ROVNER, Circuit Judge.

Since 1984, the Gary Community School Corporation ("Gary Schools") has offered early retirement incentives to teachers aged 58 to 61. Eligible teachers who elect to retire early receive monthly payments until they turn 62. Teachers who retire on their 58th birthday receive the maximum forty-eight months of benefits available under this plan; teachers who retire later receive the same monthly payments but fewer of them, as the payments terminate at age 62. A similar plan is in place for school administrators. The plaintiffs in this case are teachers and administrators who were eligible for the early retirement incentives but chose not to retire at age 58. They contend that the incentive plan is inconsistent with the Age Discrimination in Employment Act, 29 U.S.C. § 621 et seq., because the plan doles out unequal benefits based on age. The district court agreed that the plan was facially discriminatory, and after concluding that Gary Schools had waived its affirmative defenses, granted summary judgment in favor of the plaintiffs on the question of liability. After a trial focused on the plaintiffs' entitlement to relief, the district court awarded damages to those plaintiffs who had retired equal to the amount of early retirement incentives they would have received had they retired at age 58. With respect to the plaintiffs who were still working at the time of trial, the court entered an injunction requiring the school district to make the same incentive payments to these individuals when they retired that it would pay to similarly-situated 58-year-old teachers or administrators. Gary Schools has appealed the district court's finding on summary judgment that the plans are discriminatory, and the plaintiffs have cross-appealed an evidentiary ruling and the denial of relief to one plaintiff. We affirm in large part, reversing only the denial of relief to plaintiff Paul Bohney.

I.

Between 1970 and 1984, the student enrollment within the Gary public school system dropped by one-third, precipitating lay-offs among teachers and administrators. In 1982, the Gary Teacher's Union proposed that the school system adopt an early retirement incentive plan. The aim of the plan was to induce teachers at the top of the pay scale to retire sooner than they would otherwise, thereby enabling the school system to retain more teachers who were lower in seniority and earned smaller salaries.

After study and negotiations, an early retirement incentive plan ("ERIP") was included in the collective bargaining agreement ("CBA") that the union and the school system adopted in 1983 for the 1984 calendar year. The ERIP specified the following eligibility criteria for teachers wishing to participate: (1) a minimum of fifteen years of creditable service, with at least ten of those years earned in the Gary Community School Corporation; (2) a Bachelor's Degree; and (3) a minimum age of 58 and a maximum age of 61. Teachers who met these criteria could receive early retirement incentive pay for up to forty-eight months, ending at age 62. These payments were calculated with reference to the starting salary paid to a teacher with a Bachelor's Degree during the year that the early retiree became eligible to participate in the ERIP. On an annual basis, early retirees with a Master's Degree would receive fifty percent of that starting salary, while those with a Bachelor's Degree alone would receive forty percent. Early retirees were also eligible under the ERIP to continue participating in the school system's group health and life insurance programs. Both the monthly payments and the right to continued insurance coverage were benefits offered in addition to, rather than in lieu of, any and all severance and retirement benefits that the early retirees had earned in the course of their employment.

This ERIP for teachers has been included in each collective bargaining agreement negotiated since 1983. The terms have never been modified or renegotiated.

A second ERIP for administrators (who are not members of a collective bargaining unit and thus are not parties to a CBA with the school system) was proposed and adopted by the school system in 1984. Originally, its terms were essentially the same as those of the teachers' ERIP. In 1988, the minimum eligible age for participation in the administrators' ERIP was lowered from 58 to 55, giving administrators a broader window of eligibility than teachers enjoy. Also that year, retired administrators between the ages of 62 and 65 were given the option of purchasing health and life insurance through the school system. No additional modifications in the administrators' ERIP have been made since 1988.

The thirty-four plaintiffs in this case were all employees of Gary Schools when the ERIPs for teachers and administrators were first implemented in 1984. Each was below the age of 58 when the plans were adopted and subsequently remained employed through at least June 1995, shortly before this suit was filed. During that time period, each of the plaintiffs became eligible to participate in the ERIPs upon turning 58 years old and thus had the option to retire at that age and receive the maximum benefits available. Each chose instead to continue working beyond age 58, foregoing some or all of the incentives provided for in the ERIPs. At the time this case was tried, twelve of the plaintiffs had retired, most after they had reached the age of 62 (meaning they received no early retirement benefits at all). One had died before trial while still in the school district's employ. The remaining twenty-one plaintiffs were still working for Gary Schools when the trial commenced.

Asserting that the age-based nature of the Gary Schools ERIPs was discriminatory, the plaintiffs filed suit under the ADEA. At the conclusion of discovery, the plaintiffs moved for summary judgment on the question of liability and their entitlement to liquidated damages. In a pair of rulings, the district court denied summary judgment as to damages but granted the motion as to liability. Noting that "Gary Schools' plans expressly dole out benefits based on age, with younger workers receiving better benefits," Dec. 10, 1996 Order at 3, the court found the ERIPs to be facially discriminatory, id. at 6. The ADEA, as amended by the Older Workers Benefit Protection Act of 1990, does establish certain affirmative defenses which under narrow circumstances offer an employer safe harbor even when its retirement plans appear discriminatory on their face, see 29 U.S.C. § 623(f), but the court concluded that Gary Schools had forfeited these defenses because it "did not plead, present measurable evidence on, nor meaningfully argue" them. Oct. 22, 1996 Order at 7. The court concluded, consequently, that the school system's liability under the ADEA had been established. Dec. 10, 1996 Order at 7.

Gary Schools later asked the district court to reconsider its summary judgment ruling, suggesting for the first time that the plaintiffs lacked standing to sue. Each of the plaintiffs could have opted to retire at age 58 and therefore reap the maximum benefits offered by the ERIPs but chose not to. Instead, they continued working, earning the top-of-scale salaries that they would have given up had they retired. As the school system saw it, the plaintiffs had thus suffered no injury that gave them the right to sue. The court rejected the standing argument, interpreting it "as actually raising merits issues that defendant could have and should have raised earlier." Tr. 21.

A jury trial ensued, limited solely to the subject of damages. At the close of evidence, the court granted, in part, the parties' cross-motions for partial judgment as a matter of law. None of the plaintiffs who were still working when the case was tried had testified. As a result, the court found no evidentiary basis for an award of damages of any kind to these individuals. Tr. 455. As for the plaintiffs who had retired, the court discerned no dispute with respect to the early retirement incentive payments that these individuals had lost by declining to retire at age 58. Tr. 464. The only issue remaining at that juncture was the retired plaintiffs' entitlement to liquidated damages, which depended on whether or not the defendant's conduct had been "willful." See 29 U.S.C. § 626(b). That question was submitted to the jury, which found in favor of Gary Schools. Tr. 505-06; R.110. The court therefore awarded the retired plaintiffs damages equal to the amount of benefits they would have received under the ERIPs had they elected to retire at age 58. R. 146. As for those individuals who were still working, the court entered an injunction specifying that each had the right to voluntarily retire and receive the full amount of early retirement incentive benefits that would have been paid to an eligible teacher or administrator who elected to retire at age 58. Id.

II.

The ADEA bars an employer from discriminating against any individual in the "compensation, terms, conditions, or privileges of employment, because of such individual's age[.]" 29 U.S.C. sec. 623(a)(1). That bar, Congress has now made clear, extends to "virtually all employee benefits and benefit plans," S. Rep. No. 101-263, at 5 (1990), reprinted in 1990 U.S.C.C.A.N. 1509, 1510 (emphasis ours), including early retirement plans. See 29 U.S.C. § 630(l). Thus, although an employer of course has no duty to offer early retirement incentives, once the employer elects to do so it must make those benefits available on nondiscriminatory terms, just as it must with any other fringe benefit. See, e.g., Karlen v. City Colleges of Chicago, 837 F.2d 314, 318 (7th Cir.), cert. denied, 486 U.S. 1044, 108 S.Ct. 2038 (1988).

A.

Our judicial power is restricted by Article III of the Constitution to actual "cases" or "controversies," (U.S. Const. Art. III § 2) and inherent in that limitation is the requirement that the plaintiff have standing to bring her suit. E.g., Arizonans for Official English v. Arizona, 520 U.S. 43, 64, 117 S.Ct. 1055, 1067 (1997). She must have suffered an "injury in fact," that is, "an invasion of a legally protected interest which is (a) concrete and particularized, and (b) actual or imminent, not conjectural or hypothetical." Lujan v. Defenders of Wildlife, 504 U.S. 555, 560, 112 S. Ct. 2130, 2136 (1992) (citations and internal quotation marks omitted); see also Steel Co. v. Citizens for a Better Environment, 523 U.S. 83, 118 S.Ct. 1003, 1016 (1998). "Second, there must be a causal connection between the injury and the conduct complained of — the injury has to be fairly . . . trace[able] to the challenged action of the defendant, and not . . . th[e] result [of] the independent action of some third party not before the court." Lujan, 504 U.S. at 560, 112 S. Ct. at 2136 (citation and internal quotation marks omitted); see also Citizens for a Better Environment, 118 S.Ct. at 1016-17. "Third, it must be likely, as opposed to merely speculative, that the injury will be redressed by a favorable decision." Lujan, 504 U.S. at 561, 112 S.Ct. at 2136 (citations and internal quotation marks omitted); see also Citizens for a Better Environment, 118 S.Ct. at 1017.

Gary Schools insists that none of the plaintiffs has standing to maintain this action, and its arguments revolve around the first two of the three criteria for constitutional standing outlined above. All of the plaintiffs were eligible for early retirement and, had they retired at age 58, would have received the full four years of incentive pay. Relying on our opinion in Henn v. National Geographic Society, 819 F.2d 824 (7th Cir.), cert. denied, 484 U.S. 964, 108 S.Ct. 454 (1987), Gary Schools emphasizes that the offer of these retirement incentives was a benefit to older workers (see id. at 828), and that eligible employees were free to take it or leave it as they chose. Having weighed their options and chosen to continue working, the plaintiffs cannot claim to have been injured, as Gary Schools sees it; the school system points out that each of the plaintiffs either testified or stipulated that he or she earned more in wages from Gary Schools than he or she would have received in early retirement benefits. See, e.g., Tr. 125-26, 139, 146, 152-53, 160, 165, 171-72, 283, 290-91, 300, 306. Moreover, any harm that the plaintiffs did suffer was instead traceable to their own unfettered choices, in Gary Schools' view, not the terms of the ERIPs.

The explicit terms of the early retirement incentives at issue in this case make it relatively easy for the plaintiffs to establish standing, however. The thrust of the plaintiffs' claims is that the ERIPs define "early" retirement wholly in terms of an employee's age, without reference to his need or desire to work. In other words, because the incentive payments under the plans commence at age 58 and end at age 62, only retirement prior to the latter age is deemed "early." No benefits under the ERIPs are offered to an individual who retires after reaching the age of 62, even if he agrees to retire in advance of his own target retirement date. It is in this respect that persons who retire outside the time frame of the ERIPs suffer an injury that gives them standing to sue.

A simple comparison illustrates the disparity. The ERIPs would permit a 58-year-old teacher with plans to retire at age 62 to retire immediately and receive four years of incentive payments. Yet a 66-year-old teacher with plans to retire at age seventy, but otherwise identically situated with her younger colleague (same number of years of creditable service, same accumulated pension benefits, and so on), would receive nothing if she chose to retire at once, notwithstanding that her retirement would be just as premature as that of her 58-year-old colleague. Individuals like this more senior teacher, for whom early retirement comes later than their 62nd birthday, suffer a concrete injury by virtue of the express terms of the ERIPs, just as surely as they would if their age disqualified them from receiving performance bonuses, wage increases, or promotions. Compare, e.g., Trans World Airlines, Inc. v. Thurston, 469 U.S. 111, 120-21, 105 S. Ct. 613, 621 (1985).

Our opinion in Henn does not suggest otherwise. The question we addressed there was not whether the plaintiffs had standing to challenge their employer's early retirement incentive program, but whether they had made out a prima facie case of discrimination. The program at issue in Henn was a one-time offer made to all advertising salesmen over the age of 55. Those who elected to retire at that time received a severance payment of one year's salary, retirement benefits calculated as if the retiree had quit at age 65, medical coverage for life, and supplemental life insurance. Each of the four plaintiffs had accepted the offer and received all of the benefits he was promised. Nonetheless, they filed suit, contending that their separation, as induced by the early retirement package, violated the ADEA. We rejected the notion — then embraced by the Second Circuit, see Paolillo v. Dresser Indus., Inc., 813 F.2d 583, withdrawn in part on reh'g, 821 F.2d 81 (2d Cir. 1987) — that retirement under an early retirement plan by itself gives rise to a prima facie case of age discrimination. We emphasized the significant value that a benign offer of early retirement carries for the employee to whom it is extended:

Provided the employee may decline the offer and keep working under lawful conditions, the offer makes him better off. He has an additional option, one that may be (as it was here) worth a good deal of money. He may retire, receive the value of the package, and either take a new job (increasing his income) or enjoy new leisure. He may also elect to keep working and forfeit the package.

813 F.2d at 826. Persons eligible for early retirement are, therefore, "the beneficiar[ies] of any distinction on the basis of age." Id. at 827. "None can claim to be adversely affected by discrimination in the design or offer of the early retirement package." Id. We concluded that the retirees in Henn could prevail on a claim of discrimination "only by showing that [their employer] manipulated the options so that they were driven to early retirement not by its attractions but by the terror of the alternative." Id. at 829. In other words, the relevant question was "whether the existing [employment] conditions (ignoring the offer of early retirement) violate the ADEA." Id.; see Karlen v. City Colleges of Chicago, supra, 837 F.2d at 317.

Henn's inquiry does not answer the question posed in this case. The plaintiffs here are not contending that they were pressured to retire early, or that they suffered some affirmative detriment (a cut in pay, for example) as a result of their decisions to continue working. Their claim is that the way in which eligibility for participation in the ERIPs is defined by age is in itself discriminatory. This was a claim we did not confront in Henn. In that case, anyone over the age of 55 was able to take advantage of the offer. Beyond the minimum-age requirement — something that the ADEA sanctions, see 29 U.S.C. § 623 (l)(1)(A) — the terms of the plan incorporated no age-based assumptions as to when retirement is "early" and when it is not; a 75 year old could retire on the same terms as a 55 year old. See Karlen, 837 F.2d at 318.

B.

Having resolved the standing question, we can turn to the merits. The principal issue we must consider is whether the plaintiffs successfully established a prima facie case of age discrimination. As we noted earlier, the district court concluded that Gary Schools had waived the affirmative defenses set out in 29 U.S.C. § 623(f). Gary Schools does not challenge that ruling and therefore cannot resort to the statutory defenses in the effort to avoid liability. Instead, it insists that the plaintiffs have not even made out a prima facie case of discrimination, obviating any need to mount a defense. See Henn, 819 F.2d at 827. However, our opinion in Karlen v. City Colleges of Chicago makes short work of that argument.

The early retirement plan at issue in Karlen was in significant respects similar to the Gary Schools ERIPs. The plan was designed in part to encourage more senior teachers, who were of course employed at higher salaries, to retire early and enable the municipal college system to hire new teachers at lower salaries. The plan was open to any faculty member between the ages of 55 and 69 who had been employed on a full-time basis for at least ten continuous years. An individual who retired under the plan would receive a pension based on his highest four years of salary and the length of his service. That component of the plan, which was not keyed to the employee's age, was not challenged. Two other aspects were. First, upon retirement, the employee would also receive a lump sum equal to a certain percentage of his accumulated sick pay. Those retiring at ages 55 to 58 would receive fifty percent, those retiring at 59 would receive sixty percent, and those retiring at 60 to 64 would be paid eighty percent. Those who retired at 65 to 70, however, would receive only forty-five percent of their accumulated sick pay. In addition, faculty members who retired between the ages of 55 and 64 continued to be covered by the colleges' comprehensive group insurance plan until they reached the age of 70, while those who retired at age 65 or later would lose that coverage unless they elected to shoulder the premiums themselves. Thus, employees who retired at age 64 or earlier received significantly greater benefits than those who waited until age 65.

We found the terms of this plan sufficient to establish a prima facie case of age discrimination. We emphasized that this was not a case like Henn, in which the retirement incentives were offered to everyone over a given age on the same terms. Karlen, 837 F.2d at 318.

In the present case, . . . there is discrimination against the older worker. Everyone between 55 and 69 is eligible for early retirement, but those between 64 and 69 — an older age group — are disfavored relative to the younger employees in the eligible group. If the City Colleges said to their faculty, at age 65 you lose your free parking space (or dental insurance, or any other fringe benefit), they would be guilty, prima facie, of age discrimination. Early-retirement benefits are another fringe benefit — and they plummet at age 65.

Id. We proceeded to consider the City Colleges' arguments in defense of the plan disparities, and in the course of that discussion firmly rejected the notion that establishing a presumptive age of "early" retirement is permissible under the ADEA:

A feature common to both the sick-pay and insurance components of the Early Retirement Plan is the sharp drop in benefits at age 65. . . . The Colleges cannot and do not argue that the drop in benefits at age 65 is justified by the higher cost of benefits to a 65-year-old retiree as compared to a 64-year-old one (because of more accumulated sick leave, valued at a higher base pay, and because of higher insurance costs). They argue that in order to induce early retirement of faculty members in the 65-69 year bracket they have to make 65 a breaking point. They say that if the decline in benefits with age were gradual, as it would have to be to reflect accurately the changing cost of the retirement package, no one would retire before 70. The small annual decline in sick-pay distribution and in insurance coverage would be more than offset by the growth in the pension component of the retirement package as a result of salary raises and additional years of service. So the purpose of the Early Retirement Program — to induce early retirement — would be defeated.

This strikes us as a damaging admission rather than a powerful defense. To withhold benefits from older persons in order to induce them to retire seems precisely the form of discrimination at which the Age Discrimination in Employment Act is aimed. Rather than offering a carrot to all workers 55 years and older, as in the Henn case, the City Colleges are offering the whole carrot to workers 55 to 64 and taking back half for workers 65 to 69. The reason is that the Colleges want to induce workers to retire by 65. In effect they have two early retirement programs; a munificent one for workers 55 to 64 and a chintzy one for workers 65 to 69. . . .

Id. at 320.

In this case, there is an equally obvious difference in the benefits that retirees will receive under the ERIPs depending upon their age. Those retiring at age 58 will receive four years of incentive payments, those retiring at age 60 only two years, and those retiring at age 62 or later, nothing. Those employees who elect to retire at 62 or later are put at a disadvantage for not retiring when they were 58 to 61, no matter how "early" their later separation may be in terms of their length of service or previous retirement plans. And even for those within the 58 to 61 age group, we have exactly the situation that we did in Karlen — a full "carrot" for those aged 58, and an increasingly smaller piece of that carrot (25 percent less per year) for those closer to age 62. The amount of the benefits varies depending upon the retiree's age, nothing else. Just as in Karlen, the terms of the ERIPs establish a prima facie case of age discrimination. Accord, E.E.O.C. v. Crown Point Community School Corp., 1997 WL 54747, at *5 (N.D. Ind. Jan. 2) (Rodovich, M.J.).

That the disadvantage employees over the age of 58 experience is the withdrawal of a "carrot" rather than the sting of a "stick" (see Gary Schools Br. at 27-28) makes no difference to the analysis. It may well be true that teachers and administrators who choose not to retire suffer no loss in position, salary, or other benefits; indeed they will almost certainly earn more in salary and benefits by continuing to work than they have forfeited by declining to retire at age 58 to 61. The same was no doubt true in Karlen. See 837 F.2d at 316-17. But once they have reached the age of 62, all early retirement incentives are withheld, no matter how ahead of schedule the employee elects to retire in terms of his years of service, for example — and no matter that any employee who retires ahead of schedule confers a benefit on Gary Schools by reducing its salary obligations and opening a position for a junior employee. See Tr. 268-69. Later-retiring employees will thus have to work longer to make up for the early retirement benefits they would have received at age 58 to 61, incurring substantial opportunity costs as a result. Karlen, 837 F.2d at 317. In this respect, employees who retire at a younger age are treated more favorably than those who retire later, based not on years of service or some other nondiscriminatory factor, but solely on their age at retirement. This is the point of Karlen: the "carrot" of early retirement incentives cannot be extended based solely on the age of the retiree. Id. at 320.

Nor does it matter that each of the plaintiffs could have retired within the framework of the ERIPs and received the maximum available benefits. See Gary Schools Br. 22-23. The point of the plaintiffs' case is not that they were never eligible for the incentives, but that the terms of the plans put them to an unlawful choice. Employees are offered incentives to retire sooner than they otherwise plan, but "early" retirement is defined exclusively in terms of age. Yet one's ability to retire is typically dependent on a host of factors other than age: one's years of service with the employer (which will typically affect pension benefits), savings, dependents, health, and so on. Consequently, not all 58-year-olds will be equally situated to retire. One 58-year-old might have already completed thirty years of service with Gary Schools, for example, and as a result have earned the level of pension benefits that allows him to retire, but it might take a more recent employee who is also 58 and has similar financial needs another several years to reach that same level. The first could elect to retire at once and receive four years of incentive payments; the second would have to continue working and as a result forfeit some or all of the early retirement payments. In this way the ERIPs treat employees who are similarly situated in terms of their preparedness to retire differently, depending on their age.

Of course, the disparity of which the plaintiffs complain results from the maximum age (62) that the ERIPs impose on the receipt of early retirement benefits, and Gary Schools reminds us that we found such a maximum lawful in Dorsch v. L.B. Foster Co., 782 F.2d 1421, 1428 (7th Cir. 1986). The plan under scrutiny there offered employees whose age plus years of service totaled 75 or more incentive payments of $600 per month until they reached the age of 62. By virtue of the age cap, qualified younger retirees would receive the monthly payments for a greater number of years and would therefore earn greater total benefits than older workers. Nonetheless, we found nothing in that arrangement inconsistent with the ADEA. Id. at 1427-28. "`Obviously a man of 67 cannot retire at 55 and obtain benefits provided for persons of that age. And to effect the purpose of encouraging early retirement, the sliding scale of diminishing benefits is manifestly appropriate.'" Id. at 1428, quoting Patterson v. Independent School Dist. No. 709, 742 F.2d 465, 468-69 (8th Cir. 1984).

It was several years after we decided Dorsch, however, that Congress enacted the Older Workers Benefit Protection Act, which made substantial revisions to the ADEA, including changes to the provisions concerning early retirement plans. See n. 2, supra. Among the new provisions is one stating that it is not a prima facie violation of the Act for a "defined benefit plan" to offer "social security supplements for plan participants that commence before the age and terminate at the age (specified by the plan) when participants are eligible to receive reduced or unreduced old-age insurance benefits under title II of the Social Security Act . . . and that do not exceed such old-age insurance benefits." 29 U.S.C. § 623(l)(1)(B)(ii). The ADEA thus sanctions "bridge" payments which span the gap between an employee's age upon early retirement and the age at which she first becomes eligible for reduced or unreduced social security benefits. Those payments might look something like the $600 monthly payments we examined in Dorsch, which terminated when an employee reached age 62 — the minimum eligibility age for reduced social security benefits. In fact, the legislative history of the OWBPA explicitly addresses Dorsch, and limits its rationale to these types of bridge payments. S. Rep. No. 101-263, at 21 (1990), reprinted in 1990 U.S.C.C.A.N. 1509, 1526-27. Thus, as amended by the OWBPA, the ADEA does permit an employer to offer, as an early retirement incentive, monthly payments which terminate at a specified age, even though younger workers will stand to receive greater benefits under that arrangement than older workers. However, those payments must satisfy the criteria specified in the statute, key among them being the requirement that the payments not exceed the payments that the retiree is likely to receive once she is eligible for social security benefits. 29 U.S.C. § 623(l)(1)(B)(ii). Here, the record reveals no connection between the ERIP payments and the social security benefits that early retirees could be expected to receive at age 62, when the incentive payments cease. On the contrary, the assistant superintendent for fiscal integrity conceded that Gary Schools never undertook any type of analysis as to the age at which early retirees actually opt to begin receiving social security payments or the specific dollar amounts of the social security payments that teachers and administrators would receive. R. 43 at 8 para. 28; R. 44 Ex. 26, James H. Wooten Dep. 64-65; see also Tr. 211-12. Consequently, neither Dorsch (as limited by the OWBPA) nor the narrow provision of the statute permitting social security bridge payments is of any help to Gary Schools.

C.

When it granted summary judgment in favor of the plaintiffs on the question of liability, the district court observed that because the terms of the ERIPs were discriminatory on their face, the plaintiffs were not required to prove that Gary Schools intended to discriminate on the basis of age; that intent could instead be presumed. Dec. 10, 1996 Order at 6. Gary Schools argues that the court erred in relieving the plaintiffs of this obligation. Even if it is appropriate to presume discriminatory intent in other contexts, Gary Schools argues, it is improper to do so in the context of early retirement incentives. It steers us back to Henn, 819 F.2d at 828, in which we noted that because an "offer of early retirement is beneficial to the recipient, there is no reason to treat every early retirement as presumptively an act of age discrimination," and also to Karlen, 837 F.2d at 317, where we pointed out that to the extent early retirement incentives discriminate, often "the discrimination seems to be in favor of rather than against older employees, by giving them an additional option and one prized by many older employees." In view of the beneficial choices that early retirement plans make available to senior employees, Gary Schools reasons, it is impermissible to presume discriminatory intent based on the terms of the plans alone. Only if the plaintiffs can show that the terms of the plan make "arbitrary" distinctions based on age, see Trans World Airlines, Inc. v. Thurston, supra, 469 U.S. at 120, 105 S.Ct. at 621, quoting Lorillard v. Pons, 434 U.S. 575, 577, 98 S.Ct. 866, 868 (1978), and that the school system intentionally discriminated against them, can they establish liability, Gary Schools insists.

The district court was correct to presume discriminatory intent in this case, however. The terms of the ERIPs themselves explicitly establish an employee's eligibility for the early retirement incentives in terms of his age. The plans are therefore discriminatory on their face, see Thurston, 469 U.S. at 121, 105 S.Ct. at 622; Los Angeles Dep't of Water Power v. Manhart, 435 U.S. 702, 715, 98 S.Ct. 1370, 1379 (1978), and independent proof of an illicit motive is unnecessary, see International Union, UAW v. Johnson Controls, Inc., 499 U.S. 187, 199-200, 111 S.Ct. 1196, 1203-04 (1991). We recognized as much in Karlen, when we concluded that the terms of the City Colleges' early retirement plans, which sharply reduced the benefits offered to employees aged 65 and older, themselves established a prima facie case of age discrimination. 837 F.2d at 318. The reasons for the drop-off, we noted, would be relevant not to the prima facie case, but to the affirmative defenses specified by the statute. Id. Here, of course, Gary Schools was found to have waived those defenses.

The age-based distinctions drawn by the ERIPs are also arbitrary, as we have already discussed. Harkening now to the provision of the statute that permits an employer to offer "bridge" payments which will run until the retiree attains eligibility for social security, Gary Schools argues that the age cap of 62 that it imposed on the early retirement incentives is not arbitrary and hence not discriminatory. At that age, it reasons, a retiree can begin to collect reduced social security payments and therefore no longer needs a financial incentive to retire. The flaw in that argument, as we have already mentioned, is that the incentive payments that Gary Schools offers are in no way keyed to the payments that an employee can be expected to receive from the Social Security Administration, as the statute requires. 29 U.S.C. § 623(l)(1)(B)(ii). So far as the record reveals, then, these payments offered a retirement incentive entirely unrelated to an employee's expectations as to the social security income he might begin to receive at age 62. The statutory approval of social security bridge payments therefore does not endorse the age cap that Gary Schools has imposed on the incentives.

D.

Finally, Gary Schools suggests that the plaintiffs have been given a windfall by having been awarded the benefits (or the right to receive the benefits) offered by the ERIPs without having to retire at the age specified by the plans. In effect, the plaintiffs' victory has transformed the early retirement incentives into severance payments made to all employees upon retirement. Gary Schools Br. 29. That argument has some intuitive appeal. None of the plaintiffs who testified, for example, indicated that she retired sooner than she otherwise planned or was prepared to do. There is no way to know on this record, then, whether any of the plaintiffs "earned" the incentives by retiring "early." That may simply be the price Gary Schools has to pay, however, for establishing an early retirement plan which turns on the employee's age. Once that discriminatory criterion is removed, there is nothing left in the terms of the plan (but for the criteria as to the employee's minimum years of service) to objectively assess any given employee's eligibility for the incentives. In any case, Gary Schools has not appealed the terms of the judgment entered in the plaintiffs' favor. We therefore need not consider whether there were any alternative remedies available to rectify the discrimination.

III. A.

The question whether Gary Schools' violation of the ADEA was willful was submitted to the jury. As we noted at the outset, the jury found that it was not. The plaintiffs contend that this finding was tainted by an evidentiary ruling that they believe was erroneous. At trial, the district court permitted Gary Schools to elicit testimony that in 1995, after receiving a letter from Gerald Lind (the president of the Gary Schools Administrators Association) raising the possibility that the ERIPs might discriminate against employees over the age of 59, Superintendent James Hawkins requested a legal opinion from the schools' in-house counsel, who responded with a memorandum opining that the administrators' ERIP complied with the ADEA and was not discriminatory. Dr. Hawkins' letter requesting the opinion, as well as the opinion itself, were also admitted into evidence. Defendant's Exs. 5, 7. We have said that "[a]n employer acts willfully if it `either knew or showed reckless disregard for the matter of whether its conduct was prohibited by the ADEA.'" Pierce v. Atchison, Topeka Santa Fe Ry. Co., 65 F.3d 562, 574 (7th Cir. 1995) (quoting Trans World Airlines, Inc. v. Thurston, 469 U.S. at 128, 105 S.Ct. at 625). We have also acknowledged that this assessment "`turns on the employer's mental state when the alleged violation was committed.'" Tennes v. Massachusetts Dep't of Revenue, 944 F.2d 372, 378 (7th Cir. 1991), quoting Overgard v. Cambridge Book Co., 858 F.2d 371, 377 (7th Cir. 1988) (emphasis ours). Emphasizing that the relevant time period for the defendant's state of mind was that prior to 1994, when Gary Schools renewed the ERIPs for the last time, the plaintiffs contend that evidence as to the solicitation of a legal opinion in 1995 was both irrelevant and prejudicial to the plaintiffs.

We agree with the district court, however, that the plaintiffs themselves opened the door to this evidence. The plaintiffs called Dr. Hawkins to the stand as an adverse witness at trial. The following exchange occurred during direct examination:

QUESTION: Do you recall receiving any written communication from Mr. Solon [the lead plaintiff in this action] about the Early Retirement Program?

ANSWER: No.

QUESTION: Do you remember receiving any written communication from anyone else about it?

ANSWER: Yes.

QUESTION: Who was that?

ANSWER: Mr. [G]erry Lin[d].

QUESTION: That was in 1995, wasn't it?

ANSWER: I can't recall the date. But I do recall receiving something from Mr. Lin[d] about the Early Retirement Incentive Program.

QUESTION: It's true, isn't it, that you first became aware of the claims that Mr. Solon was raising about the age limitations in the retirement program in a meeting with the Gary Schools Administrator's Association?

ANSWER: That's correct.

QUESTION: And that meeting was some time in 1994; was it not?

ANSWER: I can't tell you precisely what date it was. I remember receiving something, yes.

QUESTION: Was it in 1994 that you attended a meeting with the Gary Schools Administrator's Association where the subject of the age limitations in the Incentive Plan came up?

ANSWER: I really can't tell you if it was 1994 or not. I do recall receiving something from Mr. Lin[d] relative to the early retirement incentive Plan. Whether it was '94 or '93, I really can't recollect.

QUESTION: All right. Regardless of the year, there was a meeting with the GSAA in which they raised concerns about the age limitations; correct?

ANSWER: That is correct.

QUESTION: As a result of that specific meeting, you did not request a legal opinion; did you?

ANSWER: Yes, I did.

QUESTION: The meeting, sir, as a result of the meeting?

ANSWER: As . . . a result of the communication in the meeting.

Tr. 320-21. Plaintiffs' counsel then attempted to impeach Hawkins with his deposition testimony, in which Hawkins had said that he had not requested a legal opinion as a result of the GSAA meeting (and, in fact, had never asked for a legal opinion at all). Tr. 322-23. On cross-examination, however, Hawkins explained that Lind's letter, which expressed concern that the early retirement plan was discriminatory, was a follow-up to a discussion which had taken place during one of Hawkins' meetings with the GSAA (the timing of which is left unclear by the record). Tr. 327. Once he received that letter, Hawkins testified, he sought and received a legal opinion from the schools' in-house counsel. Tr. 330-31. In other words, it was apparently Hawkins' position that he requested the legal opinion in 1995 in response to the concerns expressed at the GSAA meeting as well as in Lind's letter.

We appreciate the plaintiffs' concern as to the relevance of the solicitation and receipt of the legal opinion. Because neither occurred until 1995, after Mr. Solon had already filed his charge of discrimination with the EEOC, they shed little or no light upon the defendant's state of mind in 1994, when the ERIPs were last renewed. But we can by no means say that the district court abused its discretion in allowing these items and the testimony describing them into evidence, after the plaintiffs' counsel made an issue of what steps Hawkins took in response to the concerns raised at the GSAA meeting. Moreover, the district court delivered a limiting instruction admonishing the jury to consider the legal opinion only insofar as it bore upon Hawkins' state of mind at the time he received it. Tr. 349. That instruction left the plaintiffs free to argue, as they did, that the opinion said nothing about the schools' disregard for their rights prior to and in 1994, when the ERIPs were renewed for the final time. Tr. 479-80, 482-83.

B.

Paul Bohney, an administrator, retired from Gary Schools prior to trial. Bohney did not testify, however, and as a result, the evidence introduced at trial did not establish that he had the requisite minimum years of service with Gary Schools to have been eligible for the early retirement incentives. On that basis, the district court granted judgment as a matter of law in favor of Gary Schools on the question of Bohney's entitlement to damages. See Tr. 443-47, 456. Bohney subsequently filed a post-judgment motion asking the district court to reconsider its position. Among other things, he pointed out that the answer to the plaintiffs' first amended complaint admitted that he had been in Gary Schools' employ for 42 years. See R. 22 at 4 para. 8; R. 26 at 2 para. 8. The district court agreed, in light of the answer on file, that "Gary Schools appears to have admitted the crucial fact of Bohney's years of service." Oct. 23, 1997 Order at 7. Yet, that admission had not been introduced at trial, leaving the trial record devoid of any basis on which a jury could have awarded Bohney damages. Id. The court therefore reaffirmed its conclusion that Gary Schools was entitled to judgment as a matter of law as to Bohney. Id. at 7-8.

Gary Schools' answer to the complaint obviated any need for Bohney to present evidence of his years of service, however. There is no dispute that Bohney, having worked for Gary Schools for 42 years, had more than the minimum years of creditable service required to participate in the administrators' ERIP. That Gary Schools admitted the length of Bohney's service in its answer was not simply evidence as to this eligibility criterion, but a judicial admission which removed this point from the realm of contested issues. Judge Ripple noted the import of such an admission in Keller v. United States, 58 F.3d 1194, 1198-99 n. 8 (7th Cir. 1995):

Judicial admissions are formal concessions in the pleadings, or stipulations by a party or its counsel, that are binding upon the party making them. They may not be controverted at trial or on appeal. Indeed, they are "not evidence at all but rather have the effect of withdrawing a fact from contention." Michael H. Graham, Federal Practice and Procedure: Evidence § 6726 (Interim Edition); see also John William Strong, McCormick on Evidence sec. 254, at 142 (1992). A judicial admission is conclusive, unless the court allows it to be withdrawn; ordinary evidentiary admissions, in contrast, may be controverted or explained by the party. Id. . . .

See also Soo Line R.R. Co. v. St. Louis S.W. Ry. Co., 125 F.3d 481, 483 (7th Cir. 1997). Consequently, there was no need, as the district court assumed (Oct. 23, 1997 Order at 7) for Bohney to communicate the admission as to his years of service to the jury; for with this fact formally conceded in the pleadings, there was nothing for the jury to find. Indeed, there appears to be no doubt that had the court taken into consideration this admission, Bohney would have been entitled to judgment as a matter of law as to monetary relief just as the court concluded the other retired plaintiffs who testified were. See Tr. 464-65.

The court therefore erred in granting judgment as a matter of law in favor of the defendant as to Bohney's right to damages and in denying Bohney's post-judgment request for relief. The judgment is reversed to that extent.

IV.

For the reasons discussed, we agree with the district court that Gary Schools' system of explicitly age-based early retirement incentives violates the Age Discrimination in Employment Act. We find no reversible error in the district court's decision to admit evidence concerning Gary Schools' solicitation of a legal opinion concerning the validity of its early retirement incentives. We do find error in the refusal to award plaintiff Paul Bohney monetary relief; and we reverse the judgment in that respect alone. As it appears that Bohney was entitled to judgment as a matter of law on the question of damages, we remand so that the district court may award him appropriate monetary relief. The plaintiffs shall recover their costs of appeal.

AFFIRMED IN PART, REVERSED IN PART, and REMANDED.