I did find that out and things of this nature.
So because of this veil of secrecy, secretaries were not certainly supposed to be typing up reports. Everything was handwritten. The schematics I mentioned were drawn by the engineers, not by the draftsmen who normally do that job. [R. Addendum to Appdx., Vol. IV at pp. 6a and 10a].

After successfully copying Milgo’s modem, Rixon began marketing commercially acceptable 2400 bps and 4800 bps modems during the latter part of 1970. Prior thereto, Milgo was the only source of commercially acceptable 4800 bps modems and it was considered the sole source of 2400 bps modems capable of operating on unconditioned switched telephone lines; furthermore, prior thereto Milgo had also built strong business relationships with large accounts, including Burroughs Corporation and Honeywell Information Systems, which it lost to Rixon. This resulted after Rixon was able to force prices down and underbid Milgo.

Milgo filed the instant suit on July 19, 1971, alleging infringement of its Whang ’023 patent. Thereafter, on September 25, 1972, Milgo amended its complaint to allege the infringement of its Ragsdale ’381 and Payne ’023 patents. United Telecommunications, Inc. (United) and UBC, its wholly-owned subsidiary, were named as defendants. In their answers, United and UBC denied the validity of each patent and both denied infringement.

In upholding the Milgo patents the District Court found, inter alia: The Milgo patents were, in all respects, valid and subsisting in law as to the claims in question; the inventions defined in the claims in question would not have been obvious to one of ordinary skill in the art at the time the invention thereof was made; each of the inventions, as to the claims in question are novel and useful and meet the requirements of 35 U.S.C.A. §§ 101 and 102; evidence of copying is properly admissible on the issues of obviousness and infringement; the unob-vious requirement of 35 U.S.C.A. § 103 is fulfilled by an inventor who makes a new and useful improvement where those skilled in the art have failed after repeated efforts to do so; the Milgo patents as to the claims in question have been infringed by Rixon II by its manufacture and sale of the accused data sets, and by UBC by the sale of the accused data sets infringing the Whang ’023 patent until January 1, 1972; and after January 1, 1972, UBC actively induced the infringement of the Milgo patents by and through Rixon II. The court also determined that United was not liable for the infringement of any of the three patents.

On appeal UBC contends: (1) the Whang ’023 patent is invalid; (2) copying is a non-issue; (3) UBC did not infringe any of Milgo’s patents; and (4) the Payne ’023 and Ragsdale ’381 patents are invalid.

l.(a)

UBC contends the Whang ’023 patent is invalid as obvious under 35 U.S.C.A. § 103 and invalid as “described in a printed publication * * * or in public use or on sale * * * more than one year prior to the date of the application for patent” under 35 U.S.C.A. § 102(b) and Muncie Gear Works, Inc. v. Outboard Marine & Mfg. Co., 315 U.S. 759, 62 S.Ct. 865, 86 L.Ed. 1171 (1942).

35 U.S.C.A. § 103 provides in part:

A patent may not be obtained though the invention is not identically disclosed or described * * * if the differences between the subject matter sought to be patented and the prior art are such that the subject matter as a whole would have been obvious at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains. * * *

UBC contends, citing to Graham v. John Deere Co., 383 U.S. 1, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966) that obviousness is to be considered in light of the prior art, the differences between the prior art and subject matter claims, the level of ordinary skill in the pertinent art, along with “[secondary considerations such as commercial success, long felt but unresolved needs and the prior failure of others may be utilized as indicia of obviousness.” UBC contends that the “alleged invention of the Whang ’023 patent is nothing more than an aggregation of ideas which were known to the art, and the result of which was completely predictable.”

The ultimate determination of patent validity is, of course, one of law. Moore v. Shultz, 491 F.2d 294 (10th Cir. 1974); Hinde v. Hot Sulphur Springs, Colorado, 482 F.2d 829 (10th Cir. 1973). Patentability depends on numerous factors we identified in A. E. Staley Manufacturing Company v. Harvest Brand, Inc., 452 F.2d 735 (10th Cir. 1971), cert. denied, 406 U.S. 974, 92 S.Ct. 2415, 32 L.Ed.2d 674 (1972):

The question of invention and thus, patentability, is one of fact involving consideration of novelty, utility, commercial success, satisfaction of long-felt want, unsuccessful efforts of others, public acquiescence in validity, imitation, experiments, and independent production by others. 69 C.J.S. Patents § 70 (1951).

452 F.2d at p. 739.

A regularly issued patent is presumed valid, and when the patent office has considered prior art in accepting or rejecting an allegation of anticipation, the presumption is strengthened. Scaramucci v. Dresser Industries, Inc., 427 F.2d 1309 (10th Cir. 1970). The presumption of validity may be rebutted by the showing of obviousness. Halliburton Company v. Dow Chemical Company, 514 F.2d 377 (10th Cir. 1975). When the teachings in the prior art must be ignored to reach a desired result, they become less pertinent to the determination of obviousness. CMI Corporation v. Metropolitan Enterprises, Inc., 534 F.2d 874 (10th Cir. 1976).

An invention that is obvious is an unpatentable invention. Plastic Container Corporation v. Continental Plastics of Oklahoma, Inc., 607 F.2d 885 (10th Cir. 1979). Obviousness turns not on whether a device has, essentially, been produced, but on whether, though not yet produced, it would have nevertheless been conceivable to a worker of ordinary skill in that field. True Temper Corporation v. CF&I Steel Corporation, 601 F.2d 495 (10th Cir. 1979). In each instance, the prior art must be carefully scrutinized. Deere & Company v. Hesston Corporation, 593 F.2d 956 (10th Cir. 1979). In order for a prior art to anticipate a process, it must disclose identical or equivalent steps to accomplish the same result. CMI Corporation v. Metropolitan Enterprises, Inc., supra.

Obviousness must be determined by considering the scope and content of the prior art, the differences between the prior art and claims at issue, and the level of ordinary skill in the pertinent art. Tanks, Inc. v. Reiter Industries, Inc., 545 F.2d 1276 (10th Cir. 1976) citing to Graham v. John Deere Co., supra. Obviousness requires factual determinations which are entitled to the usual respect accorded determinations of fact, and, as such, an appellate court is bound by the trial court’s findings on obviousness unless they are determined to be clearly erroneous. Rutter v. Williams, 541 F.2d 878 (10th Cir. 1976); CMI Corporation v. Metropolitan Enterprises, Inc., supra. We are not a trial court and a case such as the one at bar cannot be tried de novo on appeal. Halliburton Company v. Dow Chemical Company, supra; Hinde v. Hot Sulphur Springs, Colorado, supra. These principles were succinctly stated in True Temper Corporation v. CF&I Steel Corporation, supra :

Obviousness, of course, is to be assessed as of the time the invention in question was made and from the viewpoint of “a person having ordinary skill in the art to which said [invention] pertains.” 35 U.S.C. § 103. The issue necessarily involves several basic factual inquiries, outlined in Graham v. John Deere Co., 383 U.S. 1, 17, 86 S.Ct. 684, 15 L.Ed.2d 545, involving the scope and content of the prior art, the differences between the pri- or art and the patent claims in issue, and the level of ordinary skill in the pertinent field. There is also to be considered, however, the general statutory presumption of validity which attaches to a patent once issued by the Patent Office. 35 U.S.C. § 282. See generally Sidewinder Marine, Inc. v. Starbuck Kustom Boats and Products, Inc., 597 F.2d 201 (10th Cir., 1979). We must, therefore, in reviewing the findings of the trial court, consider whether they are supported by the record or are clearly erroneous under the standard of Rule 52, F.R.Civ.P., taking into account the presumption of validity of the patent. See CMI Corp. v. Metropolitan Enterprises, Inc., 534 F.2d 874, 880 (10th Cir.).
601 F.2d at p. 505.

Applying these standards, we hold that the Court did not err in finding that the Whang ’023 was not obvious. The Court found, and we agree, that the Whang ’023’s utilization of differential eight phase modulation of a single carrier and narrow bandwidth filtering was contrary to the prior art; that Whang was the first to employ narrow band limiting in a phase modulated system; that modems incorporating the Whang ’023 were the first commercially acceptable modems capable of transmitting 2400 bps over ordinary switched voice-grade telephone lines; that prior to the Whang ’023 the modem industry felt the best results could be achieved by modems incorporating “wide band energy spectrum and two or four level modulation”; that Whang approached the problem with a completely opposite philosophy and was the first to combine eight level modulation and extreme band limiting into one modem.

The validity of the Whang ’023 is also reinforced when we consider the “secondary considerations, such as commercial success” mandated by Graham v. John Deere, supra. See also: Deere & Company v. Hesston Corporation, supra. It is uncontested that Western Union looked upon the Whang ’023 as a tremendous breakthrough which satisfied a long felt need. It is also uncontested that the modems were instantly successful and that they were the primary source of commercially acceptable high speed modems until the infringing modems were marketed. We hold that the trial court properly found that Whang ’023 was unobvious, and therefore valid. Query: If the Whang ’023 was as obvious as UBC now contends, why did it require two years for the Rixon employees to analyze and copy it?

l.(b)

UBC contends that the Whang ’023 is invalid under 35 U.S.C.A. § 102(b) and Muncie Gear Works, Inc. v. Outboard Marine & Mfg. Co., supra, since it was described in a printed publication, the original patent application, more than one year pri- or to the date the amended application was submitted. We hold that the Court properly applied Price v. Lakes Sales Supply R. M., Inc., 510 F.2d 388 (10th Cir. 1974) in determining that the amendment was simply clarifying in form and only made express that which was always present in the original disclosure.

2.

UBC contends that “copying is a non-issue” and that the District Court gave too much consideration to actions and events which occurred prior to the issuance dates of the patents herein. UBC argues that since Milgo did not claim damages for violation of trade secrets nor for “appropriation of trade dress or misrepresentation or misappropriation of non patented material or contract protected subject matter”, the District Court improperly gave undue attention to matters which occurred prior to the issuance of the patents herein. This Court has consistently held that the exercise of fraud, inequitable conduct, or bad faith in the prosecution of a patent application may result in the unenforceability of a patent ultimately issued. True Temper Corp. v. CF&I Steel Corporation, supra, and cases cited therein. In an analogous vein, we believe that trial courts are empowered, and in fact obligated, to determine the presence of “fraud, inequitable conduct, or-’bad faith” in patent infringement litigation, once a patent is issued. We do not accept UBC’s assertion that the District Court improperly made copying an issue; the Court correctly considered evidence of Rixon’s copying. However we are disinclined to hold that this evidence was considered out of order in derogation of the Court’s determination upholding the patent’s validity. The Court did not, in any event, overextend or enlarge upon the issue of copying in derogation of UBC’s trial rights and privileges, since, as the Court properly noted, evidence of copying is admissible on the issue of obviousness, citing to Mott Corporation v. Sunflower Industries, Inc., 314 F.2d 872 (10th Cir. 1963), and further admissible on the issue of infringement, citing to Lever Brothers Co. v. Procter & Gamble Mfg. Co., 139 F.2d 633 (4th Cir. 1943). In Mott, supra, we stated:

Appellees insist, however, that the Mott blades are improvements which would be obvious to the ordinary skilled workman. The trouble with this argument is that the record clearly shows there had long been a demand for a mowing machine which would successfully cut all types of grass under all conditions. The fact that appellees were unsuccessful in their efforts to develop such a machine and made a virtual “Chinese copy” of the Mott mower is persuasive on the issue of obviousness. The patent in suit may be simple when viewed in retrospect. But simplicity is no bar to invention where, as here, the steps taken were not obvious to the ordinary mechanic skilled in the art. Admiral Corporation v. Zenith Radio Corporation, supra [10 Cir., 296 F.2d 708]; Blish, Mize and Silliman Hdwe. Co. v. Time Saver Tools, supra, [10 Cir., 236 F.2d 913]; Neff Instrument Corporation v. Cohu Electronics, Inc., 9 Cir., 298 F.2d 82; Amp. Incorporated v. Vaco Products Co., 7 Cir., 280 F.2d 518, cert. denied, 364 U.S. 921, 81 S.Ct. 286, 5 L.Ed.2d 260. 314 F.2d at p. 880. [Emphasis supplied].

3.

UBC contends it did not infringe on any of the Milgo patents. UBC argues that the Court improperly determined that its DS-4800 modem infringed upon the Whang ’023, the Payne ’023, and the Rags-dale ’381 patents. The question of infringement is one of fact, Burger Train Systems, Inc. v. Ballard, 552 F.2d 1377 (10th Cir. 1977), cert. denied 434 U.S. 860, 98 S.Ct. 185, 54 L.Ed.2d 132 (1977), and, on review, a trial court’s finding thereon will not be set aside unless it is clearly erroneous. Black, Sivalls & Bryson, Inc. v. Keystone Steel Fabrication, 584 F.2d 946 (10th Cir. 1978). We do not try factual matters, such as infringement, de novo. Halliburton Company v. Dow Chemical Company, supra.

In determining that the Payne ’023 and Ragsdale ’381 had been infringed, the Court found:

82. The accused DS-4800 data set includes each and every element recited in claims 1-19 and 21 of the Ragsdale ’381 patent in suit or an equivalent thereof. Each of the elements of the DS-4800 data set perform substantially the same function in substantially the same manner to obtain the same end results as do the corresponding elements of both the claims in suit of the Payne ’023 and Rags-dale ’381 patents (PX 20 and PX 19 respectively) as well as the corresponding elements of the patented Milgo 4400/48 modem which is covered by the Payne ’023 and Ragsdale ’381 patents.
83. Plaintiff’s Exhibit 19 includes the claims at issue in the Ragsdale ’381 patent colored with colors which are matched to corresponding elements of the DS-4800 as depicted in drawings from the DS-4800 manual, which drawings accurately depict and correctly represent the operation of the DS-4800. The claims of Ragsdale ’381, element-by-element and function by function, were applied by Ragsdale and disclosed that each and every claimed element and function is present in the DS-4800 (R. 1167-1222).
84. Plaintiff’s Exhibit 20 includes the claims at issue in the Payne ’023 patent colored with colors which are matched to corresponding elements of the DS-4800 as depicted in drawings from the DS-4800 manual, which drawings accurately depict and correctly represent the operation of the DS^L800. The claims of the Payne ’023 patent, element-by-element and function-by-function, were applied by Ragsdale and proved that each and every claimed element and function is present in the DS-4800 (R. 1134-1165).
[R. Appdx., Vol. I at p. 74-75],

We hold that the Court properly found that the Milgo patents in question were infringed.

4.

UBC contends the Payne ’023 and Rags-dale ’381 patents are invalid as “covering nothing more than obvious combinations of digital principles and logic hardware which were well known to those skilled in the art”.

In upholding the validity of the Payne ’023 and the Ragsdale ’381 the Court found:

63. The Payne ’023 patent led Rags-dale to the development of the Rags-dale ’381 digital coherent detection patent (R. 1109-1117). The digital detector of the Ragsdale ’381 patent accomplished phase locking of two signals of different frequencies in a restricted bandwith modem in spite of the presence of repeated phase shifts in the same direction as acknowledged by defendants’ expert Dr. Beam (R. 2086). Originally, Dr. Beam asserted that the Kawai patent (DX Z) and Lender patent (DX A-l) showed the method of deriving a reference carrier for coherent detection. However, Dr. Beam finally admitted that phase locking two such sinusoidal signals of different frequencies was a difficult task (R. 2066), and further admitted that he knew of no prior art that did what Ragsdale did in the ’381 patent and that included all the technical things that Dr. Beam could think of (R. 2087). Defendants’ own technical expert admitted that the Rags-dale ’381 patent distinguishes over the prior art he was aware of, and the claimed features of the Ragsdale ’381 patent represents significant and non-obvious improvements over all prior art known by defendants’ technical expert.
64. The Bennett & Davey textbook (DX J-l) represents the state of the art that existed prior to the invention date of the Ragsdale ’381 patent. That textbook at page 258 taught that it was “impossible” to do what Ragsdale did in his ’381 patent.
if: % * * * *
65. The defendants attempted to reconstruct the principles of the Payne ’023 and Ragsdale ’381 patents from a paper by Wilson (DX 1-2). The Wilson paper includes a box labeled “computer” where there could be almost anything, including a general purpose computer (R. 2041, 2042, 2046, 2047). Dr. Beam admitted that even a general purpose computer in Wilson would have to be modified to accomplish the principles of the Payne ’023 and Ragsdale ’381 patents (R. 2046-2048). The circuits of the Payne ’023 and Rags-dale ’381 patents were admitted by Dr. Beam as being novel over the functions of the general purpose computer of Wilson (R. 2048-2054). The Payne ’028 and Ragsdale ’381 patents define features which represent significant and non-obvious improvements over DX 1-2. ******
68. Analog detectors such as those disclosed by DX G-l, DX Z and DX A-l, suffer from many problems associated with analog detectors, which problems as testified to by Ragsdale, were overcome by the digital detectors of the Payne ’023 and Ragsdale ’381 patents (R. 1035-1039, 1112; R. 2438, 2439). The digital detectors of the Payne ’023 and Ragsdale ’381 patents represent significant and non-obvious improvements over the analog detector of the HC-270 described in DX G-l, and over the analog detectors of DX Z and DX A-l.
69. Ragsdale testified that none of the defendants’ exhibits that Dr. Beam referenced taught or suggested the claimed features of the Payne '023 or the Rags-dale ’381 patents (R. 2442). None of the references introduced by the defendants teach or suggest the significant improvements over the prior art that are provided by the claimed features of the Payne ’023 and Ragsdale ’381 patents (R. 2442). The defendants have not cited any prior art that is any more pertinent to the Payne ’023 or Ragsdale ’381 patents than that cited by the Patent Office in the prosecution and issuance of the Payne ’023 and Ragsdale ’381 patents (DX B and DX C).
70. All of the patents testified to by Dr. Beam with reference to the three patents in suit were present either in the file histories of the three patents in suit or were present in the classes and subclasses (PX 168,169) which were searched by the Patent Office Examiners in conjunction with the prosecution and issuance of the three patents in suit. The defendants did not introduce any prior art having teachings that rebut the presumption of validity which is awarded in patents in suit upon their issuance by the U.S. Patent Office (PX 168 and 169, R. 1690-1692).
[R. Appdx., Vol. I at pp. 63, 64, 67 and 68],

Without repeating our prior discussions relative to the presumed validity of a patent once issued, the issue of obviousness and the weight to be afforded to findings of a trial court within the context of the clearly erroneous rule, we hold that the Court properly found the Payne ’023 and Rags-dale ’381 patents to be valid.

II.

Agency Relationship

UBC contends there are no factual findings and no evidence supporting the trial court’s conclusion that Rixon II was the mere instrumentality, alter ego, or agency of UBC. A discussion of the corporate history of United, UBC and Rixon II, will facilitate our review.

United is a corporation organized and existing under the laws of Kansas, which is, and has at all times since November 15, 1938, existed as a holding company. As such it is without operating divisions. United, as a holding company, owns the stock of a number of companies called the United Telephone System.

During 1968, Rixon Electronics Corporation (Rixon I) procured a Milgo modem and began copying it. Thereafter, on or about October 24,1968, an agreement was reached between Rixon I and United under which a subsidiary would be formed by United for acquiring the business and assets of Rixon I in exchange for United stock. This agreement was followed by an Agreement and Plan of Reorganization dated December 12, 1968.

On May 23, 1969, United caused to be organized a Maryland corporation named New Rixelco, Inc. (Rixon II) as a wholly owned subsidiary. Thereafter, on July 3, 1969, United issued 597,105 shares of its common stock to Rixon I, and Rixon I transferred and conveyed its business and assets to Rixon II. In effectuating the transfer Rixon I withheld certain monies and securities to satisfy the anticipated expenses of the transaction, and Rixon II assumed all of the liabilities and obligations of Rixon I existing at the date of the transaction, with the exception of the expenses of the transaction to be satisfied by Rixon I and certain outstanding stock options for Rixon I’s employee stock option plan which were assumed by United. (On July 11,1969 Rixon changed its name to Rixon Electronics, Inc.; however, this name change is of no moment on appeal).

UBC was organized as a Kansas corporation, and a wholly owned subsidiary of United on January 5, 1970. UBC was organized to engage in the business of selling, engineering, installing, and servicing private voice and data communications equipment. Thereafter on June 24, 1970, United transferred all of the Rixon II stock to UBC, making Rixon II a wholly owned subsidiary of UBC. Commencing in July, 1970, UBC began marketing certain products of Rixon II, including the infringing modems in controversy herein.

On January 1,1972, by mutual agreement of their respective officers, UBC discontinued marketing data modems and Rixon II began its own marketing. UBC’s inventory of data modems was thereafter held for Rixon II; payment therefor from Rixon II to UBC was made as Rixon II sold the modems. Since January 1, 1972, UBC has not sold any of the infringing modems.

On or about October 1, 1972, pursuant to an agreement between United, UBC, Rixon II and Sangamo Electronic Company, Rixon II conveyed all of its business and assets to a newly formed corporation, Rixon, Inc. (Rixon III), a Delaware corporation. Rixon III was formed and has operated as a subsidiary of Sangamo Electric, which owns 60% of Rixon Ill’s equity and has an option to purchase the remaining 40% from United. Since October 1, 1972, Rixon III has not been involved in the manufacture or sale of the infringing devices.

In ruling that Rixon II was a mere instrumentality, alter ego, or agency of UBC, the trial court cited with approval Quarles v. Fuqua Industries, Inc., 504 F.2d 1358 (10th Cir. 1974), wherein we stated:

Thus a holding or parent company has a separate corporate existence and is treated separately from the subsidiary in the absence of circumstances justifying disregard of the corporate entity. 18 Am. Jur.2d Corporations § 17 (1965). See Continental & Commercial Trust & Sav. Bank v. Garden City Co., 123 Kan. 659, 256 P. 983 (1927). Circumstances justify disregard of the corporate entity if separation of the two entities has not been maintained and injustice would occur to third parties if the separate entity were recognized. Garden City Co. v. Burden, 186 F.2d 651 (10th Cir. 1951).
In Flank Oil Co. v. Continental Oil Co., 277 F.Supp. 357, 363 (D.Colo.l967), Judge Doyle said:
Cases such as Steinway [Steinway v. Majestic Amusement Co., 10 Cir., 179 F.2d 681] properly discount formal separations of function and subtle efforts to maintain distinct corporate entities. The effort is to ascertain from the total facts the extent of actual control exercised by the parent over the internal affairs of its subsidiary .
$$$$$$
The trial court specifically held Career was not the agent of Fuqua. This conclusion can only be reversed if it is clearly erroneous. Manufacturer’s Nat’l Bank v. Hartmeister, 411 F.2d 173 (10th Cir. 1969).
504 F.2d at pp. 1362 and 1364.

Quarles, supra, was cited with approval by this Court in G. M. Leasing Corp. v. United States, 514 F.2d 935 (10th Cir. 1975), reversed on other grounds, 429 U.S. 338, 97 S.Ct. 619, 50 L.Ed.2d 530 (1977), for the proposition that a trial court’s finding that an entity is not an alter ego is presumptively correct and cannot be disturbed absent clear error:

Appellants first challenge the trial court’s finding that appellee was not taxpayer’s alter ego. This finding is presumptively correct and must be left undisturbed on appeal unless it is clearly erroneous. Quarles v. Fuqua Industries, Inc., 504 F.2d 1358 (10th Cir. 1974). A finding is clearly erroneous when, although there is evidence to support it, the reviewing court is left with the definite and firm conviction that a mistake has been committed. See, e. g., Kelson v. United States, 503 F.2d 1291 (10th Cir. 1974); Clancy v. First Nat’l Bank, 408 F.2d 899 (10th Cir. 1969), cert. den’d, 396 U.S. 958, 90 S.Ct. 430, 24 L.Ed.2d 422. 514 F.2d at p. 939.

In Fish v. East, 114 F.2d 177 (10th Cir. 1940), this Court set out some factors relevant in determining whether the corporate veil, in the parent-subsidiary context, should be pierced:

(1) The parent corporation owns all or majority of the capital stock of the subsidiary. (2) The parent and subsidiary corporations have common directors or officers. (3) The parent corporation finances the subsidiary. (4) The parent corporation subscribes to all the capital stock of the subsidiary or otherwise causes its incorporation. (5) The subsidiary has grossly inadequate capital. (6) The parent corporation pays the salaries or expenses or losses of the subsidiary. (7) The subsidiary has substantially no business except with the parent corporation or no assets except those conveyed to it by the parent corporation. (8) In the papers of the parent corporation, and in the statements of its officers, “the subsidiary” is referred to as such or as a department or division. (9) The directors or executives of the subsidiary do not act independently in the interest of the subsidiary but take direction from the parent corporation. (10) The formal legal requirements of the subsidiary as a separate and independent corporation are not observed.
114 F.2d at p. 191.

In the instant case there is no evidence that formal legal requirements of separateness were ignored, but the record contains evidence at least tending to support the following findings. UBC owned all of the stock of Rixon II; the directors of UBC and Rixon II were “virtually” the same; although UBC did not finance Rixon II, United Utilities, which owned UBC, provided the operating capital for both UBC and Rixon II through loans or by guaranteeing loans; Rixon II and UBC were caused to be organized by United Utilities; capital was grossly inadequate in that it came from loans that Rixon could not have repaid; although Rixon II paid its own officers and employees, it had to borrow from United Utilities to pay its operating expenses; pri- or to the retransfer of the marketing functions, all commercial sales activities for Rix-on products, except government sales, were in the hands of UBC — thus nearly all its products were sold to UBC. After the transfer of the marketing functions back to Rixon II in 1972, the subsidiary was apparently treated as the “Rixon Division” of UBC. [R. Appdx., Vol. VII at pp. 869E, 878E].

With respect to category (9) set out above, the trial court made findings that Rixon II acted independently of United Utilities. It found that transactions between United’s subsidiaries were at arm’s length, and that in various specific respects Rixon II operated as an independent corporation. But other findings and evidence tend to show an overlapping business relationship controlled by UBC, and particularly by Robert Liepold, president and chief executive officer of UBC. Liepold also was chairman of the board of Rixon II, but not its chief executive officer and apparently not on its payroll.

The lack of independence and blurring of separateness is evidenced by the very detailed monthly operating reports Rixon II was required to give Liepold and UBC [R. Appdx., Vol. VIII at pp. 1230E-1338E], and UBC’s detailed review of Rixon II’s decisions, [See id. Vol. IV at pp. 1665-1669], and by evidence that Liepold exercised powerful decision-making authority over Rixon II, including selection of the board of directors, [Id. at p. 1675], initiation of the decision, with the president of Rixon II, to transfer modem marketing activities back to Rixon II, [Id. at pp. 1628,1652], and establishment with Rixon II’s president of the pricing guidelines for Rixon II to follow after the transfer, [Id. Vol. VII at pp. 868E-69E] (UBC set those prices unilaterally while it had the marketing function). [Id. Vol. IV at pp. 1658-59]. In addition, the record contains evidence that in paying Rixon II for the modems UBC marketed, UBC purposefully timed the payments to benefit Rixon II’s financial position, [Id. Vol. IV at pp. 1660-61], or in one case, to achieve “a more efficient use of cash for the consolidated operation,” [Id. Vol. VII at p. 573E] (Rixon II operating report for November 1970), although Rixon II thereby incurred additional interest costs in connection with other indebtedness that could not be reduced. A letter dated January 18, 1971, sent by the treasurer of Rixon II to Liepold concerning a UBC proposal that Rixon II lease certain equipment appears to exemplify the relationship between those entities. In pertinent part, the letter states as follows:

Maury has requested that I respond to UBC’s proposal for Rixon to lease the ARD 561 PBX as presented in Rick Johnson’s letter of January 12, 1971.
As a matter of form we would like to advise you that normally Rixon, dealing at arms [sic] length in this kind of transaction, would not sign a purchase order authorizing a lessor to purchase on our behalf a complex system for which the lessor would be relieved of all responsibility for operating performance.
* * * * * *
After consideration of the above, if UBC believes that it is in the best interests of the consolidated UBC-Rixon operation for Rixon to enter into the lease agreement, as Rick has requested, it will be appreciated if you would have UBC’s authorized representative write us a letter advising Rixon of this decision.
[R. Appdx., Vol. VIII at pp. 1455E-56E].

Most of the evidence discussed above is from the time period preceding the retrans-fer of the marketing functions, but it also tends to support the conclusion that UBC control over Rixon II continued from the date of the retransfer until the formation of Rixon III. In addition, the record shows that Rixon II continued to supply Liepold with detailed operating reports. See, e. g., Id. Vol. VIII at 1230E-1311E. The inventory retransferred to Rixon II was retained physically by UBC in its warehouse for Rixon II; Rixon II did not pay for the inventory until it sold the products to its customers. The transfer price was UBC’s original acquisition cost plus interest from January 1, 1972. UBC’s warehouse was contiguous to Rixon II’s building and manned by Rixon II employees, for which UBC recompensed Rixon II on a monthly basis. [Id. Vol. Ill at 1063-64]. As noted above, Liepold continued to play a significant role in Rixon IPs pricing decisions. These arrangements inferentially support a continuing sharing of functions that belies separateness of the concerns. In addition, a letter dated July 26, 1972, sent from Rixon IPs treasurer to his counterpart at UBC seems to evidence the continuing control of UBC. The letter states in pertinent part as follows:

Terry and I have been discussing several kinds of billings UBC has been making to Rixon and question whether (1) we either have the authority to accept such items on behalf of Rixon, or (2) the items really should not remain with UBC and be disposed of as a UBC cost factor. We understand that under a product line profit and loss concept, these billings would be charged to Rixon.
However, in view of the corporate division of responsibility, we ask that you reconsider the following items for the reasons stated and accept debit memo as a charge back to UBC.
$ * * $ * *
If you people feel you can accept this, please advise. We will prepare our debit as a July item. If you have a problem with this, please refer the matter to Bob Liepold, who probably should arrange for formal instructions to be delivered to Rixon.
[R. Appdx., Vol. VIII at pp. 1218E-20E].
[Emphasis supplied].

We do not say the inference of alter ego or agency is compelled by the evidence. Mere ownership of stock is not enough to pierce the corporate veil; there must be enough commingling of business and assets that honoring the legal fiction of separateness results in injustice. See: International Union, UAW v. Cardwell Mfg. Co., 416 F.Supp. 1267, 1286 (D.Kan.1976). Most of the cases have involved fraud or a more blatant commingling than the instant case; but proof of fraud is not a necessary element in finding alter ego. E. g., DeWitt Truck Brokers, Inc. v. W. Ray Flemming Fruit Co., 540 F.2d 681, 684 (4th Cir. 1976).

In our review of the trial court’s findings we must apply a “clearly erroneous” test. Fed.R.Civ.P. 52(a). We do not reverse unless upon review of the evidence we are “left with the definite and firm conviction that a mistake has been committed.” United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746 (1948). We have reviewed the record carefully and, applying that standard, must affirm the alter ego finding.

III.

Damages

UBC contends that the damages awarded were not supported by evidence and were clearly erroneous; that the trial court’s computations of Milgo’s lost sales and leases are unsupported and clearly erroneous; and that the Court abused its discretion by awarding attorney fees and prejudgment interest.

In awarding damages to Milgo the Court entered eleven conclusions of law, including, inter alia:

4. Defendant is liable for damages caused by actual deliveries of the DS-2400 data sets from July 28,1972 through September 30, 1972 (the date of transfer of Rixon II to Rixon III), by Rixon II or UBC.
5. Milgo is entitled to recover damages as to the sales which it would have made but for the infringement, based on the entire profit which Milgo would have received from such sales. Under the circumstances, Milgo is awarded its lost profits on all deliveries (sales or leases) by defendant. Ingersoll-Rand v. Brunner & Lay, 182 U.S.P.Q. 257; National Rejec-tors v. A. B. T. Mfg. Corp., 188 F.2d 706 (7th Cir. 1951); Livesay Window Co. v. Livesay Industries, 251 F.2d 469 (5th Cir. 1958).
6. Where the wrong done Milgo in this case is so absolute, the consequences of any inability to demonstrate Milgo’s loss with scientific accuracy is a burden that must be met by the infringer. Live-say, supra; H. K. Porter Co., Inc. v. Goodyear Tire & Rubber Co., 536 F.2d 1115 (6th Cir. 1976). All doubts occasioned by Rixon/UBC’s failure to keep proper records are to be resolved in favor of Milgo. Georgia Pacific Corp. v. United States Plywood Corp., 243 F.Supp. 500, 509 (S.D.N.Y.1965); American Sterilizer v. Sybron Corp., 526 F.2d 542, 548-549 (3d Cir. 1975).
7. The award of damages for loss by Milgo of sales and leases of the patented modems copied by the defendant is proper, even though the defendant may not have made any profit of its own on the sale and lease of the infringing modems. Yale Lock Mfg. Co. v. Sargent, 117 U.S. 536 [6 S.Ct. 934, 29 L.Ed. 952] (1885).
8. In view of defendant’s willful and deliberate infringement and the unusual lengths to which defendant went in copying Milgo’s inventions, this is an exceptional case. In such circumstances, Milgo is entitled to treble damages, costs, expenses and attorneys’ fees because defendant has knowingly, deliberately, willfully and wantonly infringed the patents. 35 U.S.C.A. §§ 271 through 287. Maxon Premix Burner Co. v. Mid-Continent Metal Prod. Co., 279 F.Supp. 164 (N.D.Ill. 1967).
[R. Appdx., Vol. I at pp. 131-132].

The trial court thereafter awarded damages to Milgo for its lost profits on sales and leases by UBC and Rixon of the infringing modems in the total amount of $621,968.00. This figure was trebled in accordance with 35 U.S.C. § 284. The court added prejudgment interest from July 19, 1971, the date of the last infringement, to the date of judgment at the rate of 6 percent; attorneys’ fees of $250,000.00, and costs of $14,409.65. The total damage award was $2,340,726.23, plus postjudgment interest at the rate of 8 percent.

UBC challenges the award on several grounds. First, UBC contends that the trial court erred by using lost profits rather than reasonable royalties as the measure of damages. Second, UBC asserts that the judge erred in his calculation of lost profits. Specifically, UBC contests the percentage value assigned as Milgo’s profit margin, the treatment of certain leases as sales, and the inclusion of pre-accounting-period leases in damage computations. Third, UBC attacks the trial court’s finding that the infringement was deliberate and willful, which provided the basis for the court’s award of treble damages, attorneys’ fees and prejudgment interest. With respect to the award of attorneys’ fees, UBC argues that even if the award is proper, there is insufficient evidence that the amount awarded was reasonable.

In reviewing the trial court’s award in this case, it is important to bear in mind the principle that the trial judge has considerable latitude in assessment of damages in patent infringement actions. Maloney Crawford Tank Corp. v. Sauder Tank Co., 511 F.2d 10, 13 (10th Cir. 1975); Allen v. W. H. O. Alfalfa Milling Co., 272 F.2d 98 (10th Cir. 1959). An appellate court must affirm the award if there is substantial record evidence to support it: the trial court’s findings will not be set aside unless it is shown that they are clearly erroneous. H. K. Porter Co. v. Goodyear Tire & Rubber Co., 536 F.2d 1115, 1122 (6th Cir. 1976); Maloney Crawford Tank Corp. v. Sauder Tank Co., supra. UBC’s arguments on this appeal are not altogether without merit. Nevertheless, considering the whole record in this case, it is our view that the trial court’s estimation of Milgo’s damages falls well within a reasonable range, and should not be disturbed.

a. Lost Profits

In order to recover lost profits rather than merely a reasonable royalty in a patent infringement action, the patent-holder must demonstrate that “but for” the infringement, he would have made the sales that the infringer made. Hughes Tool Co. v. G. W. Murphy Industries, Inc., 491 F.2d 923, 929 (5th Cir. 1973); Livesay Window Co. v. Livesay Industries, Inc., 251 F.2d 469, 471-72 (5th Cir. 1958); Power Specialty Co. v. Connecticut Light & Power Co., 80 F.2d 874, 875 (2d Cir. 1936). No presumption operates in the patent-holder’s favor that he would have made the sales in question. Broadview Chemical Corp. v. Loctite Corp., 311 F.Supp. 447, 450 (D.Conn.1970). The patent-holder must advance affirmative proof of the demand for his patented product in the marketplace, the absence of acceptable non-infringing substitutes, and his production and marketing capacity to meet the demand. Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152, 1156 (6th Cir. 1978).

Yet, the “but for” rule necessarily expresses an hypothesis. Neither the trial court nor the appellate court can demand absolute proof that purchasers of the infringing product would have bought the patent-holder’s product instead. It is impossible and therefore unnecessary for the patent-holder to negate every possibility that the purchasers might not have bought another product. W. L. Gore & Assoc., Inc. v. Carlisle Corp., 198 U.S.P.Q. 353, 361 (D.Del.1978); Broadview Chemical Corp. v. Loctite Corp., supra, 311 F.Supp. at 451. The plaintiff’s burden of proof is not absolute, but rather one of reasonable probability:

If in all reasonable probability, the Patent Owner would have made the sales which the Infringer has 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.

Livesay Window Co. v. Livesay Industries, Inc., supra. See also: Hughes Tool Co. v. G. W. Murphy Industries, Inc., supra: W. L. Gore & Assoc., Inc. v. Carlisle Corp., supra; Broadview Chemical Corp. v. Loctite Corp., supra.

The trial court found that Milgo and Rixon/UBC were the only viable competitors in the marketplace, and that “in all reasonable probability” Milgo would have made the sales of the infringing modems if Rixon/UBC had not made them. UBC contends that Milgo did not satisfy its burden of proof, arguing that Milgo was required to show that if bid or solicited bids on all the sales allegedly lost to Rixon/UBC, and that there is no evidence that Milgo did so. UBC’s argument has no merit. Where the plaintiff and the defendant in a patent infringement action are the sole competitors in the marketplace, it is unnecessary for the plaintiff to prove that he bid or at least solicited bids on every infringing sale in order to recover lost profits for these sales. See Electric Pipe Line, Inc. v. Fluid Systems, Inc., 250 F.2d 697, 699 (2d Cir. 1957); W. L. Gore & Assoc., Inc. v. Carlisle Corp., supra, 198 U.S.P.Q. at 362. UBC relies principally on General Electric Co. v. Sciaky Bros., Inc., 415 F.2d 1068 (6th Cir. 1969), but in that case, the fact that the patent owner had not bid on the lost sales became significant only because it was clear on the evidence that the plaintiff had important competitors other than the infringer. See id. at 1076.

In this case, the record fully supports the trial court’s conclusion that Milgo and Rixon/UBC were the only viable competitors in the market. Only the modems manufactured and sold by Milgo and Rixon/UBC had the capacity to operate on unconditioned telephone lines. This represented a savings of from $40 to $80 per month per line for users, and in addition meant that the modem would provide more reliable operation over a longer period of time, notwithstanding changes in the characteristics of the transmission line occurring after installation. Thus Milgo’s failure to offer evidence that it had bid on all of Rixon/UBC’s infringing sales is not fatal to Milgo’s lost profits claim. The trial court’s determination that lost profits were the appropriate measure of damages was correct.

b. Calculation of Lost Profits

The court found that Milgo’s profit margin on lost sales due to infringement would have been 43.4% for the years 1970-1972. The court did not include Milgo’s general and administrative (G&A) or research and development (R&D) expenses in the profit margin figure because it found that the increase in sales would not have required additional G&A or R&D expenses. The profit margin figure was multiplied by the average sales price of comparable Milgo modems during the same years to arrive at a per unit lost profit figure.

The purpose of a damage award for patent infringement is to give the plaintiff reasonable and full compensation for the loss incurred because of the patent infringement. Calculation of lost profits is by its nature imprecise. “Lost profits cannot be computed with certainty; they are hypothetical by definition. The ‘reasonable certainty’ test . . . is no more than a test of probability as it must be in dealing with a hypothetical situation.” H. K. Porter Co., Inc. v. Goodyear Tire & Rubber Co., supra. The authorities are clear that in awarding lost profits, reasonable probability rather than precision is required. Story Parchment Co. v. Paterson Parchment Paper Co., 282 U.S. 555, 562, 51 S.Ct. 248, 250, 75 L.Ed. 544 (1931); Livesay Window Co. v. Livesay Industries, Inc., supra; W. L. Gore & Assoc., Inc. v. Carlisle Corp., supra.

It is also true that doubts concerning the calculations of profits must be resolved against the infringer. The Supreme Court summed up this reasoning in Story Parchment Co. v. Paterson Parchment Paper Co., supra, 282 U.S. at 562, 51 S.Ct. at 250:

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 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 precision that would be possible if the case, which he alone is responsible for making, were otherwise. . . . [T]he risk of uncertainty should be thrown upon the wrongdoer instead of upon the injured party. [Citations and footnotes omitted].

This standard and reasoning has been expressly applied to problems in assessing damages in patent cases. Livesay Window Company v. Livesay Industries, Inc., supra.

The rule against requiring precision in proving the extent of lost profits once infringement is established is further softened when the inability to prove lost profits is due to the infringer’s own failure to keep accurate or complete records. The consequences of such failure must rest on the infringer. American Sterilizer Co. v. Sybron Corp., 526 F.2d 542 (3d Cir. 1975); Georgia Pacific Corp. v. United States Plywood Corp., 243 F.Supp. 500 (S.D.N.Y.1965).

All of these principles were very relevant to the facts in this case and were properly applied by the trial court. Viewing the entire circumstances of the case, the damage assessment appears equitable and conservative. While it is true that some of the calculations used in assessing damages contain a degree of uncertainty, that is a necessary result of the nature of the case and is not a ground for modification or reversal. The trial court considered the evidence, it did not merely adopt the assertions of the plaintiffs.

c. Willfulness

35 U.S.C.A. § 284 provides the trial court in patent cases with discretion to increase the damage award to the plaintiff where the defendant’s conduct is intentional, willful and made with reckless disregard of the plaintiff’s patent rights:

* * * * * *
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.
$ * * * * *

An award of increased or trebled damages is a matter committed to the discretion of the trial court under this statute. Hence, an appellate court can distribute such an award only on a showing of abuse of the trial court’s discretion. Blake v. Bassick Co., 392 F.2d 879, 883 (7th Cir.), cert. denied, 393 U.S. 828, 89 S.Ct. 94, 21 L.Ed.2d 100 (1968); Marvel Specialty Co. v. Bell Hosiery Mills, Inc., 386 F.2d 287, 292 (4th Cir. 1967), cert. denied, 390 U.S. 1030, 88 S.Ct. 1409, 20 L.Ed.2d 286 (1968).

UBC contends that there was insufficient evidence to support the court’s findings that Rixon copied the Milgo modem and that Rixon/UBC had actual notice of infringement on the date that the Whang ’023 patent issued. In view of the record, this argument is wholly without merit. Indeed, UBC appears to realize the weakness of this argument, since insufficiency of the evidence is not the principal ground upon which UBC argues for reversal of the willfulness finding.

UBC contends that any copying endeavors that occurred prior to the date of issuance of the patents cannot support a finding of willful infringement. A patent application for the Whang ’023 was filed on July 14, 1966, but the Milgo Model 4400/48 modem which was covered by this patent and which was copied by UBC was not marked “patent pending”. The Whang ’023 patent issued on August 11, 1970, and this was the earliest date on which the trial court found that UBC had actual knowledge of Milgo’s patent rights. The copying activities took place before this, over a two-year time span beginning in the spring of 1968. UBC correctly notes that Milgo has not advanced any claim for common law misappropriation of trade secrets and that, under the patent laws, UBC’s liability is limited to the period following the date of issuance of the patent. UBC’s position is that at the time of the alleged copying activities, Milgo’s Model 4400/48 modem was in the public domain, and that UBC had the legal right to acquire and study it.

It is true that copying a competitor’s product which is not protected by the patent laws is not illegal. Duplex Straw Dispenser Co. v. Harold Leonard & Co., 229 F.Supp. 401, 404 (S.D.Cal.1964). See also: Sears, Roebuck & Co. v. Stiffel Co., 376 U.S. 225, 84 S.Ct. 784, 11 L.Ed.2d 661 (1964); Smith v. Dravo Corp., 203 F.2d 369 (7th Cir. 1953). And it is plain that there can be no liability for infringement before a patent issues. Inject-O-Meter Mfg. Co. v. North Plains Fertilizer & Chemical, Inc., 308 F.Supp. 538, 541 (N.D.Tex.1970), aff’d 439 F.2d 1138 (5th Cir. 1971), cert. denied, 404 U.S. 824, 92 S.Ct. 51, 30 L.Ed.2d 52 (1971) (prepatent copying does not constitute infringement); Thomson Machinery Co. v. LaRose, 306 F.Supp. 681, 693 (E.D.La.1969). But unlike the cases cited by UBC to support its contention, the issue here is not infringement, but rather willfulness, that is UBC’s state of mind. UBC’s copying efforts would not have been actionable under the patent laws before 1970; UBC cannot be held liable for patent infringement before that time. Nevertheless, UBC’s copying activities evidenced that its conduct in manufacturing and selling infringing modems after 1970 was intentional and deliberate, in willful disregard of Milgo’s rights, rather than merely accidental or negligent. UBC’s copying activities belie its contention that it proceeded to manufacture and sell modems with a good-faith belief that there was no infringement.

Once UBC had actual notice of Mil-go’s patent rights, UBC was under an affirmative duty to exercise due care to determine whether or not it was infringing Milgo’s patents. Coleman Co. v. Holly Mfg. Co, 269 F.2d 660, 666 (9th Cir.), cert. denied, 352 U.S. 952, 77 S.Ct. 326, 1 L.Ed.2d 243 (1959). UBC did not heed the suggestion of its vice president Reed Manning that its modems might be infringing, and made no effort to secure an opinion from patent counsel. Cf. Union Carbide Corp. v. Graver Tank & Mfg. Co., 282 F.2d 653, 660, 662-63 (7th Cir. 1960), cert. denied, 365 U.S. 812, 81 S.Ct. 692, 5 L.Ed.2d 691 (1961) (reliance on opinion of patent counsel that product is not infringing demonstrates good faith).

Many courts have held that faithful copying of a patented product shows an intentional disregard for the patent owner’s rights and supports an award of increased damages under 35 U.S.C. § 284. American Safety Table Co. v. Schreiber, 415 F.2d 373, 378-79 (2d Cir. 1969); Coleman v. Holly Mfg. Co., supra, 269 F.2d at 666; Saf-Gard Products, Inc. v. Service Parts, Inc., 370 F.Supp. 257, 272-73 (D.Ariz.1974); Hinde v. Hot Sulphur Springs, Colo., 359 F.Supp. 987 (D.Colo.1972), aff’d 482 F.2d 829 (10th Cir. 1973); Maxon Premix Burner Co. v. Mid-Continent Metal Products Co., 279 F.Supp. 164, 181 (N.D.Ill.1967). Apparently only a few courts have been presented with the question of prepatent copying. In the cases relied on by UBC, the courts either found that the patent was invalid, see, e. g. Sears, Roebuck & Co. v. Stiffel Co., supra; Duplex Straw Dispenser Co. v. Harold Leonard & Co., supra; or that there was no infringement, see, e. g. Inject-O-Meter Mfg. Co. v. North Plains Fertilizer & Chemical, Inc., supra. The courts thus did not reach the issue of willfulness, and the cases are distinguishable for this reason.

We hold Rixon’s “faithful copying” of Milgo’s modem, coupled with UBC’s subsequent knowledge of the existence of the patent, continued sales, and absence of reliance on the advice of counsel, are sufficient to support the court’s finding of willfulness in this case.

d. Attorney Fees

35 U.S.C.A. § 285 authorizes a trial court in patent infringement actions to award attorneys’ fees to the party prevailing if the case qualifies as “exceptional”.

The court in exceptional cases may award reasonable attorney fees to the prevailing party.

The judge found that this case was “exceptional” within the statute, and awarded Milgo attorneys’ fees in the amount of $250,000.00. An award of attorneys’ fees, like an award of treble damages, is committed to the discretion of the trial court and may only be disturbed for abuse of discretion. St. Regis Paper Co. v. Royal Industries, 552 F.2d 309, 316 (9th Cir.), cert. denied, 434 U.S. 996, 98 S.Ct. 633, 54 L.Ed.2d 490 (1977); Bolt Beranek & Newman, Inc. v. McDonnell Douglas Corp., 521 F.2d 338, 344 (8th Cir. 1975), cert. denied, 423 U.S. 1073, 96 S.Ct. 855, 47 L.Ed.2d 82 (1976); Garrett Corp. v. American Safety Flight Systems, Inc., 502 F.2d 9 (5th Cir. 1974). Of course, the prevailing party has no right to attorneys’ fees, and such an award must “be the exception and not the rule.” Q-Panel Co. v. Newfield, 482 F.2d 210, 211 (10th Cir. 1973). See also: Maloney-Crawford Tank Corp. v. Sauder Tank Co., supra.

UBC argues that this case is not “exceptional” because it did not assert sham or frivolous defenses. This argument is without merit. Assertion of a sham defense is not the only permissible basis for a finding that a patent case is “exceptional”. A finding that infringement was willful and deliberate may justify an award of attorneys’ fees to the plaintiff, as well as treble damages, depending on the circumstances of a particular case. See Jenn-Air Corp. v. Penn Ventilator Co., 394 F.Supp. 665 (E.D.Pa.1975); Saf-Gard Products, Inc. v. Service Parts, Inc., supra. The trial court’s award in this case has not been shown to be an abuse of discretion.

UBC further contends that, even if the case is “exceptional”, there was insufficient evidence presented as to the nature of the fees incurred and their reasonableness. The trial court’s award was apparently based on invoices of work performed by Milgo’s counsel, Jackson & Jones Law Corporation, Tustin, California, from the commencement of the action in April, 1971 through November 7, 1977. The invoices were identified by testimony of Harold L. Jackson, a patent lawyer with that firm. The invoices totaled $269,653.75 plus $50,-657.67 in expenses which included payments to local counsel. UBC argues that the descriptions of the work performed were obliterated by Milgo on the grounds of attorney-client privilege, and that therefore there is no indication that the amounts charged were reasonable.

It is the rule in patent infringement actions that “the grant of attorneys’ fees is erroneous where no evidence presented relative to the incurring or the reasonableness of the fees connected to the value of the services performed.” Maloney-Crawford Tank Corp. v. Sauder Tank Co., supra, at p. 14. [Emphasis added]. Milgo argues that the actual invoices submitted were the best evidence of its legal expenses, and that by failing to object or cross-examine during trial, UBC has waived its right to contest this issue now. The trial court took into account the length of time involved and the complexity of this litigation. The amount awarded is approximately $70,-000 less than the total amount requested by Milgo. While additional evidence concerning the specific services rendered and testimony as to their reasonableness might have been helpful, the case should not be remanded for this purpose alone. See American Safety Table Co. v. Schreiber, supra. The trial court did not abuse its discretion with respect to the amount of the fees awarded.

e. Prejudgment Interest

35 U.S.C.A. § 284 affords the trial court discretion to award interest and costs to the plaintiff in addition to compensatory damages for patent infringement. UBC argues that the award of prejudgment interest in this case, which ran from the date of the last infringement, September 30, 1972, constituted an abuse of discretion since the damages were unliquidated.

As a general rule, interest may be awarded only from the date a claim is liquidated. Dixie Cup Co. v. Paper Container Mfg. Co., 169 F.2d 645, 651 (7th Cir. 1948). In patent cases, however, the trial court has discretion under 35 U.S.C.A. § 284 to award interest from the date of the last infringement. Georgia-Pacific Corp. v. U.S. Plywood-Champion Papers, Inc., 446 F.2d 295, 302 (2d Cir. 1971), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971). The trial court’s finding of willful and deliberate infringement provides a basis for an award of prejudgment interest. Union Carbide Corp. v. Graver Tank & Mfg. Co., supra. UBC has not made a sufficient showing that the trial court abused its discretion with respect to the award.

AFFIRMED. 
      
      . One Hz equals one cycle per second.
     
      
      . Rixon’s relationship with UBC is discussed, infra, in II.
     