
    UNITED STATES of America, Plaintiff-Appellee, v. UNITED TECHNOLOGIES CORPORATION, Defendant-Appellant.
    No. 13-4057.
    United States Court of Appeals, Sixth Circuit.
    Argued: Dec. 3, 2014.
    Decided and Filed: April 6, 2015.
    
      BEFORE: SILER and SUTTON, Circuit Judges; CLELAND, District Judge.
    
    
      
       The Honorable Robert H. Cleland, United States District Judge for the Eastern District of Michigan, sitting by designation.
    
   OPINION

SUTTON, Circuit Judge.

In 1983, Pratt & Whitney, now owned by United Technologies, made false statements to the Air Force in the course of competing with GE Aircraft to supply the Air Force with engines for its F-15 and F-16 fighter jets. The effort failed in two respects: Pratt did not achieve its goal of obtaining more business in the first year of the contract, and the fraud did not go unnoticed.

After discovering the fraud, the government filed two actions against Pratt: (1) a 1998 action before the Armed Services Board of Contract Appeals seeking relief under the Truth in Negotiations Act, and (2) a 1999 action in federal court seeking relief under the False Claims Act and common law restitution. The government lost the administrative action. Even though Pratt’s false statements had violated the truth-in-negotiation requirements of the Act, the Board refused to lower the price of the contracts retroactively — the remedy permitted by the Act — because the Air Force had relied on the competitive bids by Pratt and GE Aircraft, not the 1983 false statements, in determining a reasonable price for the jet engine contracts with each company. The Federal Circuit affirmed.

The federal court action is now on its second trip to this court. The first appeal established that Pratt violated the False Claims Act and that it owed the government $7 million in statutory penalties due to the false cost estimates it provided to the government in 1983. The first appeal also vacated the district court’s holding that the government suffered no damages from the false statements and asked the court to address three discrete flaws that might (but might not) affect the damages calculation. On remand, the district court awarded $657 million in damages.

At stake in this sequel are two essential questions. Does issue preclusion bar the government from obtaining additional damages under the False Claims Act and common law restitution given the Board’s finding in the first action about the role of competition in determining the prices that the government paid Pratt and GE Aircraft for the jet engines? And, even if issue preclusion does not apply, is the district court’s $657 million damages award supported by the evidence given the government expert’s refusal to account for the competition between GE Aircraft and Pratt in setting a fair market value for the engines that the government purchased from Pratt?

I.

Pratt & Whitney makes jet engines. For years, Pratt served as the exclusive supplier of engines for the Air Force’s F-15 and F-16 fighter jets. That changed in the early 1980s, when the military decided that competition might improve the quality of the engines and lower their prices. In 1982, the Air Force invited aerospace manufacturers to submit competitive bids for making the next generation of engines. In addition to Pratt, GE Aircraft entered the competition. The Air Force touted the prospect of greater competition. As one officer told Congress, the bidding put Pratt and GE Aircraft “at each other’s throats.” R. 441-2 at 7. One observer called the companies’ high-stakes procurement battle the “Great Engine War.” See Editorial, The Lesson of the Great Engine War, N.Y. Times, Feb. 13, 1984, at A20, available at http://nyti.ms/lE04T5h.

In trying to stave off its new competitor, Pratt misstated the projected costs in its 1983 bid in three ways — its bill of materials, its inflation forecasts, and its expected discounts from suppliers — in an effort to discourage the military from dividing the work between Pratt and GE Aircraft. After the Air Force identified the problem, Pratt assured the Air Force that it had fixed the problems in its initial proposal and falsely certified that its offer prices “reflect[ed its] best estimates and/or actual costs.” R. 334 at 7. The deception backfired in two ways. It did not work as a business strategy. The Air Force chose to divide the engine orders anyway, and in the first year of the new six-year contract it purchased three quarters of the engines from GE Aircraft and only a quarter of the engines from the once-dominant Pratt. The deception also was uncovered, though not until the end of the contract.

In the interim, the two jet engine manufacturers continued to compete. In each subsequent year, the Air Force issued a “call for improvement” that asked Pratt and GE Aircraft to provide more favorable terms than its prior “best and final offer” — a process that allowed each contractor to decrease its existing offer' prices with the hope of selling more engines. The Air Force’s goal was to create, and benefit from, “perpetual competition.” See United Techs. Corp., ASBCA No. 53349, 05-1 BCA ¶ 32,860, at 162,813, 2005 WL 147601 (Jan. 19, 2005) [hereinafter ASBCA II]. Pratt took advantage by responding with lower prices, including by extending full-award volume discounts even for split-award contracts. In each year, the Air Force certified that Pratt’s and GE Aircraft’s prices were “fair and reasonable” based on the “market test between the competitors.” Id. And indeed, as a result of the role of competition in setting fair prices, the Air Force did not ask Pratt and GE Aircraft to submit cost and pricing data for each of the five outyears of the contract, as the regulations normally require. See 10 U.S.C. § 2306(f)(2) (1982); A.S.P.R. § 3 — 807.3(b)(ii) (1976). Pratt beat out GE Aircraft with lower prices in some years (and received additional business as a result), and in the fourth year of the “call for improvements” Pratt was the “clear winner” overall. R. 441-34 at 2. Air Force Secretary Edward Aldridge hailed the “intense competition” as “working to perfection.” Id. In response to Pratt’s improvements, the Air Force awarded the company a steadily increasing share of engine production. In the final year of the contract, Pratt won nearly two-thirds of the work.

The government first became concerned that Pratt had overstated its 1988 cost projections in a 1989 audit by the Air Force. For reasons that the record does not fully disclose, the Air Force review board closed that investigation in 1995. In 1997, Dannie Zaeharetti, an auditor with the Department of Justice and eventually the damages expert in this case, investigated the matter and determined that Pratt did not use its most accurate data in its 1983 best and final offer.

The Truth in Negotiation Act litigation. In 1998, the government filed an administrative action against Pratt with the Armed Services Board of Contact Appeals under the Truth in Negotiations Act. See 10 U.S.C. § 2306(f)(2) (1982). As permitted under the Act, it sought a retroactive decrease in the price it should have paid for the six years of jet engines due to the initial false cost estimates. The Board rejected the government’s claim. It first determined that some of the alleged misstatements — that Pratt had corrected problems in its initial proposal and had used the latest and most accurate cost data to develop its 1988 best and final offer prices — did not amount to “cost or pricing data” covered by the Act. See United Techs. Corp., ASBCA No. 51410, 04-1 BCA ¶ 32,556, at 161,024-25, 2004 WL 483216 (Feb. 27, 2004) [hereinafter ASBCA I ]. The Act, the Board noted, covers only misrepresentations about “facts which reasonably can be expected to contribute to sound estimates of future costs.” Id. at 161,025 (quoting D.A.R. § 3-807.1(a)(l)). The Board held that the Truth in Negotiations Act covered some of Pratt’s other statements — the inaccurate component-by-component breakdown of its expected costs, which is to say the underlying cost data itself. See 10 U.S.C. § 2306(f)(2) (1982). But the Board held that these statements did not cause any damages to the Air Force. Because the Air Force had relied on “competitive forces, rather than the defective ... cost or pricing data ... [,] to make the awards and to exercise the options for additional purchases,” it reasoned, the prices the Air Force paid for the jet engines were not increased by the fraud. ASBCA II, 05-1 BCA at 162,813. The government apparently did not appeal this aspect of the Board’s decision. See Brief of Appellant, Wynne v. United Techs. Corp., No. 05-1393, 2005 WL 3338206 (Fed.Cir. Nov. 14, 2005). It instead argued that it had no obligation to show that the Air Force relied on the false cost estimates or that the false statements otherwise caused it damages. It claimed that the existence of the fraud allowed it to obtain a one-for-one price reduction for every dollar Pratt overstated its costs. The Federal Circuit rejected this argument and affirmed. See Wynne v. United Techs. Corp., 463 F.3d 1261,1267 (Fed.Cir. 2006).

The False Claims Act / Restitution litigation. In 1999, the United States separately filed this lawsuit in federal district court for violations of the False Claims Act and for common law restitution. The court found Pratt hable under the False Claims Act and awarded the government $7 million in statutory penalties. The government sought additional damages caused by the false statements under the False Claims Act and under several equitable restitution theories: unjust enrichment, mistake, and quasi-contract. In support of these claims, the government presented the testimony of Zacharetti, the DOJ auditor who had uncovered the fraud. Zacharetti calculated the government’s damages on a pro rata basis by comparing the prices Pratt offered the government with the prices it would have offered the government without the cost overstatements. He made two key assumptions: (1) Pratt’s cost misstatements resulted in a dollar-for-dollar overcharge to the government, and (2) all other components of Pratt’s prices would have stayed proportionally the same with or without the overstatements. Relying on these assumptions, Zacharetti estimated Pratt’s material costs and added to them based on the company’s percentage adjustments for overhead, labor, profit, and subsequent discounts. The difference between the resulting prices and what the government actually paid, he concluded, amounted to its damages. Zacharetti made no mention of fair market value.

The district court rejected the government’s claims for additional damages on the ground that the false statements did not cause any damages to the government. The court identified several flaws in Zacharetti’s analysis. It concluded that the Air Force did not suffer any damages because Pratt’s yearly discounts from its best and final offer in the course of the calls for improvements process offset any cost overstatements. See United States v. United Techs. Corp., No. 3:99-ev-093, 2008 WL 3007997, at *12 (S.D.Ohio Aug. 1, 2008). It also rejected Zacharetti’s damages methodology because “it ignore[d] the nature” of Pratt’s scheme, which was designed to skew split-award prices relative to those under a full award, and ignored the reality that the scheme failed. The Air Force, it observed, declined to give Pratt the full award and GE Aircraft indeed received three-quarters of the business in the first year of the contract. Id. at *11. The Court then reasoned:

The Government Calls for Improvement did not request new certifications of engine prices broken down part-by-part. Instead, engine prices and warranty prices were rebid on the overall price. The new Government approach of avoiding sole-source vendors on major acquisitions and creating an atmosphere of continual competition succeeded in its goal. Had the Government requested a new BAFO [best and final offer], the Court has no doubt that Pratt, chastened by its experience of winning just 25% of FEC I, would have certified the lowest possible engine prices it could manage. Reducing the Government’s damages on a pro-rata basis over the entire parts list in this instance does not fairly estimate the Government’s damages. There is no evidence that, had Pratt reduced the’ parts affected by its originally fraudulent statements, that commensurate price reductions could have been won for all engine parts.

Id. at *12 (emphasis added).

The district court also determined that claim preclusion barred the government’s restitution claims because the Air Force could have, and should have, litigated them before the Armed Services Board of Contract Appeals. Id. It did not reach Pratt’s separate issue-preclusion argument that the Board’s competition findings in that litigation bound the parties in the federal court case.

On appeal, we affirmed Pratt’s liability under the False Claims Act and the $7 million fine levied against it under the Act. See United States v. United Techs. Corp., 626 F.3d 313, 320-21 (6th Cir.2010). We concluded, however, that the government’s restitution claims were not barred by claim preclusion because the Board did not have jurisdiction to hear them. Id. at 324-25. At the same time, we asked the court on remand to determine whether one of the findings by the Board in the administrative action — that the Air Force determined fair and reasonable prices for the Pratt and GE Aircraft jet engines based on competition, not the cost estimates covered by the Truth in Negotiation Act — precluded the government from obtaining a different finding here.

We vacated the district court’s no-damages determination and asked the court to reconsider three aspects of it. One concern was that the district court gave Pratt full credit for warranty price reductions without accounting for a corresponding reduction in the extent of the warranty coverage. Id. at 322. The second concern was that the district court gave Pratt credit for final-year discounts across the entire contract even though the government never benefitted from those discounts in prior years. Id. The last concern was that, instead of using “fair market value” as the benchmark, the court used the original contract prices. Id. We asked the district court on remand to recalculate damages based on what the government paid above “what it should have paid for what it received” in terms of “fair market value.” Id. None of this, we cautioned, necessarily would lead to a different conclusion. “[T]he government is not entitled to damages,” we pointed out, if Pratt’s prices were equal to or below “fair market value.” Id.

On remand, the government received an upgrade. In addition to the $7 million it had already obtained in penalties, it was awarded $657 million more in damages — a combination of treble damages under the False Claims Act, restitution, and prejudgment interest. In reaching this conclusion, the district court rejected Pratt’s issue-preclusion defense, holding that the Board and Federal Circuit litigation did not resolve whether Pratt’s three misrepresentations accompanying its best and final offer caused the government damages. See United States v. United Techs. Corp., No. 3:99-cv-093, 2012 WL 2263280, at *3-4 (S.D.Ohio June 18, 2012). The court then adopted the government’s damages calculation in full — premised on Zacharetti’s unaltered analysis — and rejected Pratt’s arguments that this calculation did not account for the impact of competition on fair market value, including comparable prices paid to GE Aircraft for its jet engines. United States v. United Techs. Corp., 950 F.Supp.2d 949, 952-53 (S.D.Ohio 2013). The court concluded that the fighter jet engine market was insufficiently competitive to rely on comparable sales, but simultaneously found a “free market” for the warranties, adopting their “arms-length” renegotiated price as their value. Id. at 952, 956.

II.

On appeal from a bench trial, we give fresh review to the district court’s legal conclusions and defer to its fact findings unless they are clearly erroneous. Pressman v. Franklin Nat’l Bank, 384 F.3d 182, 185 (6th Cir.2004). Under the False Claims Act, the government bears the burden to prove its damages by a preponderance of the evidence. See 31 U.S.C. § 3731(c).

III.

When litigation between two parties carries on for seventeen years in two different venues, it is only a matter of time before it will implicate a foundational objective of a fair legal system: treating like matters alike. That objective underlies three features of a precedent-bound system of law — stare decisis, law of the case, and issue and claim preclusion — all of which require judges to look backward before they resolve current disputes. Stare decisis requires courts to respect prior decisions of the courts that usually concern different parties but similar issues. If past is precedent with respect to disputes involving different parties, it follows that past is precedent with respect to disputes involving the same parties — whether in the context of prior rulings in the same case (law of the case) or prior rulings in different cases (issue and claim preclusion). All three doctrines have a role to play in today’s dispute.

A.

Issue preclusion. Up first is issue preclusion. In the Truth in Negotiation Act litigation, the Board found that the government did not meet its burden of showing that Pratt’s 1983 false statements caused higher prices for each of the six years of the Pratt-Air Force jet engine contracts. Does the Board’s finding' there — that the Air Force relied on competition between GE Aircraft and Pratt plus the ealls-for-improvements process to evaluate the reasonableness of the two companies’ engine prices — bind us here?

A few basics are in order. To establish issue preclusion, a party must show that: (1) the question in this case is the same as the one raised in the earlier litigation; (2) the answer given in the earlier litigation was necessary to the decision; (3) that decision was a final judgment on the merits; and (4) the affected party had a “full and fair opportunity” to litigate the issue in the prior litigation. See Kosinski v. C.I.R., 541 F.3d 671, 675 (6th Cir.2008) (quoting United States v. Cinemark USA Inc., 348 F.3d 569, 583 (6th Cir.2003)). Issue preclusion applies to issues litigated in prior disputes. It thus makes no difference that the earlier no-damages-due-to-competition ruling arose in a case under the Truth in Negotiation Act and that this dispute arises under the False Claims Act and the common law. See Allen v. McCurry, 449 U.S. 90, 94, 101 S.Ct. 411, 66 L.Ed,2d 308 (1980). That is why the doctrine goes by the label issue preclusion, not claim preclusion. So long as the preconditions for issue preclusion exist, the Board’s decisions carry the same preclusive effect as those of courts and other agencies. See B & B Hardware, Inc. v. Hargis Indus., Inc., — U.S. -, 135 S.Ct. 1293, 1302-04, 191 L.Ed.2d 222 (2015); United States v. Utah Constr. & Mining Co., 384 U.S. 394, 422-23, 86 S.Ct. 1545, 16 L.Ed.2d 642 (1966) (giving preclusive effect to decisions of a similar agency board of contract appeals). And so long as the losing party in the first litigation has the opportunity to appeal the adverse ruling, it matters not whether it does so. See B & B Hardware, 135 S.Ct. at 1305-06.

Just two of these considerations concern us here. Does the Board’s finding in the Truth in Negotiation Act litigation answer the same question presented here? And was the Board’s answer necessary to its decision? In considering these issues, it helps to separate the findings with respect to year one of the contract (fiscal year 1985) and those with respect to the “out-years” of the contract — years two through six of the contract (fiscal years 1986 to 1990).

Year one (fiscal year 1985). Here is what the Board said with respect to year one:

[Pratt] provided evidence — and we so found [in our prior decision] — that neither the Defense Contract Audit Agency (DCAA), the [Air Force] price analyst, the contracting officer (CO) nor the cost panel reviewed the BAFO cost or pricing data prior to award. We believe this evidence rebutted the presumption of causation.
We are hard pressed to understand how the [Air Force] could have relied on BAFO cost or pricing data — defective or otherwise — that no one reviewed.
We are mindful that the [Air Force] price analyst and the CO testified on direct examination that they relied on the fact that the BAFO data furnished by appellant were current, accurate, and complete. We find that this testimony — given roughly 17 years after the fact — was lacking in specificity and was unpersuasive.
Upon reconsideration, we conclude that the [Air Force] failed to show that it relied upon Pratt’s BAFO cost or pricing data, and that it failed to show that [Pratt’s] defective BAFO cost or pricing data caused an increase in contract price for the base year of the contract. For this reason, the [Air Force] may not recover on its defective pricing claims for FY 85. ■

ASBCA II, 15-1 BCA at 162,812-13 (citations omitted).

The Federal Circuit affirmed. But as noted the government did not appeal the Board’s decision on this point, leaving the above ruling as the relevant one for issue preclusion purposes. See Guzowski v. Hartman, 849 F.2d 252, 255 (6th Cir.1988).

Issue preclusion does not apply to the Board’s no-reliance finding with respect to the first year of the contract. In the truth-in-negotiation litigation, the Board made its no-reliance finding based on the fact that no one at the Air Force looked at the cost or pricing data behind Pratt’s offer, not on the role of competition in how the Air Force set fair and reasonable prices. See ASBCA II, 05-1 BCA at 162,-812-13. The Board’s finding in the one case does not exclude the possibility in the latter case that the government nevertheless relied on Pratt’s separate misrepresentations that it corrected ■ its proposal and that its best and final offer was based on accurate cost data. The Board had no authority to review those misstatements because the Act does not cover falsities about how a contractor arrives at its prices. See ASBCA I, 04-1 BCA at 161,-024-25.

Years two through five (fiscal years 1986 to 1990). As to the “outyears” of the contract — years two through six — the answer is trickier, indeed quite difficult. Here is what the Board found:

With respect to the awards made, and the options exercised by the [Air Force] in the outyears — FY 86 through FY 90 — neither party disputes that the [Air Force] did not exercise these options at the same terms and conditions offered by appellant in the BAFO for these options. Rather as we found in our decision, the [Air Force] sought different and more advantageous offers each year from appellant and GE — described by the [Air Force] as the annual call for improvement process — prior to the exercise of each option. Appellant offered improvements in terms and conditions from its BAFO each year — in some years offering more generous improvements than others — with the hope of obtaining a larger share of the work each year. The [Air Force] evaluated the improvements offered by both competitors, and those - improvements the AF decided to accept were considered by the source selection authority to determine the new allocation decisions each year.
For each of the outyears, the CO documented the basis upon which he believed the revised offer from appellant was fair and reasonable. This determination was made after the [Air Force] had evaluated [Pratt’s] revised offer in response to the annual call for improvement. The CO prepared a memorandum for the record each year to document the decision to exercise and to fund each option. Insofar as pertinent, each memorandum stated as follows:
By a market test between the competitors ... the prices set forth ... are considered the most fair and reasonable prices available to the Government.
We believe this evidence, properly considered, shows that for the outyears the [Air Force] relied upon this “market test between the competitors” arising out of the calls for improvement to determine the reasonableness of [Pratt’s] revised offers, not the defective BAFO cost or pricing data filed by [Pratt] in December, 1983. A letter from the CO to DCAA dated 10 April 1989 also supports this conclusion:
[T]his contract is very unique in that it is basically a perpetual competition using a split award technique decided by the [Secretary of the Air Force] annually. In this process, the Contractor’s originally submitted certified Cost or Pricing Data has been subjected to an annual Call for Improvements letter requesting improvements in prices as well as terms and conditions. Over the years, dramatic improvements have been experienced in almost all areas. [Emphasis added]
This evidence served to rebut the presumption that appellant’s defective BAFO cost or pricing data were relied upon by the [Air Force] and, as such, caused an increase in the contract price in the outyears. As we stated earlier, the [Air Force] has the burden to prove causation. Based upon our reconsideration of all the evidence of record, we believe that the [Air Force] failed to carry its burden. The CO in the out-years, Mr. Rhodeback, did not review the December 1983 BAFO cost or pricing data at any time. He relied on the predecessor CO and the.RAA for this purpose. However for reasons stated herein, these latter sources also did not show any review or reliance on the BAFO data, and hence Mr. Rhodeback’s reliance upon them was without legal significance.
Mr. Rhodeback’s statements of reliance on BAFO cost or pricing data at trial were unsupported by any contemporaneous project records. Those records of the CO that were adduced — and that we discussed above — -show that competitive forces, rather than the defective 1983 BAFO cost or pricing data[,] were relied upon to make the awards and to exercise the options for additional purchases for FYs 86-90. In the face of such credible, contemporaneous evidence, we believe that Mr. Rhodeback’s unsupported trial statements to the contrary were unpersuasive.

ASBCA II, 15-1 BCA at 162,813 (citations omitted). Because the government did not appeal this aspect of the ruling, the Federal Circuit did not reach it, leaving this aspect of the Board’s decision untouched.

In one sense, the Board’s competition finding with respect to the last five years of the contract looks like an eminently appropriate setting for the application of issue preclusion. The key issue in both cases was nearly identical, and the Board’s relevant finding was necessary to the outcome. A contract adjustment under the Truth in Negotiations Act requires proof of reliance — causation—to determine whether the contract prices should be retroactively lowered to account for any impact that negotiation misstatements had on the final contract price. Wynne, 463 F.3d at 1265. The same is true for damages under the False Claims Act. See 31 U.S.C. § 3729(a); United States ex rel. Schwedt v. Planning Research Corp., 59 F.3d 196, 200 (D.C.Cir.1995). And the same is true for the common law restitution claims. See Restatement (Third) of Restitution and Unjust Enrichment §§ 5(2)(a) & cmt. e, 13 cmt. c (2011); Cleary v. Philip Morris Inc., 656 F.3d 511, 518-19 (7th Cir.2011).

The role of competition in the Air Force’s assessment of reasonable prices also was squarely before the Board and central to its finding of no reliance over the last five years of the contract. According to the Board, “th[e] evidence ... shows that for the outyears the [Air Force] relied upon th[e] ‘market test between the competitors’ arising out of the calls for improvement to determine the reasonableness of [Pratt’s] revised offers.” ASBCA II, 05-1 BCA at 162,813. No doubt, the Board might have been clearer on this point. In view of the calls for improvement, the significant reductions in each company’s offer prices over time, and the vigorous competition between the two jet engine manufacturers, the Board might have said that competition between the companies exclusively determined the reasonableness of Pratt’s revised offers in the outyears. Had the Board been this clear, that, it seems to us, would have been that. The competition finding in the one ease would bind us in the other. Nor would it have made a difference that today’s case concerns false cost estimates not covered by the Truth in Negotiations Act, or that the government has introduced additional evidence of causation/reliance in this case. Issue preclusion does not disappear merely because the losing party puts on a better case the second time around. See, e.g., Yamaha Corp. v. United States, 961 F.2d 245, 254-55 (D.C.Cir.1992) (“Preclusion cannot be avoided simply by offering evidence in the second proceeding that could have been admitted, but was not, in the first.”); Cory v. C.I.R., 159 F.2d 391, 392 (3d Cir.1947) (“[P]arties are not entitled to have a question considered on its merits a second time merely because they failed to produce all the facts the first time.”); Falconer v. Meehan, 804 F.2d 72, 76 (7th Cir.1986) (explaining that issue preclusion applies “even if in the prior action a different legal theory was argued” and prevents the second court from “deciding the same factual issues that were decided earlier”); see also Akron Presform Mold Co. v. McNeil Corp., 496 F.2d 230, 234-35 (6th Cir.1974) (rejecting new evidence to establish violation of antitrust laws in second action).

But the Board was not that clear — and indeed less clear than the above language read by itself suggests. The quoted lanuage does not appear by itself. The full sentence is comparative in nature: It says that the evidence “shows that for the out-years the [Air Force] relied upon th[e] ‘market test between the competitors’ arising out of the calls for improvement to determine the reasonableness of [Pratt’s] revised offers, not the defective BAFO cost or pricing data filed by [Pratt] in December, 1983.” ASBCA II, 05-1 BCA at 162,-813 (emphasis added). A few sentences down, the Board states its competition finding in comparative terms again: It says that “competitive forces, rather than the defective [December] 1983 BAFO cost or pricing data [,] were relied upon to make the awards and to exercise the options for additional purchases.” Id. (emphasis added). Nor can we rely on a sentence in the first Board decision that describes a 1984 letter from the Air Force saying that the contracts were awarded “solely” on a competitive basis. ASBCA I, 04-1 BCA at 161,013. In neither its first decision nor its reconsideration decision did the Board rely on this letter as a ground for decision. The letter at most would relate to damages for year one, moreover, and the Board (as shown) plainly did not rely on this letter in discussing damages for year one.

As this case comes to us, then, it is not clear whether the Board meant to say that competition together with the calls for improvement process exclusively drove prices or merely whether those competitive forces eliminated any damages caused only by the December 1983 false cost data. In the first setting, issue preclusion would apply. In the second setting, it would not, for it would remain possible that other types of falsities at other times could have affected an assessment of reasonable prices even in the face of these competitive forces. Because issue preclusion forever precludes litigation with respect to a covered finding, courts err on the side of construing prior ambiguous findings or holdings narrowly. See, e.g., Connors v. Tanoma Mining Co., 953 F.2d 682, 684 (D.C.Cir.1992) (“If the basis of [a] decision is unclear, and it is thus uncertain whether the issue was actually and necessarily decided in that litigation, then relitigation of the issue is not precluded.”); In re Braniff Airways, Inc., 783 F.2d 1283, 1289 (5th Cir.1986) (“[I]f reasonable doubt exists as to what was decided in the first action, the doctrine of res judicata should not be applied.”); Harris v. Jacobs, 621 F.2d 341, 343 (9th Cir.1980) (“If there is doubt on this score, collateral estoppel will not be applied.”). That, it seems to us, is a sensible way to resolve this difficult question here. We thus affirm the district court’s conclusion' that issue preclusion does not bar the government’s damages claims under the False Claims Act and common law restitution.

B.

False Claims Act and Restitution. That the Board’s competition finding does not bind us here does not mean that the competition between GE Aircraft and Pratt and the calls for improvement process were irrelevant to the government’s claim for damages under the False Claims Act and common law restitution based on a similar set of misstatements. Yet that, at the government’s urging, is just what the district court held. The court relied exclusively on Zacharetti’s price estimates as the value of Pratt’s engines and- yet Zacharetti, an auditor and not a pricing expert, refused to consider either the role that competition between Pratt and GE Aircraft (among other factors) played in determining reasonable and fair prices, or whether that competition and the prices that resulted from it eliminated any damages to the government.

That was wrong for several reasons. In the first place, it misreads our prior opinion. We asked the district court after the last appeal to redo its damages calculations to address three discrete flaws in its analysis that the government suffered no damages, and to determine the “fair market value” of the engines independent of the fraud:

On remand, the district court should calculate what the government eventually paid each year ..., what it should have paid each year based on what the government received, then take the difference between the two. If the court concludes that Pratt’s prices ... represent the fair market value of the fighter jet engine contract — or were below fair market value — the government is not entitled to damages.

United Techs., 626 F.3d at 322. At the same time, we cautioned the district court that its second assessment of the government’s claims, after correcting for the three identified flaws, might well lead to its first conclusion in this area (and the Board’s conclusion to boot): that no damages resulted in view of the critical role that competition played in setting prices. For law of the case purposes, our prior decision did not require the district court to find damages; did not require the district court to use (much less follow) Zacharetti’s analysis; did not require the court to exclude expert testimony from Pratt about reasonable and fair prices in this context; indeed did not require the court to abandon any part of its earlier conclusion save to consider how the three identified flaws might affect whether the government suffered any damages.

In the second place, our opinion did not undermine several factual findings in the district court’s initial opinion. In that opinion, it found, as the Board had found, that competition affected prices due to the significant discounts Pratt offered each year of the contract from its best and final offer in the course of the calls for improvements process. See United Techs., 2008 WL 3007997, at *12. It found that Zacharetti’s damages methodology, in addition to failing to account for the role of competition in pricing, “ignore[d] the nature” of Pratt’s scheme — to skew split— award prices relative to those under a full award — which failed. Id. at *11. Not only did the Air Force decline to give Pratt the full award, but GE Aircraft received three-quarters of the business in the first year of the contract. Id. And it found “no doubt that Pratt, chastened by” its failure to obtain a. full award, had offered the lowest prices it possibly could from then on — namely the last five years of the contract — because the government had successfully “creat[ed] an atmosphere of continual competition.” Id. at *12. We are hard pressed to understand how these findings — all about the role of competition and the calls for improvement process— were altered by our opinion or remain any less true today.

In the third place, our opinion broke no new ground in asking the court to consider the “fair market value” of the Pratt engines after accounting for the three flaws in its prior analysis. When the government gets what it paid for despite a contractor’s misstatements, it has suffered no “actual damages.” See United States v. Bomstein, 423 U.S. 303, 316 n. 13, 96 S.Ct. 523, 46 L.Ed.2d 514 (1976) (collecting cases); see also United States ex rel. Harrison v. Westinghouse Savannah River Co., 352 F.3d 908, 923 (4th Cir.2003). That is not just the law of the False Claims Act; it is also the black-letter law of fraud and restitution (putting aside disgorgement of profits, which the government does not seek here). See Restatement (Second) of Torts § 549(l)(a) (1977); Restatement (Third) of Restitution and Unjust Enrichment §§49 cmt. f, 54 cmts. g-h (2011). The only benchmark consistent with this benefit-of-the-bargain theory of damages is “fair market value,” by which we meant (and still mean) “what a willing buyer would pay in cash to a willing seller at the time.” United States v. 56j,.5j, Acres of Land, 441 U.S. 506, 511, 99 S.Ct. 1854, 60 L.Ed.2d 435 (1979) (internal quotation marks omitted).

With that traditional definition comes the traditional rules for proving value. “A ‘comparable sales’ analysis has long been and remains the preferred method of establishing ... ‘fair market value.’ ” United States v. 103.38 Acres of Land, 660 F.2d 208, 211 (6th Cir.1981). Indeed, the government itself has relied on that analysis to prove damages in False Claims Act cases. See, e.g., United States v. Killough, 848 F.2d 1523, 1531 (11th Cir.1988). The comparable sales valuation method applies even though the market for fighter jet engines is heavily regulated (many markets are), it has two sellers, and it results in few sales per year. Restatement (Second) of Torts § 911 cmt. f (1979). Fighter engine sales are hardly so rare that they fall into the narrow exception for public goods like “roads or sewers.” United States v. 50 Acres of Land, 469 U.S. 24, 30 n. 12, 105 S.Ct. 451, 83 L.Ed.2d 376 (1984) (quoting 564.54 Acres of Land, 441 U.S. at 513, 99 S.Ct. 1854); see Northrop Corp. v. McDonnell Douglas Corp., 705 F.2d 1030, 1055 (9th Cir.1983) (noting “the competitive nature of the military aircraft industry”). GE Aircraft’s engine prices are thus a natural place to look for evidence of the value the government received. The only question is whether those engines are adequately comparable to Pratt’s.

The Air Force’s procurement strategy in this instance proves they are. The premise of the “head to head” competition was that the two companies’ engines were similar. R. 441-3 at 18. That is why the Air Force directly compared the engine prices side-by-side, put on the table split-award bids and full-volume bids, and judged those prices “fair and reasonable” based on the “market test between the competitors.” ASBCA II, 05-1 BCA at 162,811. And — as we noted the last time around, as the district court noted the last time around, and as we think remains highly relevant this time around — the Air Force never requested new cost and pricing data during the annual calls for improvements. United Techs., 626 F.3d at 321; United Techs., 2008 WL 3007997, at *12. For such high-dollar and otherwise significant contract modifications, only “adequate price competition” could excuse that failure — as the government’s own regulations explain. See 10 U.S.C. § 2806(f)(2) (1982); A.S.P.R. § 3-807.3(b)(ii) (1976).

What happened each year of the procurement process confirms as much. In the opening year of this multi-year contract, the rival companies made “best and final offers” to the Air Force for their jet engines. Those offers, as it turns out, were neither the “best” nor the “final” offers made by either company. The government ultimately never paid any of them. In each subsequent year, the Air Force issued “calls for improvements” to each competitor, a pencil-sharpening exercise that allowed the rivals to lower prices (Pratt did so every year) in return for the hope of obtaining a larger share of the Air Force’s business (Pratt gained more business in some years, and GE Aircraft gained more in other years). Nor did the calls for improvement lead to marginal improvements. Pratt made substantial decreases to its best and final offer prices. According to the district court’s uncontested numbers, Pratt’s combined engine and warranty price discounts were as follows: $101 million (1986), $100.5 million (1987), $106.7 million (1988), $114.5 million (1989), and $63.4 million (1990). See United Techs., 2008 WL 3007997, at *8. Pratt even applied some discounts retroactively to first year prices. ASBCA I, 04-1 BCA at 161,014-15. While these decreases do not account for other terms of the offers (including reduced warranty coverage in some years), they make it crystal clear that this was not competition in the abstract but competition in fact. All of this reliance on price competition — echoing the Board’s prior finding in the context of the same sales, the same competition, the same procurement process, and the same types of inaccurate data from 1983 — belies any claim that GE Aircraft’s engines are so dissimilar they cannot serve as comparable sales for purposes of calculating damages. The district court accordingly erred by “presuming] that the amount overpaid is equal to the fraudulent amount quoted.” United Techs., 950 F.Supp.2d at 952.

One other flaw in the district court’s analysis bears mention. It miscalculated the fair-market value of the newly capped warranties by finding their'value precisely equal to their renegotiated prices, resulting in no damages offset for its price reductions. See id. at 955-56. Because Pratt’s original scheme was to offset engine cost overstatements with artificially low warranty prices under a full award, see United Techs., 2008 WL 3007997, at *11, the district court’s methodology does not fit the fraud. One premise of the scheme was to sell the engines and warranties as a package. Valuing the warranties in isolation thus does not work. The government argued the last time around that the district court had erred by “treat[ing] the separate warranty prices and engine prices as if they were one combined price.” See Brief of Appellant, United States v. United Techs. Corp., Nos. 08-4256/4257, 2008 WL 5707433 (6th Cir.2008). We rejected that argument and affirmed the district court’s analysis, for otherwise it would have made no sense for us to instruct the court to account for the value of the corresponding decrease in coverage. And that is why we remanded for the district court to recalculate “the fair market value of the fighter jet engine contract” — as a whole — not merely the engines. United Techs., 626 F.3d at 322 (emphasis added). The proper course was to measure fair market value of the contract as a bundle, beginning with GE Aircraft’s prices and adjusting for material differences.

The government seeks to uphold the district court’s decision in several ways. First, it defends the district court’s presumption that, when someone defrauds the government, each dollar of overstated costs translates into a dollar of damages. See United States ex rel. Taxpayers Against Fraud v. Singer Co., 889 F.2d 1327, 1333 (4th Cir.1989); Universal Restoration, Inc. v. United States, 798 F.2d 1400, 1403 (Fed.Cir.1986). But the district court never applied any such presumption in its first decision — in rejecting Zacharetti’s damages calculation- — and we did not reverse that part of its decision in the first appeal. How the presumption suddenly appeared on remand is something of a mystery.

Be that as it may, we do not see how the presumption, even if we were to accept it in the justifies the district court’s decision on remand. The cases permit a party to rebut the inference of damages. Three steps, not one, describe the process: (1) The government starts with the presumption; (2) the private party may rebut it; and (3) if the private party succeeds in rebutting the presumption, the burden returns to the government to show by a preponderance of the evidence that it was injured by the false statements. See Sylvania Elec. Prods., Inc. v. United States, 479 F.2d 1342, 1349 (Ct.Cl.1973). If that sounds familiar, that is because it is what the Federal Circuit held in rejecting the government’s claim for damages against Pratt under the Truth in Negotiation Act in the administrative action. Wynne, 463 F.3d at 1267 (“[T]he Air Force has not demonstrated that the Board erred in finding that UTech successfully rebutted the presumption of causation.”). Just as Pratt rebutted the presumption there by showing that no one relied on the relevant false statements and that competition controlled prices, so Pratt has rebutted that presumption here. As the above evidence shows, the Air Force’s reliance on competition to determine a reasonable price readily rebuts any such presumption.

One other point on this score. Zacharetti’s damages analysis was before us in the last appeal. See Brief of Appellant, United States v. United Techs. Corp., Nos. 08-4256/4257, 2008 WL 5707433 (6th Cir. 2008). In concluding that the government had suffered no damages under any of its federal-court claims in the first instance, the district court rejected Zacharetti’s damages assessment. United Techs., 2008 WL 3007997, at *11. Nothing in our prior opinion contradicted that analysis. To the contrary, we cautioned that the reassessment of damages after correcting for three targeted mistakes might still lead to a zero-damages conclusion. See United Techs., 626 F.3d at 322. That possibility could not co-exist with a wholesale acceptance of the Zacharetti analysis, the dollar-for-dollar premise of which would never lead to zero damages.

Second, the government argues that Pratt forfeited any objection to the district court’s “factual finding” that -GE Aircraft’s engines are not comparable. Appellee Supplemental Br. at 2. Whether forfeited or not, the government adds, that finding is entitled to deference. See United States v. 2,635.01 Acres of Land, 336 F.2d 646, 649 (6th Cir.1964). But the district court made no such finding. Nowhere did it compare the characteristics of the two engines. The court instead rejected GE Aircraft’s prices as a matter of law — a decision deserving no deference — based on the limited number of players in the market, infrequent sales, and GE Aircraft’s costs of market entry, all legally irrelevant to comparability. United Techs., 950 F.Supp.2d at 952; see VFB LLC v. Campbell Soup Co., 482 F.3d 624, 632 (3d Cir.2007) (“[T]he proper method of valuation in a particular factual context is a legal question.” (emphasis omitted)). Pratt repeatedly argued in its opening brief that the district court erred by ignoring “conventional measures of value” such as “comparable sales.” See Appellant Br. at 3, 27-29, 39. And in its reply, Pratt properly responded to the government’s contention that GE Aircraft’s engines were insufficiently comparable. Compare Appellee Br. at 32, with Reply Br. at 17-19. No forfeiture occurred.

Third, the government maintains that regulations promulgated under the Truth in Negotiations Act establish that cost plus a reasonable profit is the way prices necessarily work in this area. Zácharetti’s method thus honors this requirement better than a comparable-sales analysis, the argument goes, because it simply removes the overstatement. Not true. This argument overstates the force of the regulations. Pratt remained free to charge whatever it wanted. The Air Force did not conduct a “cost-plus” procurement for the engines, with prices set by Pratt’s eventual costs and a predetermined profit margin. “[N]o case or regulation” required any party to base prices on Pratt’s cost data. United States ex rel. Williams v. Martin-Baker Aircraft Co., 389 F.3d 1251, 1257 (D.C.Cir.2004). Had this been a cost-plus-reasonable-profit contract, Pratt would have been required to submit new cost data for the outyears, but the Air Force never asked for it. The Truth in Negotiation Act’s disclosure requirements no doubt gave the government the upper hand in negotiations by providing a window into a contractor’s cost structure. Hence Pratt’s acknowledgment that its prices could be no higher than “expected cost, plus a reasonable profit.” R. 344 at 146-47; R. 397 at 4. But this merely prompts — it does not answer — the question of what profit margin the market could reasonably support, which requires looking at GE Aircraft’s comparable prices, among other things. And those prices internalize the regulations, as is true in every regulated market. A comparable sales approach hardly involves a fictional market free of regulation, as the government suggests. No case says otherwise. In United States v. Commodities Trading Corp., 339 U.S. 121, 70 S.Ct. 547, 94 L.Ed. 707 (1950), and United States v. Cartwright, 411 U.S. 546, 93 S.Ct. 1713, 36 L.Ed.2d 528 (1973), the Supreme Court adopted prices directly set by regulation as the measure of value. No such regulations exist here. Prices turned on negotiation, and as such a comparison between GE Aircraft’s and Pratt’s prices was the place to start.

Fourth, the government argues that GE Aircraft’s engine sales are not comparable because its prices too were tainted by Pratt’s fraud. The taint argument works only if the evidence shows that Pratt’s prices were inflated by fraud. That of course is the question that, after two rounds of appeals and counting, we are still trying to figure out. The answer begins with comparable sales, if not potentially other indicators of value as well: the government’s own price estimates at the time; prior sales by Pratt; and foreign resales of the engines. So far, the government has come up short with evidence that meets its burden of proof of showing that, after considering comparable sales (among other factors), it suffered any damages.

Amen v. City of Dearborn, 718 F.2d 789 (6th Cir.1983), says nothing to the contrary. We held that the City could not prove the value of a taking by using prices of comparable property that its own takings had depressed. Id. 799-800. That decision makes sense because the City’s actions unquestionably diminished the property’s inherent value. Put another way, the resulting sales were not truly “arms length” transactions, Welch v. Tenn. Valley Autk, 108 F.2d 95, 101 (6th Cir. 1939), because the City’s actions were “designed to force residents ... to sell their property to the City.” Amen, 718 F.2d at 795. Here, the impact of Pratt’s fraud on the prices of its jet engines is hardly self-evident — just ask the Armed Services Board — making it appropriate to consider comparable sales, here GE Aircraft’s prices, if not other factors as well.

Fifth, the government argues that GE Aircraft had unique costs of market entry, and its engines were physically different from Pratt’s — making a comparable-sales analysis unhelpful. The notion that GE Aircraft’s market entry costs defeat comparability proves too much. Why then set prices based on competition, as the Air Force plainly did? “The proper test” of comparability “is the similarity in character” of the engines — and that similarity was the premise of the Air Force’s eompany-to-company competition. Knollman v. United States, 214 F.2d 106, 109 (6th Cir. 1954). This unclothed assertion about GE Aircraft’s market entry costs at any rate may reveal less than one might expect. After all, GE Aircraft Engines was not a start-up making a debut in constructing jet engines, but rather had been producing engines (albeit different models) for years.

The engines’ physical differences do not warrant ignoring GE Aircraft’s global prices either. The two engine models had differences, to be sure. Modifications to the F-15 would have been necessary to install the GE Aircraft engines. And the manufacturers’ engines had “different thrusts,” “airflows,” and “weights.” R. 330 at 149. But “comparable” in this context “does not mean identical].” 103.38 Acres, 660 F.2d at 211 (quoting Fairfield Gardens, Inc. v. United States, 306 F.2d 167, 172-73 (9th Cir.1962)). “Completely comparable sales are not likely to be found. Sales that have some different characteristics must be considered____ [The court] should not dismiss fairly comparable sales out of hand because of certain incomparable qualities.” Piney Woods Country Life Sch. v. Shell Oil Co., 726 F.2d 225, 239 (5th Cir.1984) (footnote omitted). These differences do not make GE Aircraft’s sales irrelevant for purposes of calculating damages, as the Air Force has acknowledged from 1983 on. Before Congress, Col. Jim Nelson testified that Pratt’s and GE Aircraft’s engines have “essentially equal capabilities and either engine will satisfy system requirements.” R. 441-3 at 6. An internal Air Force memo likewise confirmed that “[b]oth engines are being developed and tested to the same basic requirements.” R. 446-5 at 2. And the 1984 source selection touted that “both [are] excellent engines and are fully acceptable for both the F-15 and F-16 aircraft. There are no overriding technical advantages to either engine in [terms of] overall capability.” R. 443-25 at 1. Most importantly, the Air Force’s direct comparison of the engine prices proves GE Aircraft’s sales were comparable. Otherwise, the comparison does not make sense. The proper approach was to start with GE Aircraft’s prices and make adjustments for any material differences between the engines.

What now? We are tempted to say that, after seventeen years of litigation about a fraud that occurred thirty-two years ago, the time has come to end this dispute. The government proved its case under the False Claims Act and will be $7 million richer as a result, as we established in the last appeal. After we remanded the case, the government had every opportunity to put on an expert to show whether competition affected its damages. It not only refused to do so, but it also successfully objected to Pratt’s own efforts to put on a‘pricing expert. On this record, there is something to be said for leaving it at that. The government had the burden of proving damages, and it never did. At the same time, we are a court of review, not first view. See 28 U.S.C. § 1291. The district court presided over the remand litigation, and it is in the best position to decide in the first instance whether the government should have another opportunity to prove that it suffered damages even after accounting for the role of competition in setting prices for Pratt’s engines.

For these reasons, we reverse the district court’s judgment and remand the case for further proceedings consistent with this opinion.  