
461 F.Supp. 1354 (1978)
ELLIPSE CORPORATION, Plaintiff,
v.
FORD MOTOR COMPANY, Defendant.
No. 66 C 1421.
United States District Court, N. D. Illinois, E. D.
November 8, 1978.
*1355 *1356 *1357 Norman Lettvin and R. Dickey Hamilton, Chicago, Ill., for plaintiff.
Albert W. Bicknell, Merriam, Marshall & Bicknell, Chicago, Ill., Hal D. Cooper of Jones, Day, Reavis & Pogue, Cleveland, Ohio, and Donald J. Harrington, Ford Motor Co., Dearborn, Mich., of counsel, for defendant.

FINDINGS OF FACT AND CONCLUSIONS OF LAW
PERRY, Senior District Judge.

Findings of Fact
1. This matter is before the Court for an accounting of damages to be awarded, pursuant to 35 U.S.C. § 284[1], to Ellipse Corporation (hereinafter "Ellipse") by reason of the infringement by Ford Motor Company ("Ford") of Claim 3 of patent No. 2,628,568, entitled "High Pressure Pump", issued to Marvin L. Rhine ("the Rhine patent").

History of the Case
2. This action was commenced on August 2, 1966, Ellipse charging in its complaint that Ford's two-speed, automatic transmission pump and Ford's power steering pump ("the F-T pump") both infringed Claims 1 and 3 of the Rhine patent. Subsequently, Ellipse abandoned the charge against Ford's transmission pumps. After a trial on the merits, this court held Claims 1 and 3 valid and infringed by Ford's power steering pump. 312 F.Supp. 646 (1969).
On appeal, the finding of infringement of Claim 1 was set aside, but the court's judgment as to validity and infringement of Claim 3 was affirmed. 452 F.2d 163 (7th Cir. 1971), reh. denied December 13, 1971; cert. denied, 406 U.S. 948, 92 S.Ct. 2041, 32 L.Ed.2d 337, reh. denied, 409 U.S. 898, 93 S.Ct. 99, 34 L.Ed.2d 157 (1972). Thereafter, the case was remanded to the District Court for an accounting to determine the damages to which Ellipse is entitled.
For the purpose of taking such accounting and determining the damages, the court appointed David J. Shipman, Esq. as a Special Master in Chancery to supervise discovery, *1358 take and hear testimony of the parties and to thereafter make a written report to the court on the accounting and a recommendation as to the final amount of money judgment to be included in a final decree.
3. Proceedings before the Special Master commenced with a pretrial conference on June 22, 1972. After more than two years of pretrial proceedings, including a series of discovery depositions attended by the Special Master, the court ordered all discovery to be concluded and trial to commence. Trial started on January 22, 1975. Hearings were held several days each month with periodic recesses of approximately six to eight weeks. Shortly after defendant Ford started presenting its evidence in mid-1976, its trial counsel, George N. Hibben, fell seriously ill and died. Later, when trial resumed, the Special Master became ill and underwent surgery. Ultimately, proofs were declared closed on May 17, 1978.
By an order entered on May 19, 1978, the original order of reference was modified; the court waived the filing by the Special Master of a written report containing his recommendations as to the final amount of the money judgment to be included in a decree and counsel for the parties were directed to submit their briefs and proposed findings directly to the court.
The court has reviewed the entire record of the proceedings before the Special Master, considered the briefs filed by the parties, together with their proposed findings of fact and conclusions of law, and has had the opportunity to hear oral argument presented by counsel.

The Rhine Patent
4. The Rhine patent discloses a high pressure pump for fluids. It is concerned with the nature and shape of the pump's stator, its rotor and the blades (or slippers) that are driven along the stator cavity by the rotating rotor. (Finding 16)[2]. This combination of a stator, rotor and blades comprises what has been referred to in this proceeding as the pumping element portion of the pump. (Tr. 11285, 12733) Other parts of a complete pump assembly include the shaft, housing, and plates, reservoir and flow control valve. (DAX-113, pp. 24-27, Tr. 11619-21). Claim 3, the only claim found to be infringed, is limited to the pumping element combination, i. e., the stator, rotor and blades.
Claim 3 provides:
"A rotary fluid displacement device comprising a stator having an out-of-round stator cavity, a rotor located therein, said rotor having blade-receiving pockets, a blade received in each of said pockets, each of said blades having contact at all times during the operation with said stator and said rotor, in which the contact between the outer surface of the blade and the inner surface of the stator is area contact to prevent complete rotation of the blade in the pocket but permit it to rock therein with free movement in relation to said pocket, and the contact of a side of the blade with the rotor pocket being along a line which varies in position with respect to the blade and the pocket during operation and which acts as a pivot for the blade, the pivot action tending to keep the outer surface of the blade in said area contact with said stator during all positions of rotation of said rotor."
The patentable distinction of the pumping element disclosed in Figure 7 of the Rhine patent, and claimed in Claim 3, was *1359 described by the Court of Appeals as the special relationship of the slippers to the stator whereby a "mismatching area contact" was achieved. 452 F.2d 163, 170. By its earlier decision this court has determined that the pumping element of the F-T pump does employ such "mismatching area contact".

The Parties
5. Ellipse was formed in 1945 by Simon Moss and the inventor, Marvin Rhine, to develop and promote the pump that is the subject of the Rhine patent. Ellipse's business of attempting to make and sell slipper pumps of both balanced and unbalanced design was carried out during 1946-48 (DAX-8-34). The business did not prosper. Neither Mr. Moss nor Mr. Rhine had either the education or the ability to properly organize and operate a manufacturing facility (Finding 6). In all, Ellipse produced a total of approximately 8 to 12 pumps (App. pages 170, 1399).
Unable to commercialize the Rhine pump, Ellipse abandoned its manufacturing operations and sold its equipment in 1948. With the exception of two pumps it sold in 1956 (DAX-7, 35-37), Ellipse has been a dormant shell corporation since 1948. Its sole asset has been the Rhine patent. The inventor, Mr. Rhine, died in 1959. Up to 1966, the stock in Ellipse was distributed among Simon Moss, his brother, Harvey, Marvin Rhine and after Mr. Rhine's death, his widow, Bess. On January 7, 1966, after Ellipse had decided to sue Ford for infringement of the Rhine patent, Mr. Moss purchased Mrs. Rhine's 1/3 interest in Ellipse (represented by 100 shares of stock) for $3,000 (DAX-166). At about the same time Norman Lettvin, plaintiff's trial counsel, purchased a 25% stock interest in Ellipse and Maurice Rosenfield, another attorney in Chicago associated with Ellipse, purchased a 39% stock interest in Ellipse. As a result of these transactions, the two lawyers obtained a controlling 64% interest in Ellipse. (DAX-182). Since 1966, the two lawyers, together with Mr. Moss, have formed the Board of Directors of Ellipse (DAX-148) and Mr. Rosenfield has controlled Ellipse's finances. (DAX-183, 184). Mr. Lettvin filed this suit and has tried the case in all proceedings in the District Court, the Court of Appeals and the Supreme Court; before the Special Master David J. Shipman; and before the District Court thereafter through final argument. He has at all times been in constant contact with Mr. Rosenfield for consultations.
Ford is a well-known marketer of automobiles. Among the various options that Ford offers for use with its automobiles is a power steering system. Commencing with its 1965 model year vehicles, Ford began using the F-T pump in its power steering systems. (Finding 11). That pump was designed by TRW, Inc. ("TRW"). (PAX-137, p. 266). Under an agreement with TRW, Ford's Transmission and Chassis Division ("T&C") manufactured approximately 65% of the F-T pumps used by Ford and TRW supplied Ford the remaining 35% of those pumps.

The Relevant Period of Accounting
6. The parties are in disagreement as to the relevant period of accounting. Plaintiff maintains that all of the F-T pumps used by Ford from 1964 (when the 1965 model year vehicles were introduced) up to February 17, 1970, the expiration of the Rhine patent, are subject to this accounting. Relying on 35 U.S.C. § 287, defendant contends that it should be required to account only for those F-T pumps it used from August 2, 1966, the date this action was filed, up to the expiration of the Rhine patent. The parties have stipulated that Ford used 9,098,945 F-T pumps during the period contended for by plaintiff, and 6,568,203 F-T pumps during the period contended for by defendant.
Relying on DAX-82 and the testimony of Mr. Closser, plaintiff contends there are an additional 482,548 "remanufactured" pumps that should be included in the accounting. This contention is inconsistent with plaintiff's stipulation on February 22, 1977 that the number of remanufactured pumps is unknown. Nonetheless, the court has reviewed DAX-82 and the testimony of Mr. *1360 Closser, but finds no basis for altering the stipulation. Plaintiff was aware of this exhibit and Mr. Closser's testimony when it entered into the stipulation. The units listed in DAX-82 are defective pumps remanufactured and sold by independent companies, not by Ford. (Tr. 9305-09)
Based on the evidence in this case, it is concluded that Ford's contention as to the relevant period of accounting is correct. In 1956, Ellipse had two fuel pumps made by an outside engineering firm which it then sold to Ford. (DAX-7, 35-37).
Both Ellipse's president (App. p. 1453) and its patent counsel (DAX-38) have asserted that those fuel pumps were produced in accordance with the invention in the Rhine patent. However, Ellipse has offered no proof that those pumps were marked with the number of the Rhine patent. Under 35 U.S.C. § 287, the failure of a patent holder to mark its own product with the patent number limits the recovery of damages to the period subsequent to notification of infringement. It is clear that Ford was given no notification prior to the institution of this action on August 2, 1966.
Ellipse did send a notice of infringement to Ford by letter dated December 21, 1962 (DAX-38). The letter did not specify any particular pump believed by Ellipse to be infringing; however, the evidence is clear that the letter was intended to refer to Ford's two speed automatic transmission pump. (PAX-90-C; Tr. 18704). Plaintiff now concedes that the transmission pump did not infringe the Rhine patent. (Finding 10).
Ellipse contends that under Wine Railway Appliance Co. v. Enterprise Railway Eqt. Co., 297 U.S. 387, 56 S.Ct. 528, 80 L.Ed. 736 (1936), the provisions of 35 U.S.C. § 287 do not apply to it since it was not a marketer of pumps. However, the facts are otherwise and Wine Railway is not controlling here. Ellipse did market two pumps which, by its own admission, came under the Rhine patent and it has presented no evidence that it marked them in accordance with the statute.
The evidence also demonstrates that Ellipse had ample opportunity to give Ford notice had it elected to do so. Ellipse purchased an F-T pump in 1965. (Tr. 18803-07). By early January, 1966, the pump had been analyzed and the decision to sue Ford had been made. (Tr. 18810, 18811-12). Mr. Moss has testified that at least six lawyers were associated with the company in connection with this suit. (Tr. 18808-09). Yet, neither Ellipse nor any of its lawyers made any effort to notify Ford that the F-T pump was believed to be an infringement. Having withheld such notice, when it plainly could have been given, Ellipse cannot now escape the consequences of its actions. Union Carbide Corp. v. Graver Tank & Mfg. Co., 282 F.2d 653, 676 (7th Cir. 1960). Ford is responsible to account only for the pumps it used from August 2, 1966 to February 17, 1970.

The Applicable Measure of Recovery
7. Ellipse has never been a competitor either of Ford or of its supplier, TRW. It asserts no lost sales, lost profits or any other competitive injury as a result of the infringement. Yet, plaintiff contends that its recovery is to be based on the profits Ford realized on its "sale" of F-T pumps as a part of a power steering option. Recognizing that Ford only uses the F-T pump as a part of the power steering system in its car and, hence, there is no identifiable "revenue" or "profit" for the pump, Ellipse has undertaken, by a method of cost ratios, to apportion a profit to the pump. From this apportioned profit, plaintiff deducts an amount which it designates as Ford's "usual" profit, the remainder or "excess" profit being claimed as a reasonable royalty.
In its post-trial brief, plaintiff sets out four computations, each premised on a theory of profit apportionment. Based on those computations, plaintiff maintains that a reasonable royalty, on a pump worth approximately $10, ranges from $4.76 to $6.51 per pump. Plaintiff has also presented a fifth method of computation in which it apportions profit to the pump and claims 50% of that profit as a reasonable royalty. *1361 Under this approach, plaintiff claims a royalty of $3.44 per pump. Plaintiff has in its computations averaged out and proposed that the court should award to plaintiff the amount of $5.79 of Ford's "profit" on each of the pumps used by Ford and on each of the pumps rebuilt or remanufactured.
In its proposed Findings of Fact and Conclusions of Law delivered to the court, Ellipse has also included various computations of "reasonable royalty". It maintains that all of the F-T pumps used by Ford from 1964 (when the 1965 model year vehicles were introduced) up to February 17, 1970 (the expiration of the Rhine patent) are subject to this accounting. As set forth in the court's finding 6 herein, the parties have stipulated that Ford used 9,098,945 F-T pumps during the period as contended for by plaintiff. Plaintiff contends that the "reasonable royalty" it calculates, with apportionment, to determine the "Option" pump revenue results in the amount of reasonable royalty to be awarded Ellipse for Ford's infringement during the period August, 1964, through February 17, 1970, in an amount of $5.79 per "Option" pump, or a total of $52,682,891 on 9,098,945 pump units, but not including rebuilt or remanufactured pumps. Plaintiff also contends that Ford induced others to infringe Patent 2,628,568 by remanufacturing infringing pumps in the quantity of 397,548 units and that Ford itself manufactured 85,000 rebuilt or remanufactured pumps. Ellipse calculates the "reasonable royalty" for Ford's infringement in connection with the remanufactured pumps, during the period August, 1974, through February 17, 1970, at $2,793,952. Ellipse seeks judgment against Ford for "reasonable royalty" in the amount of $55,476,843.
In addition, Ellipse claims it should be awarded interest on the "reasonable royalty" amounts it calculates. In its proposed findings and conclusions, Ellipse computes interest year by year at arbitrary rates and arrives at a total of $41,401,257.90. This amount of interest when added to the $55,476,843 plaintiff seeks as damages for infringement equals a total of $96,878,100.90 that Ellipse seeks from Ford in this case.
Such an award of damages and interest would be a windfall and make multi-millionaires out of the two lawyers and the Moss family for a comparatively small investment. Some estimate of this original investment is shown by the evidence herein. In 1954 Marvin Rhine sold 25 of his shares in Ellipse to H. J. Moss at $40 per share and based on that transaction (as found in finding 21 hereof), Ellipse's issued stock of 300 shares had a total value of $12,000. As time passed and there was no grant of any licenses, it was reasonable to expect Ellipse's stock would decline in value; and it appears it did, as on January 7, 1966 Mrs. Bess Rhine Conroy (who had remarried) sold her 100 share interest in Ellipse to S. Moss for $3,000 or $30 a share. (DAX-166, 182). Shortly thereafter, on January 28, 1966, an agreement was entered into between Simon H. Moss, Harvey Moss, Norman Lettvin and Maurice Rosenfield (DAX-184). At the time of the agreement S. H. Moss owned 293 shares and Harvey Moss owned 7 shares of Ellipse and they were the sole stockholders. Under the terms of the agreement S. H. Moss agreed to sell 117 common shares of Ellipse to Norman Lettvin for $1,170, and 14 common shares to Maurice Rosenfield for the sum of $140. Under the agreement, Rosenfield subscribed for 169 common shares and agreed to pay therefor the sum of $75,000 in cash within 90 days after the execution of the agreement. This agreement shows that in January of 1966 Ellipse was proposing to sue either or both of Ford and Chrysler Corporation under the Rhine patent and that Lettvin had been retained to handle and supervise the litigation. As set forth in finding 5, supra, Messrs. Lettvin and Rosenfield had by April 25, 1966 a controlling 64% interest in Ellipse. This suit against Ford was filed shortly thereafter on August 2, 1966.
Ellipse now proposes the court enter a $55,476,843 judgment against Ford for reasonable royalty under its profit theory plus $41,401,257.90 in interest, or a total just under $97,000,000. This would be a huge windfall on the stockholders' comparatively *1362 small investment. It would be grossly unfair under the circumstances of this case to make such an award of damages, plus interest, and grossly unfair to the thousands of stockholders of Ford Motor Company who have invested millions of dollars in the production of automobiles and have contributed to the social and economic development of this nation and the world. Such an award would be inequitable and indefensible both in equity and law under all the circumstances of this case.
In its DAX-157 Ford has shown the effect of patent royalties on the cost of alternative pumps available to Ford in 1963-64. A royalty of $5.79 per pump, as proposed by Ellipse, would have cost Ford almost $6 more than the Saginaw pump which was acceptable to it. TRW quoted Ford a price of $8.39 in 1963-64. Considered as a percentage, a royalty of $5.79 would result in a royalty rate of 69%. Ford paid an average price of $10 for F-T pumps during the period 1965-70. Based on this average price, plaintiff's proposal represents a royalty rate of 57.9%. The pumping element of the F-T pump (the only portion covered by the Rhine patent) represents a cost of approximately $2.50. As a percentage of that cost, $5.79 represents a royalty rate of 232%. Royalties of this magnitude are clearly unreasonable. Ford, as hereinafter in finding 26 set forth, was during the period 1955-70 paying less than 1% for a reasonable royalty on high volume items to be used in its automobiles.
The court has carefully considered plaintiff's profit theory and contentions but finds they are unsupported by either the applicable law or the facts of this case. Ellipse's damages, not Ford's profits, are the proper measure of recovery under 35 U.S.C. § 284. Zegers v. Zegers, Inc., 458 F.2d 726 (7th Cir.), cert. denied, 409 U.S. 878, 93 S.Ct. 131, 34 L.Ed.2d 132 (1972). The evidence in this case is clear that the only damage Ellipse has suffered is the loss of royalties it would have received if Ford's use of the F-T pump had been under an appropriate license agreement. The compensation to which Ellipse, therefore, is entitled under 35 U.S.C. § 284 is a reasonable royalty. The approach to be used in determining a reasonable royalty has been stated in Horvath v. McCord Radiator & Mfg. Co., 100 F.2d 326, 335 (6th Cir. 1938), cert. denied, 308 U.S. 581, 60 S.Ct. 171, 84 L.Ed. 529 (1939) in the following terms:
In fixing damages on a royalty basis against an infringer, the sum allowed should be reasonable and that which would be accepted by a prudent licensee who wished to obtain a license but was not so compelled and a prudent patentee, who wished to grant a license but was not so compelled.
In substance, application of that rule, often referred to as the "willing buyer-willing seller" rule, involves a determination of the reasonable market value of a license under the Rhine patent. Among the questions to be resolved in determining the market value are (1) what would Ford, as a prospective willing buyer, have been willing to pay for a license, and (2) what would Ellipse, as a prospective willing seller of a license, have been willing to accept. (Tr. 16948-57; 16987-17001; 17257-59).
Those questions, as well as the ultimate question of "reasonable royalty" must be resolved in light of the facts and circumstances known to the parties at the time they, hypothetically, would have negotiated a license had it been known that Ford's use of the F-T pump would infringe the Rhine patent.
None of plaintiff's proposals is based on this approach. It has entirely ignored the particular facts and circumstances of Ford and Ellipse. It has offered little evidence that is pertinent to such issues as the reasonable market value of a license under the Rhine patent in light of other pumps then available in the market place. The profits it computes for the F-T pump are not, in fact, profits but an arbitrary allocation or apportionment of profits on the basis of a cost ratio.
*1363 Based on the evidence in this case, the court is satisfied that neither a willing buyer nor a willing seller would make a decision as to a royalty on the basis of such an arbitrary allocation of profit.[3] (Tr. 17025-71), (XXXXX-XXX). Nor is there any evidence that "profits," whether allocated or otherwise, would have any relevance, under the circumstances present in this case, to what either Ford as a willing buyer would be willing to pay or Ellipse as a willing seller would be willing to accept as a reasonable royalty. For these and other reasons that appear hereafter, plaintiff's proposals for a reasonable royalty cannot be accepted.

The Time of the Hypothetical Negotiation
8. While the evidence does not precisely pinpoint when Ford's infringement commenced, Ford first received four prototypes of the F-T pump from TRW sometime after March 7, 1963. T&C engineers installed some of those pumps in a car but they failed almost immediately (Tr. 12197-99). T&C worked with TRW to resolve the problems encountered with the pump in 1963 and early 1964. (Tr. 12201). Ford's negotiations with TRW for the F-T pump were concluded on August 8, 1963 when an agreement between the two companies was executed (DAX-60) and a purchase order was released. (DAX-132). By April or May, 1964, manufacture of the F-T pump by T&C was in progress (Tr. 12207-09; DAX-127).
The hypothetical negotiations are, therefore, time placed in the period of mid-1963 to early 1964 (hereinafter "1963-64"), when Ford began to manufacture and to use the F-T pump.

THE CIRCUMSTANCES OF FORD IN 1963-64

Power Steering In the Automobile Industry
9. A power steering system provides a hydraulic assist that takes over most of the effort of steering the automobile. (Tr. 11261). The power steering system includes a power steering gear (which replaces the manual steering gear), a pump, a power cylinder, brackets, hoses, belts, pulleys and fittings. (Tr. 11259-11272; DAX-107A, B, 108A, B, 113). The only function of the pump is to provide hydraulic fluid under pressure to the system (Tr. 11261, 11264, 11301).
Since the 1950's, each of Ford's competitors has offered power steering options for their cars (DAX-113, 114). The pumps for these power steering systems have been supplied by various companies in a highly competitive market. (Tr. 11811-14, 12846-59, 12875-79; DAX142A-H; 143A). General Motors has, since at least as early as 1953, used a vane type pump manufactured first by Vickers, Inc. and later by GM's Saginaw Steering Gear Division ("Saginaw"). (DAX-113, 114; Tr. XXXXX-XXX). Chrysler Corporation has used a non-infringing slipper pump manufactured by TRW (DAX-108, 113, 114) as well as the Saginaw vane type pump (DAX-114; Tr. 11804-07). American Motors has used a non-infringing slipper pump manufactured by TRW, a non-infringing roller pump manufactured by Eaton Corporation ("Eaton") and the Saginaw vane type pump. (DAX-114; Tr. 11804-08, 12853). In the early 1960's, Ford's power steering system used a roller pump manufactured by Eaton. (DAX-114).
10. In early 1963, T&C investigated the possibility of manufacturing a portion of Ford's requirements for power steering *1364 pumps commencing with Job No. 1, 1965[4]. Several design alternatives were investigated to determine the most desirable pump from a product and manufacturing feasibility standpoint. (DAX-150G). The designs considered were:
Current Eaton design, Proposed Eaton design, Saginaw (Vickers Vane) design, Thompson (slipper) design.

The Eaton Design
11. At the time of T&C's investigation, Ford was purchasing all of its power steering pumps from Eaton, including both a crankshaft mounted roller pump for the Lincoln and a belt driven roller pump for the other Ford car lines. (Tr. 11266-68; PAX-82; DAX-150G). T&C was primarily interested in manufacturing pumps for the car lines that used the belt driven pump. Eaton was willing to permit T&C to do so under a "make-buy" arrangement whereby T&C would be permitted to manufacture a portion of its power steering pump requirements using Eaton's design and technology, provided Ford purchased the remainder of its pump requirements from Eaton. (Tr. 12843-47).
Both the then current Eaton design and the modified design were unbalanced roller pumps. (DAX-142B; Tr. 12830-31). The modified design had a wrap-around reservoir similar to the arrangement of the Saginaw and F-T designs (Tr. 11666-67, 12829-31; DAX-142B). Eaton had been selling the current design at an average price of approximately $9.39 but proposed to supply the modified design in model year 1965 at a reduced price of $7.80 with a tooling cost of $325,000. (DAX-142B, -142C). Both the current and modified Eaton designs would have been available to Ford for Job No. 1, 1965. (Tr. 12860, 12870).

The Saginaw Design
12. The Saginaw pump was a balanced vane type pump designed by Vickers, Inc. (Tr. 11797, 11811). Its construction is similar to the F-T pump except it uses flat vanes instead of slippers (PAX 137, p. 58). Saginaw manufactures products for other divisions of General Motors, and actively seeks to sell those products to outside customers as well. (Tr. 11727-28). Saginaw had previously sold products to Ford, including steering gears, under a "make-buy" arrangement. (Tr. 11730-31).
Saginaw offered to supply its vane-type pump to T&C on a "make-buy" arrangement whereby Ford would be permitted to manufacture a portion of its power steering pump requirements, using Saginaw's design and technology, provided Ford purchased the remainder of its requirements from Saginaw. (PAX-137, p. 58, Tr. 11728-32). The Saginaw pump would have been available for Job No. 1, 1965 (DAX-119A), and Saginaw would have supplied the pump to Ford at the same price it supplied the pump to divisions of General Motors. (Tr. 11728). Saginaw submitted to Ford a quote of $8.48 per pump with a tooling charge of $50,000. (DAX-119A, Tr. 11734-40).

The TRW Design
13. The F-T pump design is similar to the Saginaw pump except it uses slippers instead of flat vanes (PAX-137, p. 58). It is also similar to the slipper pumps Ford had used in its two speed automatic transmissions, except that it is a balanced pump. Ford had obtained the transmission slipper pump from Federal Industries, a predecessor of TRW, on a "make-buy" arrangement. T&C had manufactured a portion of Ford's requirements for the transmission pump so it was generally familiar with slipper pumps when the investigation was conducted in 1963. (PAX-137, pp. 45-46, 59-60, 61, 74, 266).
TRW first quoted a price of $8.69 per pump and tooling costs of $361,000 for a portion of Ford's requirements (DAX-131). *1365 Subsequently, TRW reduced the price by 25¢ to $8.44 (DAX-150L), and later to $8.39 with tooling costs of $133,000 (DAX-150F).

T&C's Evaluation of the Alternative Designs
14. On March 7, 1963, the Product Engineering Office for T&C presented an internal report to Ford management entitled, "Power Steering Pump Analysis" (PAX-82; Tr. 11686-87). The report recommended the adoption and use in Ford automobiles of the F-T pump for eight specified reasons, none of which is in any way related to the "mismatching area contact" found by the Court of Appeals to be the patentable distinction of Claim 3 over the prior art:

(a) A Diametrically Pressure Balanced Pump

The T&C engineers were interested in a pressure balanced pump, whether it used rollers, vanes or slippers (Tr. 12673-74).[5] Rhine was not the inventor of pressure balanced pumps. Vickers patent No. 1,989,900 (DAX-44) discloses a pressure balanced pump and the Saginaw pump, based on the Vickers design, was pressure balanced. Also, the Eaton crankshaft mounted roller pump was a pressure balanced pump. (Tr. 11682, PAX-82).

(b) An Axially Pressure Loaded Pump

This concerns the use of fluid pressure to apply pressure against the end plates of the pump. (Tr. 11683). This feature is not related to Rhine's contribution of mismatching area contact; end plates are not part of the combination claimed in Claim 3. The Saginaw pump also had pressure loaded end plates (PAX-82; Tr. 11684); the Eaton pump did not.

(c) Cartridge Type Pumping Element

The F-T pumping element was of a so-called cartridge construction that permitted removal and replacement of the pumping element as a unit. (PAX-82; Tr. 11684). This has nothing to do with Rhine's contribution of mismatching area contact. The Saginaw pumping element was also of a cartridge construction (PAX 82; Tr. 11684); the Eaton pumping element was not.

(d) Cartridge Type Flow Control Valve

Each of the pumps available to Ford had a flow control valve. The Rhine patent does not disclose a flow control valve of any kind (Tr. 12161). The F-T pump had a cartridge type flow control valve which, like the pumping element, could be replaced as a separate unit. The cartridge type flow control valve used in the F-T pump is disclosed in TRW patents Nos. 3,200,752 (DAX-126A) and 3,314,495 (DAX-126B). (Tr. 12157-60).

(e) Greater Manufacturing Feasibility

The F-T pumping element had fewer critical manufacturing operations as compared to the other pumps evaluated. (PAX-82, Tr. 11690). This was due to the slipper construction which did not require finishing operations either on the slippers or on the slots or pockets in which they were received. (Tr. 11690-95). This is an advantage inherent in all slipper pumps and was expressly recognized as such in the prior art Livermore patent No. 2,278,131 (DAX-117; Tr. 11703-06). The non-infringing slipper pumps Ford used in its automatic transmissions *1366 had this same advantage. (PAX-137, pp. 37, 40; DAX-58, p. 14).

(f) Slippers are Positively Loaded

This refers to the presence of springs that serve to bias the slippers out against the stator wall. (PAX-82; Tr. 12160). Neither Saginaw nor Eaton had such springs. Nor does the Rhine patent disclose the use of springs. (Tr. 12161). The positive loading of the slippers by using springs is expressly disclosed in the prior art Livermore patent No. 2,278,131 (DAX-117; Tr. 12160-61).

(g) Competitive Weight

At the time the report, PAX-82, was prepared, T&C estimated that the weight of the F-T pump would be slightly less than that of the Saginaw pump. However, by the time the F-T pump was in production, it actually weighed more than both the Saginaw and Eaton pumps. (Tr. 11714-17, 12145-46; PAX-84; DAX-118).

(h) Comparable Volumetric Efficiency

T&C's analysis in 1963 indicated that the Saginaw pump and the F-T pump would have comparable volumetric efficiencies, with Eaton somewhat lower. (PAX-82; Tr. 11718).

Ford Selected the F-T Pump Because, Among Other Things, of Its Manufacturing Feasibility and Potential For Future Design Savings
15. The evidence is that Ford selected the F-T pump because it was believed, in 1963-64, to be more desirable. (Finding 47G). Among other advantages of the F-T pump was its manufacturing feasibility and potential for future design savings. (DAX-150G).
There is no evidence that Ford expected to realize a competitive advantage in the marketing of its automobiles by using the F-T pump. The undisputed fact is that customers do not purchase Ford automobiles because of the particular power steering pump used in the power steering system. (Tr. 9127-28; 9164-69).
Contemporaneous documents in the period 1963-64 show that Ford selected the F-T pump over the Saginaw pump because, among other reasons, T&C proposed to manufacture a portion of Ford's pump requirements and it was the opinion of Ford's engineers that the F-T pumping element, due to fewer critical tolerances, would be easier for T&C to manufacture than the Saginaw vane type pumping element:
(a) The study by the T&C engineers, as reported in PAX-82, rated the pumping element of the Thompson pump superior to the pumping element of the Saginaw pump only in terms of manufacturing feasibility.
(b) In a report dated March 22, 1963 (DAX-150G) the Transmission and Chassis Division stated that, "after evaluating the design alternatives available, product engineering indicated that Saginaw and Thompson designs were superior in basic design and serviceability." The report further stated:
"While the Saginaw and Thompson pumps were relatively equal from a product standpoint, it has been determined that the Thompson design is a more easily manufactured unit and yields the most potential for future design savings. We are, therefore, recommending that we integrate the Thompson design pump, Job # 1, 1965."[6]
(c) In a meeting held on April 4, 1963, representatives of Ford's engineering, finance and purchasing staffs considered T&C's proposal to manufacture some of Ford's power steering pumps. The only advantage attributed to the Thompson pump in that meeting was its manufacturing *1367 feasibility as compared to the Eaton and Saginaw designs (DAX-150A).
(d) In a report issued on February 6, 1964, T&C rated the F-T pump equivalent to the Saginaw pump in all areas except that the "F-T pump is superior to competition for critical manufacturing tolerances in the pumping elements" (DAX-125, pages 19-22).
T&C's opinion that the F-T pumping element had greater manufacturing feasibility than either Eaton or Saginaw was based on a judgmental study in 1963 of the various components of each of the available pumps. It was concluded that the F-T pumping element would be a "few pennies" less expensive to manufacture than the Eaton and Saginaw pumping elements. (Tr. 12676-78).

Ford's Agreement with TRW
16. By May 17, 1963, the proposal to use the F-T pump designed by TRW had been approved, in principle, subject to a satisfactory piece price, manufacturing rights agreement and warranty agreement (DAX-150E). TRW held exclusive rights under a number of Livermore patents, some of which covered the F-T pump offered to Ford (DAX-150C). In addition, TRW intended to file patent applications of its own on other features of that pump (DAX-150H). Accordingly, Ford undertook negotiations with TRW, concluding, on August 8, 1963, with an agreement (DAX-60, 132) the terms of which included the following:
(a) Ford received a royalty-free, non-exclusive license under the patents TRW owned or controlled to make, use and sell the F-T pump, provided Ford purchased at least 35% of its requirements of F-T pumps from TRW. (DAX-60)
(b) TRW agreed to supply its 35% of Ford's requirement for the F-T pump at a unit price of $8.39, subject to adjustment.[7] (DAX-132).
(c) TRW had quoted a lump sum price of $133,000 for tooling (DAX-150F); the parties agreed to a tooling charge at a per unit price of 18¢ spread over a three year period (DAX-132). Ford, at that time, was projecting planning volumes at a level of 670,000 pumps per year. (DAX-150L, 150M).

Ford Had Acceptable Non-Infringing Alternative Pumps Available to it throughout 1964-70.
17. Throughout the period of 1964-70, Ford's ability to offer power steering options for its automobiles was not dependent on its use of the F-T pump. While, in 1963, Ford did believe the F-T pump was the more desirable, any one of the pumps offered to Ford at that time would have satisfactorily met Ford's power steering requirements. (DAX-128; Tr. 11300, 11612-13, 12191-97, 12882, 12690-91). Two pumps, the F-T and Saginaw, were competitive in performance, availability and price. The Eaton pump was highly competitive in price and the competitive equal of the others in terms of availability, but less competitive from a performance standpoint.
The ability of the Eaton roller pump to meet Ford's needs is apparent from Ford's use of the pump in model year 1964. In fact, when Ford required additional pumps for model year 1965, it purchased those same roller pumps from Eaton (Tr. 12871) and used them, together with the F-T pump, in its various car lines. (Tr. 11612). Eaton continued to sell the same roller pumps to American Motors up to 1970. (Tr. 12853).
That the Saginaw vane type pump would have satisfactorily met Ford's power steering requirements throughout the period 1964-70 is beyond question. The Saginaw pump offered to Ford has been in production by Saginaw and used by General Motors *1368 in all of its car lines since the 1950's; it has also been used in the automobiles of Chrysler and American Motors. (DAX-114). Millions of those pumps have been employed in power steering systems.[8] (Tr. 11801). The cost of "packaging", i. e., the pulleys, brackets and hoses, the F-T and Saginaw pumps for installation in Ford cars would have been approximately the same. (Tr. 12262-64, 12269). The cost of tooling and facilities for T&C to manufacture the Saginaw pump would have been approximately the same as for the F-T pump. (Tr. 13240).
That Ford would have entered negotiations with Ellipse in 1963-64 with the Saginaw and Eaton pumps as acceptable alternatives to the F-T pump is confirmed by a document dated April 22, 1963 (DAX-150C). In that document, those pumps were expressly recognized as alternatives that Ford could use should the then upcoming negotiations with TRW not prove to be successful.

THE CIRCUMSTANCES OF ELLIPSE IN 1963-64
18. In 1963-64, Ellipse had no manufacturing facilities. (Tr. 10635). It had no engineers, and it had no full-time employees. (Tr. 10632-35). It had but one asset, the Rhine patent (App. pp. 1389-90). Although Ellipse was willing to grant licenses under the Rhine patent to any pump manufacturer or any automobile company interested in manufacturing pumps (Tr. 10646-47), no person, firm or concern has ever requested a license (Tr. 13533) and Ellipse has been unsuccessful in interesting anyone in taking such a license (Tr. 10656). Counsel for Ellipse has stipulated that Ellipse had absolutely no bargaining power in 1963-64 (Tr. 10639).

The Hypothetical Negotiations and Determination of a Reasonable Royalty
19. In entering negotiations, a willing buyer for a patent license must make a decision as to the maximum he can pay as a royalty for the patented item and still be better off than choosing an available alternative. Similarly, the willing seller must make a decision as to the minimum royalty he can accept from the prospective buyer and still be better off than choosing an alternative course of action. Among other things, to arrive at those decisions, the normally prudent businessman will determine, in light of his particular circumstances at the time, the differences in cost (in the case of the buyer) or revenue (in the case of the seller) between the alternatives available to him and then select the more favorable course of action. (Tr. 16985-17065, XXXXX-XXX). As plaintiff's expert, Mr. Weinstein, testified:
Mr. Cooper:
"Q. As I understood your definition of a willing-buyer and willing-seller, as you understand it, it is the result of an arm's-length transaction between two parties, a buyer and a seller, neither of which is under compulsion to buy or sell. Am I generally correct, sir?
Mr. Weinstein:
A. Yes, that is the accounting concept.
Q. You have two parties to the transaction, don't you?
A. Right.
Q. A buyer and a seller?
A. Right.
Q. So when we decide what would be the outcome of that arm's-length transaction, we have to take into account the buyer and the seller; isn't that correct, sir?
A. Absolutely.
Q. If you have a buyer, a prospective buyer who is not under compulsion to buy, isn't it correct, sir, that the buyer in that circumstance would have to evaluate the alternatives available to *1369 him before he would determine what he would be willing to pay?
A. Yes.
Q. Isn't it also correct that a seller would have to evaluate the alternatives available to him before he would determine what price he would be willing to accept?
A. Yes." (Tr. 18981-82).
20. The revenue Ford receives by selling a car equipped with power steering would not vary with the pump used in the system, (DAX-105; Tr. 10824-31). From Ford's standpoint as a willing buyer, it, as a prudent businessman, would select the pump with the least cost, provided the pump was satisfactory from a performance standpoint. It had, in 1963-64, two pumps, the F-T and the Saginaw, that were equally satisfactory from a performance standpoint (PAX-82, DAX-150G). In negotiations with Ellipse, Ford, as a normally prudent businessman, would have been primarily concerned with the effect of any royalty Ellipse might demand on the cost of the F-T pump as compared to the cost of the Saginaw pump.[9] (Tr. 13681-93). Mr. Weinstein admitted Ford would not be expected to agree to pay a royalty that would increase the cost of the F-T pump above the cost of an equally acceptable alternative pump such as Saginaw. (Tr. 19065-69).[10] Ford has contended that to determine the maximum it could pay to Ellipse, Ford, as a prudent businessman, would analyze the differences in cost between the F-T and Saginaw pumps. (Tr. 19176).
In 1963-64 Ford was projecting volumes of 670,000 pumps per year (DAX-150L, 150M). At those volumes, had Ford taken a license from Ellipse commencing with its model year 1965 vehicles, it could foresee using approximately 3,685,000 pumps during the five and one-half years (August 1964 to February 1970) then remaining on the life of the Rhine patent. Based on that total number of pumps and the differences in cost between the F-T pump and Saginaw pumps as Ford would have seen them in 1963-64, the evidence establishes that Ford could have reasonably expected to save a total of $478,887.50 by using the F-T pump instead of the Saginaw pump during the 5½ year period (DAX-180). (In computing that amount the court has taken into consideration all of the differences in cost between the F-T and Saginaw pumps, assuming 35% of the pumps were to be purchased and 65% to be manufactured by T&C.) Ford contends the $478,887.50 saving by using the F-T pump instead of the Saginaw pump represents the maximum Ford could have paid as a royalty for a non-exclusive license from Ellipse without increasing the cost of the F-T pump above the cost of the Saginaw pump (DAX-180; Tr. 17257-17301);[11] and that if Ford had to pay any amount larger than that Ford would be *1370 better off with the Saginaw pump (Tr. XXXXX-XXX).
However, it is clear from the hearings before the Special Master and this court that Ford did consider the F-T pump more desirable in many respects. In addition, Ford, as a prudent businessman, probably would have paid a premium in order to have a license to produce the F-T pump which it could control rather than the Saginaw pump which was controlled by General Motors, its largest and strongest competitor.
21. From Ellipse's standpoint as a willing seller, it was confronted with a highly competitive market. Being incapable of competing in that market, the alternatives available to Ellipse in 1963-64 were limited. Ellipse could either non-exclusively license the patent to companies such as Ford and TRW, or it could dispose of the patent, either by sale or exclusive license. As Mr. Moss, Ellipse's president, testified, since the Rhine patent was Ellipse's sole asset, either selling the patent or exclusively licensing it would be the same as selling the corporation. (Tr. 18812-13). Thus, in arriving at the minimum it could accept, Ellipse would be largely influenced by the amount its stockholders would receive should they pursue such alternatives as selling the company, and with it the Rhine patent. (Tr. 17264-68, 17327-43, 17371-79).
There is evidence in the record that provides some guidance as to the amount Ellipse's stockholders could realize from the sale of the company, and with it the Rhine patent (DAX-182-188). For example, in 1954, the inventor, Marvin Rhine, sold 25 of his shares in Ellipse at a price of $40 per share (DAX-182). Based on that transaction, Ellipse's issued stock (300 shares) had a total value of $12,000. Since the Rhine patent had a finite life of 17 years, it is reasonable to expect that the value of the Ellipse stock would decrease, not increase, as time passes without the grant of any licenses and Ellipse's sole asset approaches expiration. (Tr. 17328-39). A liberal estimate of the reasonable market value of Ellipse stock in 1963-64 would, therefore, be $12,000. This is confirmed by the amount Mrs. Rhine received for her interest in Ellipse. Based on her sale of 100 shares to S. Moss for $3,000 (DAX-166), the total value of Ellipse stock in 1966 had declined to $9,000. Other transfers of stock in 1966 were at $10 per share, although the corporation issued a block of 169 shares for $75,000 (DAX-182, 184). As a normally prudent businessman, it is unlikely that Ellipse in negotiations with Ford would have been willing to accept a royalty less than $12,000 its stockholders would realize by selling the company and, thereby, ownership of the Rhine patent. (DAX-181; Tr. 17263-65, 17322-43, XXXXX-XXX).
22. The foregoing establishes one bargaining range  $478,887 being the maximum Ford contends it could have agreed to pay and $12,000 being the minimum Ellipse would have demanded. Ford contended it is reasonable to expect that rational, prudent businessmen, had they negotiated, would reach an agreement somewhere in that bargaining range.
23. Ford contended several factors in this case indicate Ford would have agreed on an amount substantially below the maximum Ford could have paid. These include:
(a) Ellipse was offering only a bare, non-exclusive license. It did not have a commercially proven product; nor did it have any manufacturing experience or other technical assistance to offer to Ford.
(b) The Rhine patent pertains only to a portion of the F-T pumpsthe pumping element. In terms of cost, the pumping element was only one-fourth of the total cost of the pump. (PAX-17, DAX-190, p. 128). Other features of the pump such as pressure loaded end plates and the cartridge type flow control valve were significant *1371 factors in the selection of the F-T pump. (PAX-82).
(c) Ford contends that Rhine's contribution of the "mismatching area contact" did not figure in Ford's decision to adopt the F-T pump, and that the key factor in Ford's decision, manufacturing feasibility, had nothing to do with Rhine.
(d) Ford had to put up the capital ($350,000) to engineer the pump to a commercial level (Tr. 12203); it had to put up the capital (over $2 million) for tooling and facilities (DAX-150G); and it had to assume all the business risks associated with manufacturing both the pump and the vehicles in which the pump would be installed and sold.
Ford contends that, in light of considerations such as these, a reasonable and just outcome of the negotiations would have been an agreement that Ford would pay, as reasonable royalty for a non-exclusive license, a lump sum of $150,000. There appears to be no testimony as to that specific amount and the figure first appears in Defendant's Post Trial Brief and again in its proposed findings of fact. Ford's counsel, in his final argument before the court, suggested that based on an average royalty of 2¢ per pump multiplied by six million pumps the figure might have been "around" $131,000 and then concluded the negotiations would have resulted in Ford paying the lump sum of $150,000. (Tr. 19936-37). During the accounting proceedings, Mr. Harris, Ford's patent counsel, had testified that an appropriate royalty rate payable to Ellipse would have been 2¢ or 3¢ per pump based on various assumptions. (Tr. 15429-44).
24. Based on the testimony and exhibits in the original liability trial and in this accounting, the court finds there was still another bargaining range for the market value of a license under the patent. Ford has relied principally upon its alternatives and costs in its contentions as to a reasonable royalty. Despite Ford's contentions, the evidence indicates Ford would have paid more than the $150,000 it suggests as the outcome of the negotiations and even more than the $478,887 saving by using the F-T pump.
The court found upon the liability trial that Ford selected the F-T pump because it was more desirable; and the evidence adduced upon the taking of this accounting has further substantiated that finding. Ford did have alternatives available in 1963-64 that would have met Ford's power steering pump requirements and after evaluating them it found the Saginaw and F-T pumps technically superior. Ford did select the F-T pump because it believed at the time it would be easier and less costly to manufacture and had the most potential for design savings. However, the evidence here indicates the choice of the F-T pump over alternatives was not based solely on manufacturing feasibility and costs. In late 1962 and early 1963 Ford had decided it would be a good idea if it began to make power steering pumps; and it was interested in the possibility of manufacturing internally a portion of its requirements for such pumps. There were other advantages Ford saw in the F-T pump that would have been considered by Ford as a willing buyer in the hypothetical negotiations.
The Saginaw pump was controlled by General Motors, Ford's largest and strongest competitor. General Motors set the standards for the pump. It was manufactured in General Motors' environment, not in Ford's. As Fred M. Ison, General Sales Manager of Saginaw Steering Gear Division of General Motors, testified, there are good business reasons why a company wants to make its own product, including control of quality, better availability, better supply, serviceability, and compatibility of the pump with its own gear. He also admitted that in going into an agreement a company wants to control the manufacture and research so as to introduce the best improvements on a product it can. (Tr. 11818-21, 11833).
Plaintiff has contended that Ford made a decision to ignore Saginaw's design as a *1372 matter of policy. Ocie Walthall, Manager of Ford's Steering Gear Department in August, 1961, to July, 1965, admitted upon a deposition in connection with the liability trial that it would be better for Ford to have its own product rather than to buy a General Motors design. He also testified that Ford's policy is not to buy outside purchase parts from General Motors if Ford can get them at the same price from someone else. Mr. Walthall also admitted Ford was also considering whether with its own pump it might have a product on which it could pick up added sales. (PAX-137A, Item "R" at pp. 7, 8; Walthall Dep. pp. 220-227). The benefit of having its own product and its own design rather than a General Motors design is an advantage that would have entered into the negotiations for a reasonable royalty.
Plaintiff has also contended that there is no equivalent of the infringing balanced F-T pump and that there is no equivalence, of substantially the same structure operating in substantially the same way, between the F-T pump and either the Eaton or Saginaw pump. As this court found upon the liability trial (Finding 56), Ford believed the balanced slipper pump it proposed to make and sell was superior to existing pumps and that it included what it proclaimed to be new and useful concepts. (PAX-135, p. 1628). TRW subsequently patented devices that embodied Rhine's development of a balanced slipper pump and Ford sought out and obtained rights under such subsequent patents by becoming licensed thereunder. (Finding 50; PAX-135, p. 1625).
Despite Ford's contention that Rhine's contribution did not figure in Ford's decision to adopt the F-T pump, the Rhine contribution was embodied in the pump Ford considered more desirable; and rather than to have infringed, Ford would have negotiated for a license from Ellipse. Although a willing seller, Ellipse was not unaware of the interest of the automotive industry in balanced power steering slipper pumps. Ellipse has remained persistent in its efforts to interest others in taking a license under the Rhine patent. Simon Moss, Ellipse's president, did not believe that if hypothetical negotiations had not gone forward with Ford in 1963-64 that those negotiations would have represented to Ellipse the last chance to realize any return on the Rhine patent. (Tr. 10656). Although Ellipse lacked bargaining power (finding 21, supra), it is likely it would have, under the circumstances, bargained for considerably more than $12,000.
Although the evidence does not disclose what, if any, communications Ford might have had with TRW about the Rhine patent in the 1963-64 period of hypothetical negotiations, TRW manufactured and sold to Ford approximately 35% of the power steering pumps held to infringe Claim 3 of the Rhine patent. The pumps were sold pursuant to an August 8, 1963 agreement in which TRW agreed to indemnify Ford for the costs of defending any accounting proceeding and for any judgment based on patent infringement by the pumps purchased from TRW (DAX-60). On August 30, 1972, TRW filed a civil action (case No. 72 C 2167) against Ellipse and Ford, as defendants, seeking a declaratory judgment to establish Claim 3 of Patent 2,628,568 was invalid and void and seeking a stay of the accounting proceedings in this case. The court dismissed the action and the Court of Appeals affirmed. TRW, Inc. v. Ellipse Corporation, 495 F.2d 314 (7th Cir. 1974).
Rhine did not grant any licenses and there is no established royalty rate for the Rhine patent. Ellipse had not marketed a product. Therefore, the court must determine, retroactively, the question of what the market value of a license was under the Rhine patent and this market value will become the reasonable royalty to which Ellipse is entitled. The court, supra, has treated Ford's alternatives and costs in detail. Plaintiff's expert, Mr. Weinstein, admitted that based on an assumption of equal performance of the Saginaw and F-T *1373 pumps, Ford would not be willing to pay anything more than 9¢ per pump as a royalty, that being the difference between the quotation of Saginaw of $8.48 per pump and the quotation of $8.39 for the F-T pump. (Tr. 19068). Mr. Harris, Ford's patent counsel, testified that based on certain assumptions and under the circumstances in the 1963-64 period, an appropriate royalty rate payable to Ellipse would have been 2¢ or 3¢ per pump. (Tr. 15429, 15434, 15444). He justified the payment of a higher royalty rate to Vickers Corporation, for example, on, among other things, Vickers being a knowledgeable manufacturer, being able to offer services and having a proven product. However, the assumptions made in the questions upon which these answers were based did not include an assumption of the value to Ford of having a product not controlled by General Motors, Ford's largest and strongest competitor. T&C would have been permitted on a make part  buy part basis to manufacture a portion of Ford's steering part requirements using Saginaw's design and technology, provided Ford purchased the remainder of its requirements from Saginaw. Ford would have been subject to such limitations as General Motors might choose to make in connection with the Saginaw pump. Ford would have been concerned with the effect of the cost of a royalty to Ellipse on the F-T pump, but as prudent businessmen Ford's management would have recognized the advantage of having the F-T pump rather than one controlled by General Motors.
The foregoing advantages should be taken into consideration together with alternatives and costs in determining reasonable royalty. The court reaches a conclusion as to the reasonable and just outcome of the hypothetical negotiations in its Conclusion, infra. In reaching the conclusion, the court has taken into consideration the following additional factors, including an assessment of the impact of the facts and events transpiring subsequent to 1963-64, other patent licenses granted to Ford and Ford's negotiations for other power steering pump licenses.

Facts and Events Transpiring Subsequent to 1963-64
25. (a) Due to the changes required to make the F-T pump commercially acceptable (Tr. 12197-12203; DAX-133-135), the price actually paid by Ford for the F-T pump turned out to be in excess of the price at which Ford could have purchased the Saginaw pump throughout the infringing period. (Saginaw's prices are found in DAX-119C-L)[12]
(b) To the extent Ford experienced an increase in installation rate of power steering options in Ford automobiles, that increase merely paralleled that of the auto industry as a whole.[13] This was the case both during 1960-1964 when the Eaton pump was used and during 1965-1970 with the F-T pump (DAX-122M). Since Ford cars are not purchased because of the particular pump in it, the fact that Ford sold more cars equipped with power steering pumps than was anticipated in 1963-64 cannot be attributed to Rhine.
(c) Ford expected the F-T pump, because of the cartridge construction of the pumping *1374 element and flow control valve, to be more serviceable. In fact, the dealers encountered extreme difficulty in servicing the pump. (DAX-83).
(d) Ford purchased F-T pumps from TRW at the following average prices: $9.84 (1965), $10.30 (1966), $10.39 (1967), $10.34 (1968), $10.48 (1969), $10.37 (1970).[14] T&C, which operates as a separate profit center in the Ford organization, "sold" the F-T pumps it manufactured to the Ford Division at a transfer price governed by TRW's prices. During the period 1964 to February, 1970, T&C lost an average of 28¢ per pump (DAX-158, 159; Tr. 14812-24). TRW had a similar experience during the same period, sustaining a loss of 2.3% on its sales of the F-T pump to Ford. (DAX-136; Tr. 12619-34)

Examples of Patent Licenses Granted to Ford
26. DAX-160 summarizes all of the patent licenses taken by Ford on high volume items to be used in automobiles during 1955-70. That exhibit, and the testimony of Robert Harris, Ford's patent counsel for 35 years, establishes that a reasonable royalty on such high volume items is less than 1%, usually 0.1% to 0.5%, of the price the automotive company pays for the item. In the automotive field, the royalty is usually expressed in the license agreement either as a lump sum or as a fixed amount per unit[15] with a specified paid-up maximum royalty or "cap" (Tr. 15215-31; DAX-160). The following are examples from that exhibit:
(a) In 1956, Ford negotiated a non-exclusive license on a group of patents for automatic transmissions. The unit royalty was 50¢-60¢ on transmissions costing approximately $150. Ford sold millions of the transmissions covered by these patents. (Tr. 15265). Expressed as a percentage, the royalty ($0.60 ÷ $150) is 0.4%. (DAX-160, License G-57; Tr. 15259-66).
(b) In 1953, Ford negotiated, and in 1963, renegotiated, a non-exclusive license on automatic transmissions. The royalty varied by car line, ranging from 5¢ to 15¢ per car with a paid-up cap of $200,000. Millions of transmissions were sold by Ford. Expressed as a percentage, the maximum per unit royalty ($0.15 ÷ $150) is 0.1%. (DAX-160; License S-73; Tr. 15281-85).
(c) In 1959, Ford negotiated a non-exclusive license on an anti-dive suspension system that was used on a number of Ford's car lines. The royalty was 5¢ per vehicle. (DAX-160, License T-36; Tr. 15275-77).
(d) In 1963, Ford negotiated a non-exclusive license under a patent on synchronizers for manual transmissions. The specified royalty was a lump sum of $200,000. (DAX-160, License P-53; Tr. 15275-77).
(e) In 1965, Ford negotiated a non-exclusive license under a patent for an automatic choke that Ford then used in millions of its carburetors; the carburetors each cost in the range of $10-20. The royalty specified was a flat 5¢ per carburetor. Expressed as a percentage of $10, the royalty is 0.5%. (DAX-160, License G-73; Tr. 15267-70).
(f) In 1967, Ford was non-exclusively licensed under a group of patents on storage batteries. Ford paid a lump sum of $225,000 for the license and an additional $225,000 for technical assistance from the licensor. Millions of the batteries were produced *1375 at an average cost of $10. Assuming production of five million batteries, the royalty expressed as a percentage $225,000 ÷ $50,000,000 is 0.45%. (DAX-160, License G-78; Tr. 15271-74).
Other evidence on licenses in the accounting record is also pertinent:
(g) Mr. Snyder, one of Ellipse's patent experts, was a former employee of Borg-Warner Corporation. In describing his licensing experience, he identified a license negotiated with Ford under certain Roche patents pertaining to transmissions. (Tr. 7499-501, 7514, 7520). That license (DAX-161) required Ford to pay a flat rate of 18.5¢ per unit on transmissions that cost Ford approximately $150. Expressed as a percentage, the royalty ($0.185 ÷ $150) was 0.12%. (Tr. 15369-80)
(h) As a result of litigation with International Nickel Company, Ford, in 1959, took a non-exclusive license under a patent on nodular iron technology useful in Ford's production of crankshafts. The royalty rate was 1.14 per ton. Ford was producing about 40 crankshafts per ton for an average royalty of 2.8¢ per crankshaft. The price of a crankshaft was about $5.00 so the royalty, expressed as a percentage ($0.028 ÷ $5.00) was 0.5%. (Tr. 16626-42).

Other Power Steering Pump Licenses
27. (a) In 1960, Ford negotiated a nonexclusive license under 14 patents owned by Vickers on its vane type power steering pumps. In addition, Vickers agreed to supply Ford with blueprints and technical assistance in manufacturing the pump. (DAX-151; Tr. 13679-80). The royalty specified was 30¢ per pump with a paid up maximum royalty of $700,000. Allocating the amount over the total number of F-T pumps used by Ford up to February 17, 1970 represents a unit royalty of 7.7¢ per pump. Vickers was a knowledgeable manufacturer with a demonstrated commercial product.[16] It could provide substantial technical assistance for producing the pump and, because of its demonstrated commercial use, the licensee assumed little risk in producing and using it. Ellipse had no manufacturing knowledge to provide a licensee and the pumps it had made were neither commercially proven nor acceptable. (Tr. 13693-98, 15429-33).
(b) In 1952, Federal Industries (a predecessor of TRW) negotiated an exclusive license from William T. Livermore under a number of Livermore patents on slipper pumps. (DAX-53B). At least one of the licensed patents (No. 2,599,927) also covered the F-T pumps here at issue. (DAX-150C). The license provided for royalties on the following scale:


First           10,000 Licensed Pumps        5% of Net Sales
Next            10,000 Licensed Pumps        4% of Net Sales
Next            10,000 Licensed Pumps        3% of Net Sales
Next           170,000 Licensed Pumps    1 2/3 % of Net Sales
Next           300,000 Licensed Pumps        1% of Net Sales
Next         1,000,000 Licensed Pumps     2/3 % of Net Sales
Next         2,000,000 Licensed Pumps     1/3 % of Net Sales
Remainder              Licensed Pumps     ¼% of Net Sales
                                                  (DAX-53B)

Applying the foregoing scale of royalties to the total number of F-T pumps in this case, the average royalty rate would be 0.846%. (DAX-156A, B; Tr. 14799-14804, 14809-10). At TRW's average sale price of approximately $10 for each F-T pump, the Livermore royalty on a unit basis would have been 8.5¢ per pump. Livermore was a well known inventor in this field (App. II pp. 1528-29, 1549-50), and the license he granted to Federal was exclusive under a number of patents. Ellipse had no reputation in this field and the license it would grant would be nonexclusive under a single patent.

Conclusion
28. In 1963 the Saginaw pump, which would have served the same purpose as the F-T pump, was offered to Ford at a price of $8.48 per pump (DAX-119A, Tr. 11734-40) at about the same time that the F-T pump was offered to Ford by TRW at a price of $8.39, a price which was 9¢ less per *1376 pump. (DAX-132, DAX-150F, Tr. 19065-68).
As Ford considered the F-T pump more desirable and advantageous, it is reasonable to assume that Ford as a prudent buyer would have paid some larger amount than 8.5¢ or 9¢ per pump for the F-T pump but very little more. The court finds that, under all the circumstances and facts as they existed immediately prior to the time Ford began using the F-T pump, Ford would not have paid more than 10¢ per pump as a reasonable royalty to Ellipse. The court finds Ellipse would have accepted 10¢ per pump as a reasonable royalty at the time and that 10¢ per pump would have been agreed upon as a reasonable royalty if Ford had known that Ford's use of the F-T pump would infringe Rhine's patent. Ellipse would have accepted such a royalty as it then had no other market for its patent. By entering into such a royalty agreement Ellipse would have been assured a substantial income from a royalty on millions of pumps using its patent.
Accordingly, the court finds that a reasonable royalty to which Ellipse is entitled is 10¢ per pump upon 6,568,203 pumps used by Ford, or $656,820.30. This amount is Ellipse's damages. The court further finds that Ellipse should be awarded judgment for that amount less certain adjustments as set forth in the following Additional Findings of Fact.

Additional Findings of Fact
29. On September 1, 1978, Special Master David J. Shipman filed herein a Master's Certificate for Compensation in which he sought to have the amount of his compensation determined and assessed by the court. Counsel for the parties filed responses thereto. Thereafter a signed stipulation, dated October 25, 1978, was presented to the court in which counsel for the parties and the Master stated (1) that in accordance with an earlier joint proposal of the parties on September 25, 1978, the Master had agreed that under all the circumstances a fair and reasonable fee for the Master as his total compensation for this matter would be $150,000; (2) that $110,000 had already been paid to the Master by payments of $80,000 by Ford and $30,000 by Ellipse; and (3) that counsel for the parties and the Master stipulate that an additional sum of $40,000 is due the Master and that this amount may be incorporated in the court's Final Judgment in this case. The court then ordered Ford to advance the $40,000, in accordance with the stipulation, on behalf of itself and Ellipse, and specifically provided that Ford should receive credit for the $40,000 against any judgment entered against it in favor of Ellipse and that said sum of $40,000 should be only an advance by Ford and in no way fixed liability of the parties for any part of the Master's fees. The court agrees that the $150,000 stipulated to by counsel for the parties and the Master is, under all the circumstances, a fair and reasonable fee.
A general standard for setting the Master's compensation is set forth in 5A Moore's Federal Practice, ¶ 53.04[1] at 2926 (1971):
The court should consider the time necessarily spent by the Master, his ability and distinction, the thoroughness of his services, the amount of money or the importance of the matter involved, and the assistance he has given to a final disposition of the issues that were referred to him.
The court has read the record of the taking of this accounting and at various times has been personally involved in the accounting. It, therefore, is in a good position to consider the factors entering into a determination of reasonable compensation for the Special Master's services. The Master in his Certificate states that there were approximately 250 trial sessions which produced 231 volumes of transcript totalling over 19,500 pages and that by the end of 1977 he had spent over 4,000 hours in this reference. Counsel for each of the parties *1377 in their responses state that counting pretrial conferences, depositions and all days of trial, the Master participated with counsel in proceedings a total of 226 days and both estimate that the Master devoted a total of 636 to 795 hours to actual trial during 1975-77. Counsel for both parties also stated in their responses that they have no way of knowing how much time was spent by the Master, out of the presence of counsel, on this case.
The Master held some 35 pretrial meetings in order to seek agreements and narrow issues of fact and law. He conducted tri-party telephone conversations, and spent 16 days taking depositions in Chicago and Dearborn, Michigan. A variety of motions were made regarding issues which were contested by the parties and the Master spent considerable time studying briefs and preparing his rulings. There was involved an unusual amount of time in correspondence and other informal methods of communications. This accounting was bitterly contested and the record reflects many problems encountered by the Master in dealing with some of the counsel. It is obvious from the record that the Master spent many hours outside the presence of counsel in legal research and in dealing with the complex factual and legal problems involved.
The court finds that the Special Master devoted at least 4,000 hours to this case over approximately a six year period and that the sum of $150,000 is a reasonable amount to be awarded to him as compensation for his services and his contribution to final disposition of the issues referred to him.
Under ordinary circumstances, the whole of the Special Master's compensation for an accounting should be assessed against the infringer but the court has discretion to apportion the Master's fees and costs among the parties. In this case the court finds that part of such fees and costs should be charged against Ellipse. Ellipse offered extensive testimony and a voluminous number of exhibits in contending for its theory that an award should be based upon Ford's profits rather than Ellipse's damages. Ellipse abandoned some of its charges against Ford on the eve of the liability trial. The Court of Appeals reversed the decree of this court in part. Ellipse offered an excessive amount of irrelevant evidence upon the taking of this accounting. Ellipse has needlessly prolonged this litigation and added to the expense of this accounting. The foregoing are among many factors considered by the court in apportioning the Master's fees and costs.
The court finds it would be inequitable to assess the entire cost of this accounting against Ford. Having reviewed the entire record, it is the court's judgment that each of the parties should bear its own costs and that the parties should share equally both the transcript costs and the Master's fees and costs.
The total amount payable for the Master's fees and costs is $150,000 and a one-half share is $75,000. Ellipse has made advances totalling $30,000 toward payment of the Master's fees and costs, and the amount remaining due from Ellipse under the apportionment is $45,000. Ford has made advances of $55,000 on its own behalf and has made advances totalling $25,000 on behalf of Ellipse, and has further advanced $40,000 on behalf of itself and Ellipse, for a total of $120,000 in payments to the Master. Having already paid $120,000, Ford has an overpayment of $45,000 on its $75,000 share of the Master's fees and costs; and Ford is entitled to a credit therefor against Ellipse's award, thereby reducing Ellipse's award to $611,820.30.
30. Pursuant to the court's orders, Ford has advanced $16,211.13 in payment of Ellipse's share of the court reporter's charges. Ellipse is liable for said sum and Ford should be credited with that amount. The court finds said $16,211.13 should be deducted from Ellipse's award, already reduced to $611,820.30, leaving the sum of $595,609.17.
*1378 31. The court has found that each of the parties should bear its own costs in connection with this accounting proceeding. However, there remains outstanding the matter of an award of certain attorney fees to Ford. On appeal, following the liability trial, the United States Court of Appeals in its decision stated:
We affirm, however, the award of attorney fees to Ford representing the added costs borne by Ford because of the prosecution under the original complaint, until abandoned at the beginning of the trial. Until the abandonment Ford was necessarily put to defending the charge that its transmission pumps infringed the Rhine patent. We think the district court could properly award it attorney fees under Section 285 as a "prevailing party." A proper construction of "prevailing party" applies in the award to Ford under Section 285 because Ford effectually prevailed as to the charge with respect to the transmission pump. Moreover, the award is valid under F.R.C.P. 41(a)(2). 452 F.2d 163, 172
Having reviewed the record in the liability trial, the court finds that it is familiar with the amount of time Ford's attorneys spent in defending that part of the complaint that was abandoned by Ellipse and with the fair value of attorneys' services therefor, and finds that $5,000 is a reasonable amount to be awarded Ford for attorney fees as provided in the opinion of the Court of Appeals. Said $5,000 should be credited to Ford and deducted from Ellipse's award, thereby reducing Ellipse's award further to $590,609.17.
32. The amount of $590,609.17 is the amount of the judgment that should be entered herein in favor of Ellipse and against Ford.
33. The court finds that a reasonable royalty could not be determined until the conclusion of the accounting proceedings, and that damages accrue, and that interest thereon should run, only from the date of the court's entry of a judgment establishing the amount of reasonable royalty.
A judgment in this cause is being entered simultaneously with the court's Findings of Fact and Conclusions of Law; and interest on that judgment should be awarded only for the period following entry of the judgment.
This accounting proceeding was needlessly prolonged by Ellipse's persistence in its fallacious theory of profit apportionment. Had this accounting proceeded upon the lawful issue of damages to Ellipse, this court estimates the accounting proceedings could have been concluded within six months instead of six years.

CONCLUSIONS OF LAW
1. Ellipse is entitled to damages adequate to compensate it for defendant's infringement, but in no event less than a reasonable royalty. 35 U.S.C. § 284.
2. Ellipse having failed to mark its own pumps with the number of the Rhine patent and having failed to notify Ford of its infringement, the relevant period of accounting commences on August 2, 1966, the date this action was instituted. 35 U.S.C. § 287. Dunlap v. Schofield, 152 U.S. 244, 14 S.Ct. 576, 38 L.Ed. 426 (1894); Union Carbide Corp. v. Graver Tank & Mfg. Co., 282 F.2d 653 (7th Cir. 1960), cert. denied, 365 U.S. 812, 81 S.Ct. 692, 5 L.Ed.2d 691 (1961); Smith v. Dental Products Co., Inc., 140 F.2d 140 (7th Cir.), cert. denied, 322 U.S. 743, 64 S.Ct. 1146, 88 L.Ed. 1576 (1944).
3. In patent law terms, what the infringer makes by his infringement are "profits," and what the patent holder loses through the infringement are "damages." Aro Mfg. Co., Inc. v. Convertible Top Replacement Co., Inc., 377 U.S. 476, 84 S.Ct. 1526, 12 L.Ed.2d 457 (1964).
4. While, prior to 1946, a patent holder whose patent had been infringed was permitted to recover the profits realized by the infringer from his infringement, it is well settled under 35 U.S.C. § 284 that the *1379 patent holder's damages, not the infringer's profits, are the sole basis of recovery. Aro Mfg. Co. v. Convertible Top Replacement Co., Inc., supra; Zegers v. Zegers, Inc., 458 F.2d 726 (7th Cir.), cert. denied, 409 U.S. 878, 93 S.Ct. 131, 34 L.Ed.2d 132 (1972); W. L. Gore & Assoc., Inc. v. Carlisle Corp., 198 U.S.P.Q. 353 (D.Del.1978), Georgia-Pacific Corp. v. United States Plywood Corp., 243 F.Supp. 500 (S.D.N.Y.1965).
5. It is the pecuniary loss that the patent holder has suffered from the infringement that is the basis for computing damages under 35 U.S.C. § 284. Aro, supra, at 507; Foster v. American Machine and Foundry Co., 492 F.2d 1317 (2nd Cir. 1974), cert. denied, 419 U.S. 833, 95 S.Ct. 58, 42 L.Ed.2d 59 (1974). Where the patent holder has not and cannot itself exploit the patent, the only pecuniary loss suffered is the loss of royalties the patent holder would have, hypothetically, received had the infringing use of the patent been made under an appropriate license agreement. Trio Process Corp. v. L. Goldstein's Sons, Inc., 533 F.2d 126 (3rd Cir. 1976), Zegers v. Zegers, Inc., supra.
6. In determining the magnitude of the royalty lost by the patent holder, the court endeavors to determine, retroactively, the reasonable market value of a license under the patent; this market value is what the courts have called a "reasonable royalty". Egry Register Co. v. Standard Register Co., 23 F.2d 438 (6th Cir. 1928). To arrive at market value and, hence, the amount of the reasonable royalty, the court applies the willing buyer  willing seller rule as stated in Horvath v. McCord Radiator & Mfg. Co., 100 F.2d 326, 335 (6th Cir. 1938), cert. denied, 308 U.S. 581, 60 S.Ct. 171, 84 L.Ed. 529 (1939):
In fixing damages on a royalty basis against an infringer, the sum allowed should be reasonable and that which would be accepted by a prudent licensee who wished to obtain a license but was not so compelled and a prudent patentee, who wished to grant a license but was not so compelled.
This statement of the rule was approved and applied in this circuit in Union Carbide Corp. v. Graver Tank & Mfg. Co., 282 F.2d 653 (7th Cir. 1960), cert. denied, 365 U.S. 812, 81 S.Ct. 692, 5 L.Ed.2d 691 (1961), and the same rule has been applied in other circuits. See, e. g., Foster v. American Machine & Foundry Co., supra; Georgia-Pacific Corp. v. U. S. Plywood-Champion Papers, Inc., 446 F.2d 295 (2d Cir.), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971); Egry Register Co. v. Standard Register Co., supra; A. Mecky Co. v. Garton Toy Co., 277 F. 507 (E.D.Wisc.1921); Olsson v. United States, 25 F.Supp. 495, 87 Ct.Cl. 642 (1938), cert. denied, 307 U.S. 621, 59 S.Ct. 792, 83 L.Ed. 1500 (1939); W. L. Gore & Assoc., Inc. v. Carlisle Corp., supra.
7. Determination of a reasonable royalty by application of the willing buyer  willing seller rule assumes a hypothetical negotiation in advance of infringement between the patent owner and the potential infringer, the court viewing the situation from the respective positions of the parties in light of the facts and circumstances as they existed at that time. Panduit Corp. v. Stahlin Brothers Fibre Works, Inc., 575 F.2d 1152 (6th Cir. 1978); Foster v. American Machine & Foundry Co., supra; Tektronix, Inc. v. United States, 552 F.2d 343, 349 (Ct.Cl.1977); Georgia-Pacific Corp. v. U. S. Plywood, Inc., 446 F.2d at 296; Egry Register Co. v. Standard Register Co., 23 F.2d at 443; A. Mecky Co. v. Garton Toy Company, supra; Tights, Inc. v. Kayser-Roth Corp., 442 F.Supp. 159 (M.D.N.C.1977).
8. An important factor to be considered in determining a reasonable royalty is the advantage of the patented item over other alternatives available in the market place. Hughes Tool Co. v. G. W. Murphy Industries, Inc., 491 F.2d 923 (5th Cir. 1973); Malleable Iron Range Co. v. Lee, 263 F. 896, 899 (7th Cir.), cert. denied, 251 U.S. 562, 40 S.Ct. 342, 64 L.Ed. 415 (1920); United States Frumentum Co. v. Lauhoff, 216 F. 610, 617 (6th Cir. 1914). The patent owner may recover only for the difference *1380 between the patented product and such other products as the infringer could have used had he known he infringed. Union Carbide Corp. v. Graver Tank & Mfg. Co., 345 F.2d 409, 411 n. 2 (7th Cir. 1965); Union Carbide Corp. v. Graver Tank & Mfg. Co., 282 F.2d 653 (7th Cir. 1960), cert. denied, 365 U.S. 812, 81 S.Ct. 692, 5 L.Ed.2d 691 (1961); Columbia Wire Co. v. Kokomo Steel & Wire Co., 194 F. 108, 110 (7th Cir. 1911).
9. Profits have been considered a relevant factor in negotiations between a willing buyer and willing seller only where the patent holder has had an established practice of maintaining the patent monopoly to himself for his own exploitation and profit. See, e. g., Georgia-Pacific Corp. v. U. S. Plywood-Champion Papers, Inc., 446 F.2d 295 (2d Cir.), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971); Tektronix, Inc. v. United States, 552 F.2d 343 (Ct.Cl.1977). Those facts are not present here. Nor does Ford, as a user of pumps in the power steering systems incorporated in its cars, have a separate "profit" on such pumps. Cf. Sessions v. Romadka, 145 U.S. 29, 45, 12 S.Ct. 799, 36 L.Ed. 609 (1892). Plaintiff's attempt to apportion a "profit" to the pump has no relevance to the determination of reasonable royalty. Congress amended the patent statute in 1946 to eliminate the recovery of profits precisely because of the impossibility of apportioning profits to a piece or part of a larger entity. See, Recovery in Patent Infringement Suits: Hearings on H.R. 5231 (5311) Before the House Comm. on Patents, 79th Cong., 2d Sess. (1946); Senate Report No. 1503, U.S.Code Cong.Service, 79th Cong., 2d Sess. p. 1386 (1946).
10. In applying the willing buyer  willing seller rule, the court determines in light of the facts and circumstances at the time of the hypothetical negotiations, the maximum that a willing licensee would have been willing to pay for a license and the minimum that a willing licensor would have accepted. Georgia-Pacific Corp. v. United States Plywood Corp., 318 F.Supp. 1116, 1121-22 (S.D.N.Y.1970), modified, 446 F.2d 295 (2d Cir.), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971); W. L. Gore & Assoc., Inc. v. Carlisle Corp., 198 U.S.P.Q. at 369-70.
11. Considering the amount that Ford, as a prospective willing buyer, would have been willing to pay and the amount that Ellipse, as a prospective willing seller, would have been willing to accept, it is concluded, under the circumstances of this case, that the sum of $656,820.30 is a reasonable royalty and constitutes damages adequate to compensate Ellipse for Ford's infringement. This amount is subject to adjustment, as set forth in findings 29, 30, 31 and 32, supra, to an amount of $590,609.17.
12. It is the rule in this circuit that interest should run from the date damages are liquidated, absent exceptional circumstances. Wahl v. Carrier Manufacturing Co., Inc., 511 F.2d 209, 215 (7th Cir. 1975). Exceptional circumstances require a clear showing of bad faith and fraud which would constitute a gross injustice if not remedied. Columbia Broadcasting System, Inc. v. Zenith Radio Corp., 537 F.2d 896 (7th Cir. 1976). Exceptional circumstances are not present in this case, as the Court of Appeals has so held. Ellipse Corp. v. Ford Motor Co., 452 F.2d 163, 172 (7th Cir. 1971). Ellipse, therefore, is entitled to interest only from the date damages accrue. In the case of a reasonable royalty damages accrue, and interest runs, only from the date of the judgment establishing the amount of the reasonable royalty. Wahl v. Carrier Mfg. Co., Inc., supra.
13. Rule 53 of the Federal Rules of Civil Procedure vests the court with discretion to apportion the Master's fee among the parties. Stromberg Motor Devices Co. v. Detroit Trust Co., 44 F.2d 958 (7th Cir. 1930); Cold Metal Process Co. v. Republic Steel Corp., 233 F.2d 828 (6th Cir.), cert. denied, 352 U.S. 891, 77 S.Ct. 128, 1 L.Ed.2d 86 (1956). See generally, Moore's Fed.Prac. ¶ 53.04[1]; Reid v. Silver, 354 F.2d 600 (7th Cir. 1965). Similar discretion is granted under Rule 54 with respect to the taxation *1381 of costs. Wahl v. Carrier Mfg. Co., Inc., supra; Popeil Bros., Inc. v. Schick Electric, Inc., 516 F.2d 772 (7th Cir. 1975); Jones v. Schellenberger, 225 F.2d 784 (7th Cir. 1955), cert. denied, 350 U.S. 989, 76 S.Ct. 476, 100 L.Ed. 855 (1956). Having reviewed the entire record, it is this court's judgment that each party should bear its own costs and that the parties should share equally both the transcript costs and the Master's fees.
14. The court concludes $5,000 is a reasonable amount to be awarded Ford for certain attorney fees as provided in the opinion of the Court of Appeals in this case. Ellipse Corp. v. Ford Motor Co., supra.

FINAL JUDGMENT
This cause came on before the court as to the matter of damages to be awarded the plaintiff Ellipse Corporation ("Ellipse") to compensate it for defendant Ford Motor Company's ("Ford") infringement of Claim 3 of the Rhine Patent No. 2,628,568.
The court has considered the testimony and the exhibits presented by the parties in the accounting proceedings before the Special Master and before the court; and the court has also considered the briefs of counsel and has heard oral argument of counsel. The court has further considered the petition of the Special Master for fees and costs; the responses thereto; and the Stipulation regarding the Master's fees filed thereafter by counsel for the parties.
Being fully advised in the premises, the court has this day entered simultaneously herewith its Findings of Fact and Conclusions of Law, and in accordance therewith it is ORDERED, ADJUDGED and DECREED as follows:
1. Damages in the total amount of $656,820.30 are awarded Ellipse as full, complete and adequate compensation under 35 U.S.C. § 284 for Ford's infringement less certain credits to Ford as hereinafter set forth.
2. Each of the parties shall bear its own costs of this accounting and the parties shall share equally both the transcript costs and Special Master's fees and costs.
3. The Special Master, David J. Shipman, is allowed the total amount of $150,000 for his fees and costs. In accordance with the court's orders and taking into account the advances heretofore made by the parties to the Special Master, the amount due the Master is apportioned between the parties, as detailed in the court's accounting Finding of Fact 29 and Conclusion of Law 13 and as summarized as follows:
(a) Ellipse's one-half share of the Master's fees and costs is $75,000. Having made advances of $30,000 toward payment of its share, the amount remaining due from Ellipse under the apportionment is $45,000. Ellipse is liable for that amount.
(b) Ford has made advances of $55,000 on its own behalf and $25,000 on behalf of Ellipse; and Ford has further advanced $40,000 on behalf of itself and Ellipse. Having already paid $120,000, Ford has an overpayment of $45,000 on its $75,000 share of the Master's fees and costs.
(c) Ford is entitled to, and shall have, a credit for its $45,000 overpayment against Ellipse's award, thereby reducing Ellipse's award to $611,820.30, and thereby eliminating Ellipse's obligation to the Master for the remaining $45,000 of its share of the Master's fees and costs.
4. Pursuant to the court's orders of July 18, 1977 and November 11, 1977, Ford advanced $16,211.13 in payment of Ellipse's share of the court reporter's charges. Ellipse is liable for said amount and Ford shall be credited with that amount against Ellipse's award. Ellipse's award, already reduced to $611,820.30, shall be further reduced by said $16,211.13, leaving a total of $595,609.17.
5. In accordance with the court's Finding of Fact 31 in this accounting proceedings, Ellipse shall pay to Ford the sum of $5,000 as reasonable attorney fees for time spent in defending that part of the complaint abandoned by Ellipse in connection with the liability trial. Said $5,000 shall be credited to Ford and against Ellipse's award, thereby reducing Ellipse's award further to $590,609.17.
*1382 6. Ellipse shall recover from Ford the total sum of $590,609.17, together with simple interest at lawful rate from the date of this Judgment.
7. Upon payment by Ford to Ellipse of said $590,609.17, Ellipse shall execute and deliver to Ford a written release of all claims arising under U.S.C., Titles 28 and 35, based on the manufacture, use or sale of any and all of the infringing devices included in this action.
NOTES
[1]  35 U.S.C. § 284 provides in pertinent part:

"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.
* * * * * *
The court may receive expert testimony as an aid to the determination of damages or of what royalty would be reasonable under the circumstances."
[2]  Abbreviations used herein are:



  "Tr. ___"   - The accounting trial transcript.
  "PAX ___"   - Plaintiff's accounting exhibit.
  "DAX ___"   - Defendant's accounting exhibit.
  "App. ___"  - The appendix on appeal in the liability
                phase.
  "T&C"       - Transmission & Chassis Division
                of Ford Motor Co.
  "TRW"       - TRW, Inc., previously Thompson
                Ramo Woolridge, Inc.
  "F-T pump"  - The pump that is the subject of
                this accounting, sometimes referred
                to as the Thompson pump.
  "Findings"  - Findings of the court in the liability
                trial.
  "Master"    - David J. Shipman, Special Master
                appointed for the purpose of taking
                the accounting.

[3]  Even if a cost ratio apportionment was relevant, the approach plaintiff has used is unsatisfactory. For example, plaintiff's cost ratio omits a number of elements of cost that are incurred by Ford before an automobile equipped with a power steering pump leaves the factory. Having erroneously omitted these costs, the resulting "profit" computation is erroneous as well (Tr. 14717-20, 14675-76). Plaintiff also separates the pump and the power steering system from the car in which they are sold, in effect treating Ford as a marketer of pumps. Since the car is a necessary part of any sale of a power steering system, any apportionment of profit must include the vehicle in which the pump is installed and sold. Defendant has demonstrated that, had plaintiff included the vehicle in its cost ratio methodology, there would be no "excess" profit. (DAX-155D, 162, 163).
[4]  Job No. 1 refers to the start of a new model year. The model year 1965 started at approximately August 1, 1964.
[5]  Eaton's belt driven pump was pressure unbalanced and this was the major reason it was rejected by T&C. (Tr. XXXXX-XXX; 12690-91). In 1962 Ford had encountered problems with that pump and the T&C engineers believed that the root of the problem resided in its unbalanced design. While Eaton assured Ford that the problem was only one of quality control and that the problem had been corrected, T&C engineers were skeptical. It was not until mid-1963 that it became apparent that Eaton was correct. By that time the T&C engineers had recommended that the F-T pump be adopted (Tr. 12212-13, 12256-61). Ford did continue to purchase the crankshaft mounted roller pump from Eaton throughout the period 1963-70 (Tr. 12143) and, in fact, purchased and used the unbalanced Eaton belt driven pumps in model years 1964 and 1965 without any problems. (Tr. 11612, 12207, 12871).
[6]  "Design savings" refers to savings achieved through a change in design. (Tr. 14432) In the case of the F-T pump, the changes in design ultimately required to make it acceptable increased the cost of the pump very substantially. See, Finding 25(a), infra.
[7]  The price of $8.74 in DAX-132 included tooling amortization at 18¢ per unit and a warranty charge of 17¢ per unit, with the base pump price set at $8.39.
[8]  In fact, Ford commenced purchasing vane type pumps from Saginaw in 1971; those pumps were basically the same pumps offered by Saginaw in 1963. (Tr. 12689-90). By 1977, Ford was using the Saginaw pump on 6 car models. (Tr. 11612, 12681)
[9]  Plaintiff's profit theory on which it has based its entire case ignores this fundamental point. All of the witnesses to have addressed the point are unanimous in their testimony that when revenue will not vary among several alternatives, the prudent businessman looks to the relative costs of the alternatives, not to profit. (See the testimony of Mr. Soper, Tr. 14767-72; Mr. Harris, Tr. 15222-26; Mr. Cameron, Tr. 14459, 14601-04; Dr. Weil, Tr. 16985-17065, 17066-71; Mr. Weinstein, Tr. 18986-88, 19065-69). There is no evidence that Ford, as a prospective licensee, would have considered "profits" in negotiations for a license. In fact, since the F-T pump is but a part of a larger entity, there is no identifiable "profit" on the pump.
[10]  Plaintiff's proposed royalty would have converted the F-T pump from one highly competitive in cost to one that was almost $6 more expensive than the equally acceptable Saginaw pump. (DAX-157).
[11]  In Union Carbide Corp. v. Graver Tank & Mfg. Co., 345 F.2d 409 (7th Cir. 1965), the court held, at 411, n. 2:

... in calculating damages, the patent owner may recover only for the difference between the patented product and such other as the infringer could have used had he known he infringed....
Mr. Weinstein agreed that DAX-180 assesses the difference between the F-T and Saginaw pumps. (Tr. 19006-9). Mr. Weinstein was unable to identify any relevant item of cost overlooked in DAX-180 (Tr. 19065). Nor was he able to identify any specific costs, known to the parties in 1963-64, that should have been used in place of those used in DAX-180 (Tr. 19063-65; 19010-27). Plaintiff's proposed royalty computations wholly ignore the differences between the alternatives available to Ford and the effect of such alternatives on negotiations for a royalty. See, e. g., Hughes Tool Co. v. G. W. Murphy Industries, Inc., 491 F.2d 923, 930-31 (5th Cir. 1973).
[12]  For example, due to the numerous engineering changes required in the F-T pump, TRW's original price had, by Job No. 1, 1965, risen by 84¢ (DAX-133-135). As a result, the average price of an F-T pump in 1965 was $9.84; Saginaw's price was $8.57. (DAX-119H). Adjusting the F-T price to eliminate 35¢ for tooling amortization and warranty (items not included in the Saginaw unit price) and the cost of painting and identification tags (11¢) (DAX-133-135) which would have been applicable to all pumps, Saginaw's pumps were still less expensive than the F-T pump. However, by the time that became apparent, Ford had invested over $2 million at T&C in tooling and facilities (DAX-150G) and $350,000 in engineering costs (Tr. 12203) to make the F-T pump.
[13]  The popularity of power steering on an industry wide basis is reflected in the installation rate of power steering systems in automobiles which rose from 4.6% in 1952 to approximately 50% in 1963-64 and continued to increase until by 1970 the rate had reached 85%. (DAX-122L, M).
[14]  Ellipse erroneously contends these prices represent Ford's costs for the F-T's pump and has used those amounts in its cost ratio to apportion a profit to the pump for each of the model years. There are many other elements of cost, such as transportation, labor and overhead, associated with the pump and incurred by Ford before an automobile equipped with a power steering pump leaves the factory. (Tr. 14717-20)
[15]  Ellipse's patent expert, Mr. Snyder, testified that a fixed per unit royalty is frequently used for devices that may be incorporated in a larger unit and it is difficult to assess what the value of the device is to the overall structure. (Tr. 7599). A royalty on a percentage basis is used, according to Mr. Snyder, when the patented item is sold separately (Tr. 7600) and a lump sum royalty is also sometimes used. (Tr. 7602-4).
[16]  The Saginaw pump was based on the Vickers design. (Tr. 11797, 11811).
