31 Fed. Cl. 481 | Fed. Cl. | 1994
OPINION ON DAMAGES
Hughes Aircraft Company owns U.S. Patent No. 8,758,051, entitled “Velocity Control and Orientation of a Spin-Stabilized Body,” which describes an apparatus for controlling the attitude of a spin-stabilized spacecraft. The patent was issued to Hughes on September 11, 1973, as assignee of inventor and former Hughes employee, Donald D. Williams. The patent, commonly referred to as the Williams patent, expired on September 11, 1990.
I
Hughes brought this action pursuant to 28 U.S.C. § 1498, seeking just compensation for the unlicensed use or manufacture by or for the government of spacecraft containing an embodiment of the patented apparatus.
Hughes filed its complaint on November 13, 1973. A description of the course of this litigation, including appeals of trial court determinations, is set forth in an Opinion on Liability dated August 16, 1993, 29 Fed.Cl. 197, 201-02. It will suffice for present purposes to recite that over the course of this litigation, a total of 108 spacecraft have been accused and that a determination of eligibility for just compensation has been made with respect to 81 spacecraft.
This opinion addresses all remaining issues in the case, to wit, the damages issues pertaining to royalty rate and delay damages.
II
Any determination of damages in patent litigation against the government must begin with contemplation of 28 U.S.C. § 1498(a):
Whenever an invention described in and covered by a patent of the United States is used or manufactured by or for the United States without license of the owner thereof or lawful right to use or manufacture the same, the owner’s remedy shall be by action against the United States in the United States Court of Federal Claims for the recovery of his reasonable and entire compensation for such use and manufacture.
Section 1498 does not instruct a court on how to compute damages: the only congressional intent expressed ensures that a claimant receive “reasonable and entire compensation.” “The size of an award is left to the trial court’s sound discretion.” Paper Converting Machine Co. v. Magna-Graphics Corp., 745 F.2d 11, 21 (Fed.Cir.1984) (construing analogous provisions of 35 U.S.C. § 284).
Ill
A
Among several methods employed by courts for determining reasonable compensation for patent use, the preferred method, and the one most frequently employed, is determination of a reasonable royalty. Decca, Ltd. v. United States, 225 Ct.Cl. 326, 336-345, 640 F.2d 1156, 1167-72 (1980), cert. denied, 454 U.S. 819, 102 S.Ct. 99, 70 L.Ed.2d 89 (1981). In this case, the parties agree that determination of a reasonable royalty is the appropriate first step in the calculation of compensation; thus, there is no occasion to address other methods.
The legal principles controlling determination of royalty rates are ably set forth in Penda Corp. v. United States, 29 Fed.Cl. 533, 573-74 (1993)
The Second Circuit, in its review of the district court opinion just cited, stated: “We realize that no one can be sure what the parties would have done had they actually negotiated. But determination of an assumed reasonable royalty is in essence a device for retroactively reaching a just result....” Georgia-Pacific Corp. v. U.S. Plywood-Champion Papers, Inc., 446 F.2d 295, 300 (2d Cir.1971). The court then quoted with approval an opinion by Judge Learned Hand: “The whole notion of a reasonable royalty is a device in aid of justice, by which that which is really incalculable shall be approximated....” Id. n. 5 (quoting Cincinnati Car Co. v. New York Rapid Transit Corp., 66 F.2d 592, 595 (2d Cir.1933)).
In the instant case, there plainly was no established royalty rate or other royalty compensation formula for the Williams patent. The parties concur on this threshold factor (Tr. 18,227). In fact, after the patent issued in September 1973, there was never a license agreement with anyone pertaining to its use (with the sole exception of a general, nonexclusive license pertaining to future use as part of a major settlement of past infringement, see Hughes Aircraft Co. v. United States, 15 Cl.Ct. 550, 552-53 (1988)), despite plaintiff’s efforts to enter licensing agreements with at least three major spacecraft manufacturing firms.
Given the absence of an established royalty, the focus shifts to determination of a reasonable royalty rate by a consideration of the factors which would have influenced reasonable businessmen resolved to enter a mutually agreeable licensing arrangement.
There is no fixed formula for calculation of a reasonable royalty. “The [willing buyer-willing seller] rule is more a statement of approach than a tool of analysis.” Georgia-Pacific Corp. v. United States Plywood Corp., 318 F.Supp. 1116, 1121-22 (S.D.N.Y. 1970), modified and affirmed, 446 F.2d 295 (2d Cir.), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971). Essentially, the rule suggests a process for evaluation of all relevant factors which knowledgeable, prudent businessmen would likely consider as having a bearing on an appropriate royalty rate.
The parties agree in principle that on the facts of this case the appropriate method for fashioning a reasonable royalty is to select a percentage of total spacecraft cost as the royalty with respect to each infringing vehicle. The parties further agree that it is appropriate to select a single rate to apply to every infringing spacecraft no matter when during the patent term the unlicensed use occurred and regardless of the extent of use.
C
To state the obvious, a royalty rate has significance only in relation to the base to which it is applied. Here, the parties agree that the royalty rate, however determined, is for application to the total cost of each infringing spacecraft,
D
Application for the Williams patent was filed in April 1960. During the 1960’s, Hughes demonstrated the worth and reliability of the Williams technology on the SYN-COM and INTELSAT communications satellites. (For a more complete description of this early development, see Hughes Aircraft
By letter of July 15,1974, Hughes’ director of domestic patent licensing corresponded with Philco-Ford Corp. (later renamed Ford Aerospace and Communications Corp.) (DX 2047). The letter offered to license both the Williams and McLean patents
Although at the time of the July 15, 1974 letter there was pending a suit by Hughes against Philco-Ford for alleged infringement of the Williams patent, there is nothing in the July 15 letter to suggest that the license terms were proposed merely in settlement of that litigation. Indeed, an exchange of correspondence between the two aerospace companies makes it plain that Philco-Ford was inquiring about and Hughes was responding concerning whether it had decided upon a proposed royalty (the patent term had only recently commenced) and the terms upon which a license may have been offered to others unrelated to their pending patent dispute (DX 2073 through DX 2076, DX 2047, DX 2078).
Philco-Ford never responded to the July 15, 1974 proposal of royalty terms. Presumably the offer stayed open until March 23, 1976 when it was expressly withdrawn by letter (DX 2078).
By letter of September 16, 1974, approximately two months after the July 15 offer to Philco-Ford and approximately one year into the patent period, Hughes made an identical offer to TRW, Inc., another major aerospace competitor (PX 1375-18 at D40653). There was not then and never has been at any relevant time any litigation or threat of litigation between Hughes and TRW pertaining to the Williams patent. TRW never responded to the proposal; presumably the offer stayed open until March 26, 1976 when it was expressly withdrawn by letter (PX 1375-18 at D40654).
It is important to note that the royalty rate (three percent for use of Williams alone) offered by Hughes to two of its major domestic competitors early in the patent term was made with respect to a base that would not include government furnished equipment (rather only the sales price moving to the licensee) and would not include the value of any launch and orbital support services or the value of any post-launch incentive awards based on spacecraft performance. Consequently, the three percent royalty suggested in the letter for Williams alone, if adjusted for application to a base consisting of “total spacecraft cost” as used in this case, would be significantly smaller. (At all times material in this litigation, the government has enjoyed the right to use the McLean patent, the other patent mentioned in the letters.)
The May 2, 1978 letter to MBB demonstrates that less than five years into the patent term Hughes was characterizing as its “normal royalty rate” for use of both Williams and McLean in scientific or experimental space vehicles two percent of a base significantly less than “total spacecraft cost” as defined in the instant case. It is reasonable to infer that Hughes was then willing to license Williams alone for use on scientific or experimental space vehicles for 1.2 percent (i.e., 60 percent of two percent, the same proportion of the rate for two patents twice proposed to competitors in 1974 as the rate for either patent separately) of a base consisting of total spacecraft cost less the value of scientific or experimental payloads not fabricated by a competitor licensee.
All of the 81 spacecraft found to infringe in this case would meet the description of “scientific or experimental space vehicles” designated by Hughes in connection with its “normal royalty rate.” Thus, it is reasonable to infer that Hughes was then willing to license Williams alone for a rate significantly less than 1.2 percent of “total spacecraft cost” as defined in this case for use on the kind of vehicles found to infringe.
E
Plaintiff has suggested that because the rates proposed to Philco-Ford in 1974 and the “normal royalty rates” related to MBB in 1978 were communicated when litigation over the Williams patent was pending with each prospective licensee, the communications constitute “statements made in compromise negotiations” and are consequently inadmissible in light of Rule 408 of the Federal Rules of Evidence. However, Rule 408 provides:
This rule does not require the exclusion of any evidence otherwise discoverable merely because it is presented in the course of compromise negotiations. This rule also does not require exclusion when the evidence is offered for another purpose ... [i.e., other than to prove liability for or invalidity of a claim or its amount].
Here, Hughes’ determination of and statements concerning its normal royalty rates available to competitors early in the patent term whether or not litigation was pending or infringement was suspected are “otherwise discoverable.” Further, evidence of Hughes’ representations concerning its normal royalty rates are not offered in the instant case to prove anything concerning its infringement claims against Philco-Ford or MBB but rather “for another purpose.” Thus, statements pertaining to Hughes’ own valuation of the patent contained in the above-cited letters to Philco-Ford and MBB meet the criteria of both the “otherwise discoverable” and “another purpose” exceptions and are not rendered inadmissible by the provisions of Rule 408.
These actual, historical licensing offers pertaining to the Williams patent are highly significant in two respects. First, they have the effect of placing a ceiling on the consideration of a royalty rate. In Pitcairn v. United States, 212 Ct.Cl. 168, 186, 547 F.2d 1106, 1118 (1976), cert. denied, 434 U.S. 1051, 98 S.Ct. 903, 54 L.Ed.2d 804 (1978), the Court of Claims stated: “[T]here is no reason why the [patent] owner himself should not be held to his own offer[s]____ It is appropriate to take them into account and to give them great weight.” One of the patent valuation witnesses called by the plaintiff, George E. Frost, stated in an article entitled “Accountings” (DX 2109 at 115; also found at George E. Frost, Accountings, 15 Intell.Prop.L.Rev. 107 (1983)): “The patentee’s actions in granting licenses can be a prime factor in determining the reasonable royalty____ License offers made to the trade and rejected by all can fix the ceiling below which the reasonable royalty must fall----” (Emphasis added.) Based on this logical concept, hypothetical negotiators for the parties, presumed to have knowledge of all relevant facts even though occurring after the date of initial infringement, would start with the rate offered by Hughes for scientific and experimental spacecraft like the 81 found to infringe in this ease. As discussed above, this starting rate would likely be something less than 1.2 percent of “total spacecraft cost” which includes the value of all payload furnished by the government.
The second significant fact concerning the offers actually made by Hughes early in the patent term is that there were no takers at this “ceiling” rate despite the proven utility and reliability of the invention. (See Hughes Aircraft Co., 717 F.2d at 1352-53, for description of the need for and usefulness of the technology). Hughes was entirely unsuccessful in licensing the Williams patent. During the full 17-year patent period, not one aerospace company entered a license agreement with Hughes (with the exception of the prospective license granted to Ford Aerospace and Communications Corp. as part of a general release of infringement claims and a mutual exchange of patent rights, see Hughes Aircraft Co., 15 Cl.Ct. at 552, which was included as part of a lump-sum settlement amount and not related to a percentage of the cost of future uses). This means that a royalty arrived at through the hypothetical negotiation process must fall below the universally rejected level of the offers made by Hughes at the time of its greatest value. Of course, in this ease the rate cannot fall below one percent of total spacecraft cost since even the government acknowledges that a royalty at that level is reasonable.
A negotiation which starts with a ceiling of something significantly less than 1.2 percent, which will end at a rate less than the starting point and which will not fall below one percent will quickly settle on one percent. Support for a royalty rate of one percent of total spacecraft cost is furnished by a consideration of the other factors which hypothetical negotiators would deem relevant.
G
1
It is axiomatic that the larger the potential compensation base to which a royalty rate will be applied, the lower will be the rate. Here, the actual base to which a royalty will be applied has been determined to exceed $3.5 billion dollars. This sum is the value of the 81 spacecraft found to infringe; Hughes accused an additional 27 spacecraft during the course of this litigation.
Hypothetical negotiators in 1973 would see a number of successful aerospace companies, both American and European, as well as both a civilian and a military space agency within the federal government, in a position to design the proven Williams invention into their spacecraft, either as the primary, transition or backup attitude control system, and thus contribute to á large royalty base. Such negotiators are presumed to have knowledge of the Federal Circuit’s 1983 ruling that “store-and-execute” spacecraft which otherwise literally use the Williams process would be found to infringe under the doctrine of equivalents, 717 F.2d at 1363-66, thus vastly expanding the potential compensation base.
2
The Williams invention was not a “pioneer” invention, i.e., one covering a function never performed before, 717 F.2d at 1362; rather the patent was of the “improvement” type and was dominated by the McLean patent. McLean was the pioneer patent concerning controlled precession of a spin-stabilized body by use of a pulsed jet, id., and the government, as of 1973, already had a nonexclusive license to use McLean. Although the absence of “pioneer” status in no way denigrates the undeniable desirability and utility of Williams, it is a factor which would likely cause negotiators to settle upon a rate lower than if the patent had pioneer status.
3
The license taken by the government as the result of use compensable under 28 U.S.C. § 1498 was a non-exclusive license. Hughes remained free to exploit the patent to the maximum with other customers, e.g., International Telecommunications Satellite Organization (Intelsat), and to negotiate nonexclusive licenses with other manufacturers. Hughes enjoyed considerable success with the patent in the manufacture of satellites for commercial customers (Pl.Br. (6/25/89) at 44-54). It is axiomatic that a non-exclusive license earns a lower royalty than an exclusive one.
4
The non-exclusive license taken by the government was a mere “naked” license to use the attitude control process described in the Williams patent, unaccompanied by technology or practical know-how necessary to design and incorporate the invention into a complex spacecraft. The user of the license was left to expend the financial resources to develop the spacecraft design necessary for implementation of the attitude control system. All risk associated with selection and use of a particular attitude control system was taken by the user. This factor would have the effect of lowering rather than enhancing the level of a reasonable royalty.
5
A negotiator for Hughes in 1973 would have every, incentive to set a rate which would simultaneously encourage use of the Williams invention in every space vehicle capable of being spun up (even if only as a redundant backup system), thus contributing to the size of the compensation base, and discourage or delay the development of alternative, competing technology.
The most effective way to accomplish this twin objective would be to set the royalty rate at a level sufficiently attractive to induce use of the patent on every spinning spacecraft, even when not essential to the mission, and to encourage concentration of government and industry talent on remaining, unresolved space engineering problems. A rate of one percent would have been an acceptable “insurance premium” even when the Williams system was not to be the primary attitude control system on a spacecraft; a rate significantly higher would discourage use of Williams as a redundant system and guarantee concentration of effort on alternatives.
One of plaintiffs valuation experts, George E. Frost, formerly director of the Patent Section of General Motors Corporation, wrote for a program in June 1979 (General Motors’ Approach to Licensing, DX 2315-A at 2-3): ‘When we do not license we know that the possible licensee will almost surely find an alternative. So granting a license usually provides some income where none would otherwise exist.” He also wrote, id at 5: “[I]t is a mistake to assume that any patent is free of alternatives, and the terms of any good license reflect this.”
Relevant to concerns that designers might try to “design around” Williams, there were other systems available. By no means did
By September 1973, enormous effort and talent in government and industry in Europe and North America were being successfully devoted to improvements in all aspects of space technology, including alternatives to Williams. At that time, there was already the capability of launching a 1600-pound, three-axis stabilized spacecraft into synchronous orbit using the comparatively inexpensive Atlas-Centaur booster (PX 1350). Indeed, in May 1966, an Atlas-Centaur had launched the 2200-pound Surveyor 1 to the moon (PX 1237 at 208); in 1977, an Atlas-Centaur launched the 2200-pound, three-axis stabilized FLTSATCOM directly into synchronous orbit. Many of the spacecraft in this compensation base were not placed into geosynchronous orbit but rather had comparatively low earth orbits for which an Atlas-Centaur could be used to launch a three-axis satellite directly into final orbit. Further, for low earth orbits, alternative attitude control systems such as magnetic torquing were possible, though less desirable alternatives. Hughes would have wanted to discourage all such alternatives.
More important for present purposes, other systems and more powerful rockets were on the way. Just eight months after the patent issued, the ATS-6, a three-axis stabilized, geosynchronous-orbit communications satellite weighing 3000 pounds, was launched into final orbit aboard a Titan IIIC rocket. It did not employ the Williams technology. Although the Titan IIIC was approximately four and a half times as expensive as the less powerful Atlas-Centaur, use of which would have required a transfer orbit ($180 million v. $40 million), the Titan IIIC could launch several spacecraft simultaneously, bringing its per-vehicle cost close to that for single-vehicle launches on the Atlas-Centaur. Although such use would involve increased risk in the event of a launch mishap, there was very early in the patent period a reliable, technically possible alternative means to launch heavy satellites into geosynchronous orbit.
By 1974, some major commercial customers had elected to use three-axis attitude control systems on broadcast satellites (DX 2100). By 1982, slightly more than one-half way through the patent period, technology had advanced to the point that heavy spacecraft could be launched into high orbit using a transfer orbit without the use of the Williams attitude control system.
The hypothetical Hughes negotiator would have wanted to discourage development and exclusive use of competitive alternatives, or at least remove any incentive to concentrate effort in this area until near end of the patent period. A royalty rate of one percent would have contributed to this goal.
6
For the sake of completeness, we note that plaintiff is not entitled to any premium or other favorable consideration in the hypothetical rate negotiation by reason of the fact that the government’s use of the patent has resulted in plaintiff’s competitors receiving contracts to manufacture spacecraft incorporating the Williams invention and thus reducing Hughes’ otherwise exclusive control over its patent. Hughes never had any right to exclude such use, only a right to compensation for any such use which occurred. The government had a perfect legal right to use the patent-in-suit (and any other U.S. patent) without prior authorization of the patentee. Bendix Corp. v. United States, 230 Ct.Cl. 247, 250, 676 F.2d 606, 608 (1982) (“unlike the private infringer, the United States in a § 1498 case is doing what it has a right to do”); Decca, Ltd., 225 Ct.Cl. at 335, 640 F.2d at 1166 (“Because section 1498 authorizes the Government to take a license in any ... patent, the Government is never ‘guilty’ of ‘direct infringement’ of a patent insofar as ... [this] connotes tortious or wrongful conduct.”). See Leesona Corp. v. United States, 220 Ct.Cl. 234, 244-54, 599 F.2d. 958, 964-70, cert. denied, 444 U.S. 991, 100 S.Ct. 522, 62 L.Ed.2d 420 (1979).
Plaintiff asserts entitlement to a royalty rate of 15 percent. For support, Hughes points to a 1965 agreement between it and Communications Satellite Corporation (Comsat) pertaining to the manufacture of Intelsat II satellites (PX 1375-8 at C13663, C13685). Although the Williams patent had not been issued at the time, the 1965 agreement contained a provision, appearing at page 22 thereof (id. at C13685), that after the issuance to Hughes of two patents, only one of which involved the Williams technology which is the subject of this case, Comsat would pay a royalty of 15 percent of spacecraft cost for future use of the attitude control system “described and claimed” in two patent applications. Such royalty was to be payable, however, only if a satellite using the control system “is placed in a satisfactory orbit and commences satisfactory communications operation” (id.).
We find no support in this agreement for Hughes’ current, position. As an initial matter, even if the agreement were otherwise supportive of Hughes’ claim, the agreement on its face provides a 15 percent royalty only with respect to successfully launched satellites whereas plaintiff is claiming 15 percent with respect to all government spacecraft whether or not successfully launched. Gayle Parker, a valuation expert called by Hughes, conceded that even if this agreement resulted in an “established royalty,” Hughes would be entitled to no more than 13.3275 percent of the cost of the accused spacecraft after taking account of unsuccessful launches (Tr. 2275, 2287-88). Further, the 1965 Comsat agreement provides liability for the royalty upon use of the technology described in two patent applications, whereas we are here dealing with only one patent. However, there are more fundamental reasons for rejecting this agreement as guide for negotiations.
For one thing, the agreement was entered eight years before the Williams patent was issued to Hughes, at which time the claims of ■the Williams application were far broader than those of the patent-in-suit. Subsequent to this agreement, Hughes abandoned all claims in the Williams application referred to in the 1965 agreement and substituted three others. Further, the 1965 Comsat agreement was entered at a time when Hughes was literally the world’s only aerospace contractor to have successfully manufactured satellites for geosynchronous orbit. Consequently, Hughes then had some leverage which it could not have applied (and, more importantly, did not try to apply) after the Williams patent issued in 1973. The tremendous effort devoted to scientific and engineering advances in the space field during the 1960’s (the United States landed a man on the moon in 1969) and early 1970’s by both government and private industry resulted in the existence of several experienced major aerospace companies by 1973. Further, by the time the Williams patent issued in 1973, far more powerful launch boosters were available, making the use of the Williams attitude control system less critical.
We find more convincing the conduct of Hughes (described above) after the patent issued, a time when plaintiff had reason to feel secure concerning its royalty-rates bargaining position and when the Williams invention was well established as the desirable, reliable and light-weight attitude control system for any spacecraft capable of being spun up. After the patent issued in 1973, Hughes never asked from anyone, in the context of seeking a voluntary licensing arrangement pertaining solely to the Williams patent, a royalty of as much as three percent (when adjusted to “total spacecraft cost”). One may fairly inquire: If a reasonable royalty was 15 percent or even 13 percent of total cost, why was Hughes offering to license the Williams invention to its major commercial competitors early in the patent term — the time of maximum value — for less than three percent of total spacecraft cost (making no mention of the 1965 Comsat agreement), and why were there no takers among three of the world’s leading satellite manufacturers, not even a counteroffer from two of them.
I (EYE)
Based on all the foregoing, we conclude that a reasonable royalty rate to be applied to total spacecraft cost for the government’s use of the Williams invention is one percent.
IV
A
“Reasonable and entire” compensation necessarily includes delay damages, i.e., recompense tantamount to interest for loss of use of royalties which a prevailing patentee would have enjoyed had payment of such royalties been timely.
B
There is a strong judicial policy in favor of uniform rates to apply to all those entitled to delay damages for a given period. See Georgia-Pacific Corp. v. United States, 226 Ct.Cl. 95, 154, 640 F.2d 328, 365 (1980) (stating in a takings ease: “[I]n order to avoid discrimination among litigants, we ... place great weight on the strong judicial policy requiring uniformity of treatment of eondemnees.”); Miller v. United States, 223 Ct.Cl. 352, 402, 620 F.2d 812, 838 (1980) (“There is ... a strong judicial policy in favor of the establishment of a uniform rate of interest applicable to condemnation cases in order to avoid discrimination among litigants.”); Pitcairn, 212 Ct.Cl. at 196, 547 F.2d at 1124, (rejecting as discriminatory the suggestion that a plaintiffs actual cost of borrowing be applied as delay damages rate: “A plaintiff with a poor credit rating could theoretically receive an award of just compensation at very high interest rates because its actual cost of borrowing money might be very high, while another might be penalized for having a good credit rating.”); Arkansas Valley Ry. v. United States, 107 Ct.Cl. 240, 259, 68 F.Supp. 727, 730, cert. dismissed, 330 U.S. 811, 67 S.Ct. 1083, 91 L.Ed. 1266 (1947) (stating in a takings case: “A uniform rate does in fact avoid discrimination among litigants.”).
C
Plaintiff, a successful corporation, urges use of its own return on equity as the measure of delay compensation, arguing that only this method can adequately place it in the financial position it would have enjoyed if the government had paid the royalties on a timely basis (Pl.Br. (4/13/89) at 10-39). Based on the long-standing, strong judicial policy in favor of uniform, non-discriminatory rates, we decline to adopt plaintiffs suggestion and instead adopt uniform rates.
D
1
The earliest date for commencement of delay damages in this litigation is September 11,1973, see Appendix B to Opinion on Compensation Base filed April 29,1994. Court of Claims precedent requires that a rate of 7.5
Based on this consistent Court of Claims application of rates for periods covering 1973 through 1979 in just compensation cases, we adopt those same annual rates for application in this case, to wit, 7.5 percent for the period 1973 through 1975 and 8.5 percent for the period 1976 through 1979. Because, as explained below, we adopt the tax overpayment rates prescribed by 26 U.S.C. § 6621 for delay damages accruing on or after February 1, 1980, we hold, for the sake of administrative convenience, that the 8.5 percent rate shall also apply during the month of January 1980. (The Court of Claims similarly extended the 1976-79 rate through January 1980 to reach the same practical result in Bendix Corp., 230 Ct.Cl. at 265, 676 F.2d at 616.)
2
The uniform rates applied in the delay damages cases just cited were applied as simple interest. We must determine if it is appropriate to allow compound interest when using those rates and, if so, what the period of compounding should be. As a matter of general principle, both parties in this case agree that compounding is appropriate. Experts for both sides testified to the effect that, at all times relevant in this case, no rational investor would consider investing at simple interest.
We find that just compensation in this case requires compounding of interest at least annually. Because we are mindful that rate of interest and compounding period are inextricably related so that a change from simple to compound interest necessarily increases the effective rate of interest after the initial interest period, we select an annual compounding period for application between September 11, 1973 and January 31, 1980, even though we would otherwise be inclined to select a shorter compounding period. On the other hand, we are persuaded that the unavoidable modification to the simple interest rates we apply as annually compounded rates does not do violence to the precedent upon
E
For delay damages accruing on or after February 1, 1980, we award the tax overpayment rates prescribed by 26 U.S.C. § 6621 (as modified from time to time), compounded daily as provided in 26 U.S.C. § 6622(a).
The amount of effort and the volume of materials devoted in this case just to the subject of delay damages approach the absurd. Approximately seven days of trial time were devoted to testimony and argument pertaining solely to this issue; voluminous exhibits on the subject were received. A generally-agreed, standard, objective method of fixing delay damages when the government has been found liable for past due royalty payments is sorely needed.
We find the current statutory overpayment rate to be a fair, easily ascertained, commercially reasonable, objective measure of delay damages automatically adjusted from time to time to take account of changing rates and conditions in the marketplace. The basic rate to be derived by the Secretary of the Treasury involves some aspects of the financial markets and presumably reflects investors’ conclusions regarding a rate that will keep pace with inflation plus provide a measure of “real” return. Then, the addition of two percent insures that one entitled to delay damages will receive an additional margin of “real” return; this takes account of the likelihood that a prudent investor will place a portion of his assets in long-term securities which typically earn higher rates than short-term obligations. The result appears fair to a patentee entitled to past due royalties, yet also fair to the government which has statutorily declared this to be an appropriate rate when it has had the use of federal tax over-payments.
F
Although not objecting to the periodic compounding of delay damages rates as a matter of general principle, defendant argues that an award based on compound interest would provide a substantial benefit due to delayed federal income taxation (the “Individual Retirement Account effect”) and urges application of an elaborate calculation to reduce the award of interest for each year by the presumed amount of federal income taxation which would have been due.
We decline to adopt defendant’s approach for four reasons: First, case law rejects this approach. See Hanover Shoe, Inc. v. United Shoe Machinery Corp., 392 U.S. 481, 503, 88 S.Ct. 2224, 2236-37, 20 L.Ed.2d 1231 (1968); ITT Corp., 17 Cl.Ct. at 242-43. Second, a fair application of defendant’s theory would require findings concerning a plaintiff’s actual tax situation for each applicable year (more than 20 in this case) and speculation concerning actions which a reasonable recipient might have taken to reduce taxation on awards if received when due, e.g., tuning of
Third, defendant’s hypothetical taxation method would result in the same kind of discrimination among just compensation claimants that non-uniform rates of interest would cause. A plaintiff with chronic heavy losses or who resides or does business in a state with high state income taxes (deductible for federal income tax calculations) would receive more delay damages for a given period than an otherwise similarly situated plaintiff with chronic healthy profits or residence in a state with low taxes. Similarly, a foreign patentee not subject to United States income taxation would be treated more favorably than a domestic patentee.
Finally, Congress is undoubtedly aware of the beneficial effect of a compound interest award which presumes reinvestment of the full amount of interest earned at the end of each compounding period without reduction for taxes. Even so, although 26 U.S.C. § 6622 provides for daily compounding of interest on awards against the government in a variety of situations, Congress has not chosen to require any reduction of interest in the manner suggested by defendant.
G
In summary, we conclude that plaintiff is entitled to an award of delay damages computed at an annual rate of 7.5 percent over the period from September 11, 1973 through December 31, 1975 and at an annual rate of 8.5 percent from January 1, 1976 through January 31,1980, compounded on January 31 of each year, and, commencing on February 1, 1980, computed in accordance with the tax overpayment rate prescribed from time to time in 26 U.S.C. § 6621 and compounded daily in accordance with 26 U.S.C. § 6622(a).
V
Despite efforts to be objective and precise in determinations of royalty rate and delay damages, it is well to keep in mind the conclusion of the Court of Claims with respect to these subject areas: “Determination of the amount of reasonable and entire compensation to which a successful plaintiff is entitled under 28 U.S.C. § 1498(a) is, in the final analysis, a matter of subjective judgment. There is no set formula or equation to fit all circumstances.” Bendix Corp., 230 Ct.Cl. at 266, 676 F.2d at 616.
VI
This opinion resolves all heretofore undetermined damages issues in this litigation. Application of the royalty rate and the delay damages rates set forth above to the valuations and royalty payment dates contained in Appendix B to the Opinion on Compensation Base, dated April 29, 1994, will yield the precise damages award to which plaintiff is entitled.
It is requested that the parties confer and attempt to reach agreement on the precise amount of a damages award which combines the royalty award and all delay damages accrued through March 31, 1994. It is contemplated that judgment shall be entered for such total amount of damages calculated as of March 31, 1994 plus interest on said sum calculated pursuant to 26 U.S.C. §§ 6621(a)(1) & 6622 (the tax overpayment rate compounded daily) from March 31, 1994 until paid.
The parties shall file a joint status report not later than Monday, July 18, 1994 setting forth their agreement on the precise amount of an award inclusive of delay damages through March 31,1994 (without prejudice to appeal rights pertaining to any underlying court ruling), or, in the absence of agreement, their respective positions on an appropriate award and the precise matters requiring resolution by the court.
Judgment shall be entered upon such stipulation or other resolution of the precise amount of damages.
. The appendix to the Opinion on Liability, 29 Fed.Cl. at 243-48, lists each of the 108 spacecraft accused during any stage of this litigation and sets forth, with references, the liability ruling with respect to each one. Appendix B to the Opinion on Compensation Base, dated April 29, 1994, lists the 81 spacecraft with respect to which liability has been determined and sets forth the precise royalty payment dates and valuations with respect to each.
. See Hughes Aircraft Co. v. United States, 15 Cl.Ct. 550, 551 n. 2 (1988), for a list of previously published opinions in this case and other cases involving the Williams patent. Two additional published opinions in this case are the Opinion on Liability, 29 Fed.Cl. 197 (1993) and the Opinion on Compensation Base, dated April 29, 1994. The instant opinion is the 16th published opinion directly involving the Williams patent.
. Other damages calculation methods applied in patent litigation against the government are described in Decca, 225 Ct.Cl. at 336-37, 640 F.2d at 1167-68; Leesona Corp. v. United States, 220 Ct.Cl. 234, 255-57, 599 F.2d 958, 968-71 (1979); Tektronix, Inc. v. United States, 213 Ct.Cl. 257, 268-69, 552 F.2d 343, 349 (1977), reh’g denied, 216 Ct.Cl. 144, 575 F.2d 832, cert. denied sub nom. Hickok Elec. Instr. Co. v. Tektronix, Inc., 439 U.S. 1048, 99 S.Ct. 724, 58 L.Ed.2d 707 (1978); Penda Corp. v. United States, 29 Fed.Cl. 533, 573 (1993). These methods include patentee's lost profits and savings to the government.
. Penda, 29 Fed.Cl. at 573, sets forth the following general principles pertaining to “reasonable and entire compensation” under 28 U.S.C. § 1498:
The government may take a license in any United States patent. The patentee’s sole remedy is a suit in this court for its "reasonable and entire compensation” under section 1498. This remedy is premised on a theory of eminent domain. The property interest taken by the government is a compulsory, compensable, nonexclusive license.
The "reasonable and entire compensation” owed the patent holder is equivalent to just compensation under the fifth amendment. Thus, the court has traditionally turned to the law of eminent domain for legal precedents to apply in determining "reasonable and entire compensation.” Basic principles of fairness are the governing consideration in determining just compensation for an eminent domain taking. These same principles guide in assessing reasonable and entire compensation.
(citations omitted) (emphasis added).
. A full explanation of the "willing buyer-willing seller” rule is set forth in Georgia-Pacific Corp. v. United States Plywood Corp., 318 F.Supp. 1116, 1121-22 (S.D.N.Y.1970), modified and affirmed, 446 F.2d 295 (2d Cir.), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971).
. Among items considered by such suppositious negotiators are those set forth in Georgia-Pacific Corp., 318 F.Supp. at 1120. Although originally presented as a list of “some" of the factors “seemingly more pertinent to the issue” in that particular case, 318 F.Supp. at 1120, the 15 “Georgia-Pacific factors” have become enshrined in case law as the definitive criteria for determination of a reasonable royalty. See, e.g., Tektronix, 213 Ct.Cl. at 268-69, 552 F.2d at 349; Penda, 29 Fed.Cl. at 573-74; ITT, 17 Cl.Ct. at 202, 223.
The factors considered significant in this case are discussed in text. Although the "amount” arrived at through hypothetical negotiation is listed as the 15 th and last factor in Georgia-Pacific Corp., 318 F.Supp. at 1120, it essentially subsumes all of the first 14 factors.
. A potential, more complicated alternative to a single royalty rate applicable to the total cost of each infringing spacecraft would be two or more rates to apply depending on whether a particular space vehicle used Williams as the primary attitude control system or merely as a backup or whether Williams was used only in the transfer orbit rather than throughout the life of the space mission.
. The term "total spacecraft cost” in this litigation is understood to mean the total procurement cost to the government for an airborne (or proto- . type, qualification test) vehicle including the total cost of the design, fabrication and testing of the spacecraft, the cost of government furnished equipment aboard the spacecraft and the cost of payload, as well as the cost of launch support and initial orbital support services customarily performed by an aerospace contractor and the value of performance incentives and awards.
. For a description of both the Williams and McLean patents and their relationship with each other, see Hughes Aircraft Co., 717 F.2d at 1353-56. By the time Hughes acquired the right to license both Williams and McLean in September 1973, the United States had independently acquired a non-exclusive license to use the McLean patent.
. Rule 102 of the Federal Rules of Evidence provides: “These rules shall be construed to secure fairness in administration ... and promotion of growth and development of the law of evidence to the end that the truth may be ascertained and proceedings justly determined.”
. “The ‘reasonable and entire compensation' due plaintiff under 28 U.S.C. § 1498 includes not only reasonable royalties but also an appropriate amount which compensates plaintiff for defendant's delay in payment of those royalties.” Pitcairn, 212 Ct.Cl. at 189, 547 F.2d at 1120. See Waite v. United States, 282 U.S. 508, 51 S.Ct. 227, 75 L.Ed. 494 (1931).
. Adoption of the plaintiff's proposal to award delay damages to it on the basis of its unique return on equity would result in obvious discrimination between it and other just-compensation claimants entitled to delay damages by reason of the government's withholding of timely payment of principal over the same time periods. The anomaly is starkly illustrated by contemplating the result if the Williams patent had been owned half by the inventor Donald Williams and half by his employer, Hughes Aircraft Company. Under plaintiff's proposed method, the delay damages awardable to plaintiff would be based on generally high rates of return on equity while the delay damages recoverable by the actual inventor for the identical withholding periods would be substantially less (presumably based on objective rates recoverable by a prudent investor).
. The series of specific rates set forth in Pitcairn, 212 Ct.Cl. at 191, 547 F.2d at 1121, based on long-term corporate bond yields, was adopted as the interest rates to be paid "from now on” in just compensation cases “without need of proof in the individual instance." Tektronix, Inc. v. United States, 213 Ct.Cl. 257, 274, 552 F.2d 343, 352 (1977), cert. denied, 439 U.S. 1048, 99 S.Ct. 724, 58 L.Ed.2d 707 (1978). For the years 1971—75, the rate adopted was 7.5 percent. See Decca, 225 Ct.Cl. at 337, 640 F.2d at 1168.
. The suggestive language from Miller is as follows:
Applying an analysis similar to that employed in Pitcairn, we conclude that a rate of 816 percent would be appropriate for the years 1976-79. For the year 1980 to the date of payment, we approve a rate of 12 percent. Since this is only a short period of time, the 1980 rate here allowed will not be regarded by the court as a precedent for other cases.
223 Ct.Cl. at 405, 620 F.2d at 840.
. We adopt for this case the conclusions of the court in ITT Corp., 17 Cl.Ct. at 242, as follows:
[Rjequiring plaintiff to adduce evidence of a market or commercial fact not subject to debate, i.e., that any commercial player borrows at compound interest, is not a meaningful evi-dentiaiy effort.... The court is prepared to take judicial notice that compound interest is a market or commercial reality for any corporation that does business in the United States.
. Although urging use of its own return on equity as the measure of delay compensation, plaintiff acknowledges that if uniform rates are to be adopted, the tax overpayment rate set pursuant to 26 U.S.C. § 6621, combined with the daily compounding provided in 26 U.S.C. § 6622(a), should be used to calculate delay damages (Pl.Br. (4/13/89) at 40, 44-46; Tr. 17,-712, 17,715).
. We have tremendous sympathy with the views expressed by Judge Oscar Davis in Tektronix, Inc., 213 Ct.Cl. at 274, 552 F.2d at 353:
"[I]t is too burdensome to require parties to make specific proof in every case as to the appropriate interest rate____ It will further the goal of equal justice, reduce the costs and complexity of litigation, and facilitate decision (as well as settlement) to accept and establish ... [uniform rates].”
. Pursuant to RCFC 54(d), costs shall be allowed to the plaintiff (“the prevailing party”).