I.

BOGGS, Circuit Judge.

The plaintiffs in this class action receive pensions from the United States Steel Corporation ("US Steel"), administered pursuant to the United States Steel Corporation Plan for Employee pension Benefits ("Plan") by the defendant, United States Steel and Carnegie Pension Fund ("Fund"). The Plan allows the Fund to set off against the plaintiffs' monthly pension any workers' compensation benefits that the plaintiffs receive for which US Steel pays, "directly or indirectly."

In addition to their pensions, the plaintiffs receive workers' compensation benefits from the Kentucky Special Fund, awarded to them during the years 1977-1986. The Special Fund is a state program designed to spread the costs of workers' compensation claims, especially claims against employers in the coal industry. The Special Fund is financed by annual employer contributions. Each year, an employer must pay either (i) a percentage of the total cost (the discounted value of the expected life-time benefit stream) of all awards to its employees during the year ("Estimated Cost Method"), or (ii) a percentage of a predicted total cost based on the number of employees on the payroll and the type of work they perform ("Payroll Method"). US Steel contributed to the Special Fund on behalf of the plaintiffs from 1976 to 1986, using the Estimated Cost Method for all years except 1977. In 1986, US Steel ceased its operations in Kentucky. Because no additional awards were made to US Steel's workers, the company made no further contributions to the Special Fund. The central issue in this litigation is the amount of the plaintiffs' Special Fund benefits that the Fund can set off against the plaintiffs' pensions, under the terms of the Plan.

II.

The facts that gave rise to this action are set out in detail in Wells v. United States Steel Carnegie Pension Fund, Inc., 950 F.2d 1244 (6th Cir. 1991) ("Wells I"). that appeal involved the district court's review, under the "arbitrary and capricious" standard, of the Fund's decision to set off against the plaintiffs' pensions the entire amount of their Special Fund benefits. We reversed the district court, holding that the complete setoff was arbitrary and capricious in light of evidence that US Steel contributed to the Special Fund only part of the money that would be necessary to pay for the plaintiffs' benefits over time. Wells I, 950 F.2d at 1253-55. We remanded so that the district court could determine the correct amount of the setoff. For clarity, we will call the appropriate rate of setoff the "contribution percentage," defined as the percentage of each workers' compensation check that is attributable, under the terms of the Plan, to US Steel's contributions to the Special Fund.

On remand, both parties presented the court with formulas for calculating the contribution percentage. These formulas, even under the abbreviated scrutiny described below, are clearly inappropriate. Convinced — perhaps by the difficulty of the subject matter, perhaps by the obstinacy of the parties — that no middle ground existed, the court eventually picked the plaintiffs' formula. The parties have timely appealed, and present three issues: (1) whether the formula adopted by the district court is appropriate and, if not, what formula is; (2) whether the district court erred in awarding attorney's fees to the plaintiffs; and (3) whether the district court erred in awarding the parties prejudgment interest.

III.

The formulas for calculating the contribution percentage proposed by the Fund on remand are so obviously flawed that we can affirm the district court's rejection of them without inquiry into the appropriate standard of review. The Fund's "universal approach" compares the total contribution of US Steel to the Special Fund between 1977 and 1986 on behalf of all employees with the total compensation that the plaintiffs could expect from the Special Fund over their lifetimes. The formula is unacceptable because of the large number of non-plaintiffs on whose behalf US Steel made Special Fund contributions during these years.

The Fund's "year-to-year" and "cash-flow" approaches make a different mistake. Both methods set the contribution percentage equal to the total contribution of US Steel to the Special Fund in the award year divided by the total benefit received by US Steel employees from the Special Fund in that year. The methods ignore the fact that an employer makes its entire contribution during the award year, while workers receive benefits over their lifetimes. Comparing the entire contribution to a temporal fraction of the benefits received results in ridiculous numbers. Using its "year-to-year" method, for instance, the Fund calculates that US Steel financed an average of 298% of the Special Fund payments to the plaintiffs.

The formula proposed by the plaintiffs, and accepted by the district court, is equally inappropriate. The plaintiffs' method determines the contribution percentage for each benefit payment by dividing US Steel's total annual contribution to the Special Fund by the total annual revenue of the Special Fund for the year in which the individual plaintiff received the benefit payment. For example, in 1985, US Steel contributed less than one percent of all payments made to the Special Fund by all employers in Kentucky; it can set off, therefore, less than one percent of the Special Fund benefits received by the plaintiffs in that year. Furthermore, since US Steel ceased Kentucky operations in 1986, making no contributions to the Special Fund thereafter, it cannot set off any of the Special Fund benefits received by the plaintiffs after that date. In the end, the plaintiffs' formula results in a total setoff, for all the plaintiffs, of less than $5,000, compared to US Steel's estimate that it contributed over one half million dollars to the Special Fund on behalf of the plaintiffs.

The general use of the plaintiffs' formula would have ludicrous consequences. A small employer (contributing, for example, .001 percent of the total Special Fund) could set off virtually nothing against the pensions it paid; while a huge employer (contributing twenty percent of the state-wide total) could set off a full fifth of its payments, even though the relative pension payments were exactly the same! US Steel could set off benefits for ten years for awards that it funded in 1976, but only for one year for awards that it funded in 1986. And, if US Steel moves back to Kentucky in 1997 and has some horrible accident, the current class of plaintiffs could suddenly have their pensions decreased because of mandatory Special Fund contributions wholly unrelated to their awards.

The district court believed that it was required to accept the plaintiffs' formula because the exact contributions of US Steel to the Special Fund were not earmarked for particular plaintiffs. We do not agree. The Special Fund may be an undifferentiated pool of money, but we know, at a minimum, that US Steel contributed a definite amount of money in the award year because of each particular plaintiff's claim. The presence of but-for causation between the award and US Steel's contribution supports a conclusion that US Steel "indirectly paid" for some amount of the benefits due to particular employees, to the extent of the particular contribution.

After it lost below on remand — and only then — the Fund abandoned its earlier position. It now advocates a somewhat fairer reading of the Plan. It is unfortunate that the Fund did not present the district court with this reading, which represents a substantial step towards an appropriate resolution of the dispute, during the proceedings on remand — choosing instead to criticize the moderate position as "artificial" and unworkable. Essentially, the Fund's latest method would cap the total, lifetime setoff for each plaintiff by the total amount US Steel paid to the Special Fund because of the plaintiff's award. Although it is enticingly simple, the method cannot differentiate between legitimate workers' compensation (benefits received by an employee during his working life as a replacement for lost wages) and "double-dipping" (benefits received by a retiree that duplicate his pension). Nor does it indicate how the total allowable setoff should be distributed over the stream of monthly benefits checks.

Under other circumstances, after rejecting all of the solutions proposed below as inadequate, we would remand in hopes that the parties and district court would discover an acceptable solution. Given the complexity of this case and the amount of resources already spent to resolve it, however, we think it appropriate to resolve the methodological dispute now, and leave only calculation for remand. The matter demands some patient mathematics, however, which we will now discuss.

IV.

US Steel's Special Fund contribution on behalf of an employee occurred at the end of the year in which that employee received his award. The amount of the contribution was a proportion of the total cost (discounted value of the expected life-time benefit stream) of the employee's award. The proportion for each award year varied according to political considerations and the Special Fund's needs. However, for each employee, US Steel's records contain the amount of US Steel's contribution, the estimated total award cost in award-year dollars, and the part of that estimated total award cost to be paid by the Special Fund (usually 75% of the award would be paid to the employee out of the Special Fund, with US Steel paying the remaining 25% to the employee directly).

An appropriate contribution percentage can be calculated by dividing US Steel's contribution into the Special Fund on behalf of a plaintiff during the award year by the total cost of benefits to be paid to a plaintiff out of the Special Fund. For any expenditure by the Special Fund on behalf of a plaintiff, whether it be for health care or pension benefits, the contribution percentage can be used to determine what part of that expenditure the employer has indirectly funded (we note that the employer's initial contribution was not earmarked for any particular type of expenditure).

Only one modification of this formula is necessary: an adjustment to remove administrative costs from the set-off calculation. The Plan allows the Fund to set off only those "benefits" "paid to . . . any participant," and it would contradict this language to place the burden of administrative costs on the retirees. For the sake of simplicity, this "administrative cost multiplier" to account for such costs is best set at an average value, the same for all the plaintiffs. The appropriate multiplier is one minus the proportion of the administrative expenses of the Special Fund from 1976 to 1986 (all the award years) to the total revenue of the Special Fund during this period. This results in a relatively simple equation to determine the contribution percentage for each plaintiff:

V.

The second issue on appeal is the propriety of the district court's award of attorney's fees to the plaintiffs. District courts have discretion to shift attorney's fees in ERISA actions, although there are five factors that courts should consider:

(1) the degree of the opposing party's culpability or bad faith; (2) the opposing party's ability to satisfy an award of attorney's fees; (3) the deterrent effect of an award on other persons under similar circumstances; (4) whether the party requesting fees sought to confer a common benefit on all participants and beneficiaries of an ERISA plan or resolve significant legal questions regarding ERISA; and (5) the relative merits of the parties' positions.

Armistead v. Vernitron Corp., 944 F.2d 1287, 1301 (6th Cir. 1991) (citing Secretary of Dep't of Labor v. King, 775 F.2d 666, 669 (6th Cir. 1985)). No single factor is determinative. Rather the court should consider each before exercising its discretion. Armistead, 944 F.2d at 1304.

The district court's decision to award fees rested, in substantial part, on a finding of bad faith that was clearly erroneous. The finding of bad faith was adopted along with the recommendation of the Magistrate Judge, and based "on the fact that the defendant continued to set off Kentucky Special Fund benefits at a time when it was not only not making contributions to the Kentucky Special Fund, but at a time when it wasn't even operating a coal mine in Kentucky." This rationale does not fit our understanding of the nature of US Steel's Special Fund obligations. However, the record does contain other evidence that suggests an award of attorney's fees in this case may be appropriate. For eight years, until this appeal, the Fund refused to put forward a defensible interpretation of the Plan documents. The district court held that the plaintiffs did actually confer a benefit on other participants, and that the Fund would be deterred from an overly broad reading of similar setoff provisions. Furthermore, there is evidence in the record that the plaintiffs would not have brought this suit, and continued to litigate it for eight years, if recovery of fees was not a possibility.

We might conclude that fee awards are proper when, as in this case, there is litigation to establish the rights of a class of plaintiffs under an ERISA-protected plan and the economic situation of the plaintiffs is such that they could not bring suit except for the prospect of fee-shifting.

Armistead, 944 F.2d at 1304.

We believe that this last factor carries the day. The plaintiffs in this case submitted detailed records of their financial situation, alleging that they would be unable to pay their considerable attorney's fees. The amount of these fees, approximately $180,000, represents a substantial part of the money the Fund took from them when it decided to withhold the pensions. Furthermore, the amount of these fees is directly related to the many meritless positions the Fund has taken since 1986. Failure to affirm the award of fees now may cause fewer plaintiffs to join suits of this sort, and encourage funds to take unrealistic positions to prolong litigation. In light of all this additional evidence in the record, we affirm the district court's award of attorney's fees despite the inaccuracy of the Magistrate Judge's finding of bad faith.

The plaintiffs contend that the district court erred by failing to enhance the lodestar calculation by a factor of 1.5 because of the complexity of the case and the extent of the plaintiffs' eventual victory below. The decision to enhance the lodestar calculation is in the discretion of the district court, and we will reverse only if the district court abused that discretion. The plaintiffs' arguments as to why the district court abused its discretion are not convincing. Attorneys are compensated for the complexity of a case by the high number of billable hours complex issues generate. We also note that the extent of the plaintiffs' victory — if this is an appropriate concern in deciding to enhance a lodestar calculation — is considerably narrowed by our present opinion.

VI.

The final issue before this court is whether the district court's award of prejudgment interest to the plaintiffs on the amount of the Fund's underpayments and to the Fund on the amount of its overpayments was proper. We have held that ERISA is silent on the issue of prejudgment interest and that, in the absence of legislative direction, "the decision to grant or deny prejudgment interest should hinge on whether to do so would further the congressional purposes underlying the obligations imposed by the statute in question." Bricklayers' Pension Trust Fund v. Taiariol, 671 F.2d 988, 989 (6th Cir. 1982) (citing Rodgers v. United States, 332 U.S. 371, 373, 68 S.Ct. 5, 5, 92 L.Ed. 3 (1947)).

Generally, the beneficiaries of pension plans have a right to prejudgment interest on benefits wrongly withheld. Short v. Central States, Southeast and Southwest Areas Pension Fund, 729 F.2d 567 (8th Cir. 1984); Sweet v. Consolidated Aluminum Corp., 913 F.2d 268, 270 (6th Cir. 1990). The Fund alleges that interest is inappropriate in this case because the plaintiffs' claims were unliquidated, citing Bituminous Casualty Corp. v. Lynn, 503 F.2d 636, 645 (6th Cir. 1974). As an initial matter, it is unclear whether the plaintiffs' claim was unliquidated, in the sense that the "amount . . . can[not] be ascertained readily by reference to a formula" in the contract. Id. at 646. The amount due to each plaintiff monthly was fixed, and the Fund had paid the amounts for several years. The Fund's unilateral setoff, therefore, appears to be a refusal to pay a definite amount. Of course, the amount of setoff was uncertain and unliquidated, but the setoff, at heart, is a claim by the Fund against the plaintiffs, not vice versa. A holding for the Fund would allow any party to a contract to render a claim unliquidated merely by proposing a plausible counter-claim. Furthermore, even if the claim was unliquidated, we hesitate to apply this distinction, used in contract cases such as Bituminous Casualty, to suits under a statute such as ERISA, with its own set of policy concerns. See Wickham Contracting v. Local Union No. 3, 955 F.2d 831, 836 (2nd Cir. 1992) (unliquidated nature of damage claim does not bar award of prejudgment interest in LMRA case when the district court decided such interest was appropriate and purposes of labor statute would be served). Because the claim was arguably liquidated, and because of the general ERISA policy favoring awards of prejudgment interest to plaintiffs when a pension fund wrongfully withholds benefits, it would be inappropriate to reverse the trial court's award of interest as an abuse of discretion. See Tiemeyer v. Community Mut. Ins. Co., 8 F.3d 1094, 1102 (6th Cir.), cert. denied, ___ U.S. ___, 114 S.Ct. 1371, 128 L.Ed.2d 48 (1993) (district court has broad discretion to award prejudgment interest to plaintiffs in an ERISA action against a pension fund).

The question of whether the Fund is entitled to prejudgment interest on the amount it overpaid certain of the plaintiffs is not so clear. On the one hand, the Fund has lost the interest value of the money it overpaid. See e.g., Short, 729 F.2d at 576 (prejudgment interest appropriate where "the relief granted would fall short of making [a party] whole because he has been denied use of money which was his."). See also Drennan v. General Motors Corp., 977 F.2d 246, 253 (6th Cir. 1992), cert. denied, ___ U.S. ___, 113 S.Ct. 2416, 124 L.Ed.2d 639 (1993), cited in Tiemeyer, 8 F.3d at 1102 ("Awards of prejudgment interest are compensatory, not punitive, and a finding of wrongdoing by the defendant is not a prerequisite to such an award."). On the other hand, the Fund voluntarily overpaid and, unlike the plaintiffs, was in a position to control the amount of the setoff. Being in control, the Fund has a much weaker claim that its adversary received an unjust enrichment than do the plaintiffs. Cf. Sweet, 913 F.2d at 270 (prejudgment interest appropriate because "[t]o allow the Fund to retain the interest it earned on funds wrongfully withheld from a beneficiary would be to approve of an unjust enrichment.") (emphasis added). The focus on control is consistent with federal ERISA policy against deliberate unjust enrichment. Although there are many ways to characterize an award against a fund that withheld benefits — e.g., compensation, penalty — there is only one way to characterize an award against people whom the pension fund has, by its own mistake, overpaid: restitution. We have held that purely restitutionary awards under ERISA should not include prejudgment interest. Whitworth Bros. Storage v. Central States, Southeast and Southwest Areas Pension Fund, 982 F.2d 1006, 1019 (6th Cir.), cert. denied, ___ U.S. ___, 114 S.Ct. 67, 126 L.Ed.2d 36 (1993) (employer in ERISA action is not entitled to prejudgment interest on funds it mistakenly overpaid multi-employer pension fund). The logic of that holding requires an extension to cover the present situation, when a fund seeks restitution of money it overpaid plan beneficiaries.

This apparently unequal outcome — affirming an award of interest for the plaintiffs, but reversing an award of interest for the Fund — is required by federal policy; the general situation and incentives of employers, pension funds, and beneficiaries; and the particular facts of this case. There may well be situations when an award of prejudgment interest in favor of an employer who mistakenly overpays can be justified, but this case is not such a situation, and the award in favor of US Steel should be reversed.

VII.

In conclusion, we reverse the district court's adoption of the plaintiffs' formula for calculating the setoff. On remand, the district court should apply the formula contained in this opinion. We also reverse the district court's award of prejudgment interest in favor of the Fund. On remand, prejudgment interest should be awarded only to the plaintiffs. The remainder of the judgment appealed from is AFFIRMED.