The defendant, an ERISA pension plan, appeals from a judgment of some $300 million in a class action on behalf of plan participants. The plan (in the sense of the pension contract, as distinct from the entity that provides the pensions required by the contract — we use the word in both senses and trust to context to disambiguate) is what is called a "cash balance" plan. It is a defined benefit plan rather than a defined contribution plan, but resembles the latter. The ordinary defined benefit plan entitles the employee to a pension equal to a specified percentage of his salary in the final year or years of his employment. The plan might provide for example that he was entitled to receive 1.5 percent of his final year's salary multiplied by the number of years that he had been employed by the company, so that if he had been employed for 30 years his annual pension would be 45 percent of his final salary. A cash balance plan, in contrast, entitles the employee to a pension equal to (1) a percentage of his salary every year that he is employed (5 percent, in the case of the Xerox plan) plus (2) annual interest on the "balance" created by each yearly "contribution" of a percentage of the salary to the employee's "account," at a specified interest rate that in the Xerox plan is the average one-year Treasury bill rate for the prior year plus 1 percent. These annual increments of interest are called future interest credits.

The reason for the scare quotes in our description of the cash balance plan is that the employee has no actual account, the employer makes no contributions to an employee account, and so there is no account balance to which interest might be added. In a defined contribution plan, the employee's pension entitlement is to the value of his retirement account to which contributions (whether from the employer, the employee, or both) have been made, while in a defined benefit plan, as our numerical example illustrated, the entitlement is to the pension benefit that the plan promises. The cash balance form of defined benefit plan resembles a defined contribution plan because it provides the employee with a hypothetical account balance. He can compare that with the actual balance of a defined contribution plan if, as is commonly and in this case true, the employee is enrolled in both types of plan and when he retires will get to choose between the two pension entitlements (this is what is known as a floor-offset arrangement). At age 60 a Xerox employee might have $100,000 in his defined contribution account and $120,000 in his cash balance (hypothetical) account, and he would know that the former would be growing by the amount of the employer's annual contribution plus the investment performance of the account while the latter was growing by the specified percentage of his salary plus the one-year T-bill rate plus 1 percent. If he retired at the normal retirement age of 65, he would choose between the two plans on the basis of which had a larger expected value.

If an employee has worked for his employer for at least five years, his defined benefit pension benefits will have vested by operation of law. That is, they will have become an entitlement, specifically an entitlement to the "normal retirement benefit," 29 U.S.C. § 1053(a), defined, so far as applicable to this case, as "the benefit under the plan commencing at normal retirement age," id. § 1002(22), which is 65. If the employee leaves the company before he reaches the normal retirement age, his "normal retirement benefit," which is to say his pension entitlement, is the benefit that he has "accrued" to the date of his leaving. Id. § 1002(23)(A). In the case of a defined contribution plan (the benefits of which, incidentally, vest immediately), that benefit is simply the amount in his retirement account when he leaves the company's employment. Id. § 1002(23)(B). In the case of a standard defined benefit plan, the kind that entitles the retiree to a pension equal to a percentage of his salary based on his years of service, the entitlement is to a pension beginning at age 65, the amount depending on his years of service and his salary. But what about a cash balance plan? Xerox's cash balance plan entitles the departing employee not to the balance in his (hypothetical) account, but to the balance when he receives the "distribution" of his pension benefit. If he defers the distribution until reaching the normal retirement age of 65, the cash balance will grow between when he leaves Xerox's employment and when he turns 65 by the one-year T-bill rate plus 1 percent.

The plaintiff class, consisting of those employees of Xerox enrolled in the cash balance plan who left Xerox's employ between 1990 and 2000 and elected to take a lump sum when they left in lieu of a pension commencing when they reached 65, contends that the amount of the cash balance at age 65 (more precisely, the estimated amount, since the T-bill rate will vary over the period between the employee's leaving Xerox's employment and his turning 65) is the employee's accrued cash balance benefit and thus the basis for calculating the size of the lump-sum entitlement. Xerox acknowledges that employees who defer taking their pension benefits until they reach the age of 65 are entitled to an annuity, commencing then, or a lump sum then, either one reflecting the future interest credits. However, it is employees who leave Xerox before reaching age 65 but rather than waiting till they reach that age to receive their pension benefits ask for a lump sum now who compose the plaintiff class; and while Xerox gave them all a lump sum, they contend that the amount they received was not the actuarial equivalent of what they would have received either as an annuity or a lump sum had they waited until age 65. ERISA requires that any lump-sum substitute for an accrued pension benefit be the actuarial equivalent of that benefit. 29 U.S.C. § 1054(c)(3); May Dept. Stores Co. v. Federal Ins. Co., 305 F.3d 597, 600 (7th Cir.2002); Esden v. Bank of Boston, 229 F.3d 154, 164, 173 (2d Cir.2000).

The basic tradeoff involved in determining actuarial equivalence between a lump sum and an accrued pension benefit is between a present and a future value, and the method of equating them is the application of a discount rate to the future value. There is no single actuarial equivalence, because there is no single discount rate. A discount rate is simply an interest rate used to shrink a future value to its present equivalent, as distinct from swelling a present value to its future equivalent. If you have a right to receive $100 a year for 10 years beginning 15 years from now, and your discount rate is 10 percent (that is, you value receiving $90 today the same as receiving $100 a year from now), the present value of that right is the sum of $100 discounted at 10 percent 15 times, $100 discounted 16 times, and so forth to $100 discounted 25 times. Discounting produces dramatic differences between present and future values. For example, at a 10 percent discount rate the present value of $100 a year in perpetuity is only $1000, and even at a discount rate of only 5 percent that present value is only $2000. But at a zero discount rate, the present value of $100 a year in perpetuity would be infinite.

In the case of a standard defined benefit plan, the present value of the pension benefit is easily determined. The accrued benefit is determined by years of service and final salary when the employee leaves his employment — these are known quantities — and the application to the benefit of a discount rate generates the present value. Moreover — and critically as we are about to see — the discount rate is determined by the Pension Benefit Guaranty Corporation. Specifically, for pension plans of the vintage of the Xerox plan at issue in this case, the discount rate is the "rate which would be used (as of the date of distribution) by the Pension Benefit Guaranty Corporation for purposes of determining the present value of a lump sum distribution on plan termination." 29 U.S.C. § 1053(e)(2)(B) (1993); see also 26 U.S.C. § 417(e)(3)(B) (1993). That rate purportedly is derived from data on market interest rates. See 58 Fed.Reg. 5128-01, 5130 (Jan. 19, 1993), 40844-03, 40845 (July 30, 1993). For new pension plans, the 30-year T-bill rate is to be used as the discount rate. 26 U.S.C. § 417(e)(3); 29 U.S.C. § 1053(e)(2).

Because salary is not added to the employee's cash balance "account" after he leaves Xerox's employ, the key question, so far as the adequacy of the lump sum that he receives if he elects a lump-sum payout is concerned, is whether future interest credits are part of his accrued benefit. If they are, then in determining his pension entitlement (a future value, obviously, since we are dealing with employees who leave Xerox before reaching retirement age) the plan must add the credits to the employee's cash balance account. The resulting balance, discounted at the prescribed discount rate back to the date on which the employee left Xerox's employ, would then be the lump sum to which ERISA entitled the employee. The Xerox plan computed the lump sum differently. Instead of adding future interest credits to the departing employee's cash balance at the plan's future-interest-credits rate (that is, the T-bill rate plus 1 percent), it added interest at a rate exactly equal to the discount rate prescribed by the Pension Benefit Guaranty Corporation. The two rates, the interest rate and the discount rate, being identical, canceled, with the result that the lump sum that the departing employee received was his cash balance on the date of his departure.

Since the future interest credits are not fixed, but vary with the one-year T-bill rate, and the discount rate fixed by the PBGC varies over time as well, it is not certain that Xerox's method of computing the lump sum always produces a lower number than would the one-year T-bill rate plus 1 percent, the interest rate that is used to compute the future interest credits. Thus, even if the accrued pension must include those credits, as the plaintiffs argue they must, determining the present lump-sum equivalent of a pension benefit swelled by those credits requires estimating their value as of the date at which the employee left Xerox's employment. It is estimation rather than determination that is required because the T-bill rate fluctuates. One method of estimation would be just to use the current one-year T-bill rate, on the theory that it is an unbiased estimator of future such rates. An alternative would be to average several recent years of one-year T-bill rates. These were indeed the alternatives considered by the district court; and Xerox, while denying that future interest credits should figure in the plaintiffs' lump-sum entitlements at all, does not make an issue of the method of figuring those credits into the lump sum if they have to be figured in. A Treasury regulation requires that one of these two methods be used. Treas. Reg. § 1.401(a)(4)-8(c)(3)(v)(B). The judge chose the single-year approach, and the plan does not complain, because it yields a smaller lump sum than use of the five-year average (the alternative prescribed by the regulation to using the current rate) would do.

Despite the uncertainty noted in the preceding paragraph, the discount rate fixed by the PBGC, and thus used by the plan in lieu of estimating future interest credits in determining the plaintiff's lumpsum entitlements, was lower, over the period relevant to the suit, which is to say during the 1990s, than the interest rate that the plan used to compute the future interest credits. In the 1990s the PBGC-decreed discount rate varied from 4 percent to (rarely) 6.5 percent, while the interest rate used to compute future interest credits (the one-year T-bill rate plus 1 percent) varied from 4.4 percent to 9.7 percent. It is the difference between these ranges that generated the $300 million judgment, since the lower the discount rate, the greater the present value of a future benefit.

While arguing that the accrued pension benefit under the cash balance plan does not include future interest credits, the plan concedes that the employee has an absolute, vested, indefeasible entitlement, upon leaving Xerox's employ, to a pension at age 65 based on his cash balance as increased by future interest credits accruing between his departure and his reaching that age, provided only and obviously that he does not demand an earlier distribution. That pension entitlement, to which future interest credits contribute because after the employee leaves Xerox his cash balance will continue to grow by virtue of those credits, is an accrued benefit and if the employee prefers its lump-sum equivalent that equivalent has to include a fair estimate of those credits.

Xerox argues that because the employee's entitlement to future interest credits terminates when he takes a distribution, which he can do at any time after his entitlement to a pension vests, the only benefit that he accrues is the benefit on the date of distribution, which is to say the hypothetical cash balance on that date; and so that is his lump-sum entitlement. If he remains employed by Xerox until he is 65, his cash balance account will be enriched by future interest credits that accrued in every year of his employment, but, as in all previous years, the account remains the measure of his entitlement. In the words of the reply brief, the plan "does not determine accrued benefits by reference to a participant's CBRA [cash balance retirement account] at normal retirement age. Rather, it determines accrued benefits by the participant's CBRA balance when he receives a distribution."

The argument is emptily semantic. The employee who defers receiving benefits until he reaches his normal retirement age "receives a distribution" then, and thus his accrued benefits include future interest credits to that date. Any distribution that he receives earlier is the commutation of those accrued benefits to their present-value lump-sum equivalent. If Xerox believed the argument, it would not go through the motions of first projecting future credits at the PBGC rate and then discounting them at the same rate to present value; it would just say, as it does in its brief, that the employee's entitlement is just to whatever his hypothetical cash balance is when he takes his retirement benefits.

The argument makes transparent Xerox's objective of equating the cash balance plan to a defined contribution plan, where the employee's only entitlement is to the amount in his account when he decides to leave or retire. But a cash balance plan is not a defined contribution plan; it is a defined benefit plan, and so triggers the congressional policy of requiring that a lump-sum distribution of pension benefits equal the value of the benefits if the employee decides to wait to the normal retirement age and take them then in the form of a pension. Xerox tells its employees who leave the company before they reach that age that if they leave their money with the company they will obtain a pension beginning at age 65 that will reflect future interest credits. They are offered the alternative of taking a lump sum now in lieu of a pension later, but the lump sum is not the prescribed actuarial equivalent of the pension that they are invited to surrender by accepting the lump sum because it excludes those credits.

They are, in short, being invited to sell their pension entitlement back to the company cheap, and that is a sale that ERISA prohibits. They might be happy with such a sale, because their personal discount rate may exceed that fixed by the PBGC (or, for plans of more recent vintage, the 30-year T-bill rate). And they might be better off if Xerox could use a higher discount rate, for then it could afford a higher schedule of pension benefits because it would be paying out less to those early-retiring employees who opted for a lump sum. (Notice that a discount rate that exceeded the one-year-T-bill-plus-1-percent rate at which future interest credits accumulate would yield a lump-sum entitlement smaller than the cash balance account that Xerox offers the early retirees.) But the PBGC has decreed otherwise, and Xerox challenges neither its authority to fix a discount rate applicable to the Xerox cash balance plan nor the discount rate it did fix.

It might seem that Xerox should not be penalized for its generosity in reckoning future interest credits, even in severely diminished form, into the lump-sum entitlements of employees who choose cash balance plan benefits over their defined contribution benefits. Actually it had no choice. To be tax-qualified, a cash balance plan must be "frontloaded," IRS Notice 96-8, "Cash Balance Pension Plans," 1996-1 C.B. 359 (Feb. 5, 1996), that is, must include interest on the money in the employee's hypothetical account for the period between his leaving the employer and his reaching age 65. Otherwise, because of discounting, the cash balance pension benefit would be worth very little if the employee left the company's employ many years before he reached 65, and the Internal Revenue Code denies tax benefits to, and ERISA outright forbids, pension-plan terms that tend to lock an employee into his current employment by "backloading" his pension entitlement excessively, id.; 26 U.S.C. §§ 411(a), (b)(1); 29 U.S.C. § 1054(c)(3); Jones v. UOP, 16 F.3d 141, 143-44 (7th Cir.1994); Smith v. Local 819 I.B.T. Pension Plan, 291 F.3d 236, 238 (2d Cir.2002); Esden v. Bank of Boston, supra, 229 F.3d at 158-59, that is, by configuring it so that it is worth very little unless the employee stays with the company until normal retirement age.

The Internal Revenue Service's Notice 96-8, cited earlier, is an authoritative interpretation of the applicable statutes and regulations for reasons explained in Esden v. Bank of Boston, supra, 229 F.3d at 168-69, and it defines frontloaded cash balance plans in words that are an exact description of Xerox's plan (as distinct from Xerox's method of determining actuarial equivalence): "under a cash balance plan, the retirement benefits payable at normal retirement age are determined by reference to the hypothetical account balance as of normal retirement age, including benefits attributable to interest credits to that age" (emphasis added). The Notice makes clear that the future interest credits provided by such plans are part of the employee's accrued benefit: "benefits attributable to interest credits are in the nature of accrued benefits ... and thus, once accrued, must become non-forfeitable." A forfeiture will occur, therefore, "if the value of future interest credits is projected using a rate that understates the value of those credits or if the plan by its terms reduces the interest rate or rate of return used for projecting future interest credits." Which is just what Xerox did.

Xerox argues that its cash balance plan is not the same as the plan described in the IRS Notice, but is instead what it calls a "hybrid" cash balance plan. But the only thing that makes it hybrid, according to the plan's own description, is that it specifies a lump-sum entitlement that is not the prescribed actuarial equivalent of the pension benefit to which the plan entitles employees who leave their money in the plan until they reach their normal retirement age. So for "hybrid" read "unlawful." The plan conditions the employee's right to future interest credits on the form of the distribution that he elects to take (pension at age 65 rather than lump sum now), which is precisely what the law forbids. We conclude, in agreement with the Second Circuit which considered a materially identical plan in the Esden case, that the Xerox plan's method of computing the plaintiffs' lumpsum entitlements violates ERISA.

It remains to consider a few procedural and remedial issues (others are raised but do not have sufficient merit to warrant discussion). The first is whether the class action was properly certified under Fed.R.Civ.P. 23(b)(2). That rule authorizes a class action from which opting out is not permitted if the suit seeks injunctive or declaratory relief on a ground common to the entire class. In contrast, Rule 23(b)(3), which authorizes class actions when common issues predominate over issues that differ among claimants, requires that members of the class be given an opportunity to opt out of the class action and pursue their claims independently. Xerox contends that this suit does not seek injunctive or declaratory relief, but really just damages equal to the difference between the lump sums to which ERISA entitled the members of the class and the smaller lump sums that they actually received.

This issue has become hideously confounded in the briefs of both sides with the unrelated question whether a suit for monetary relief can be equitable. That question is important under ERISA when suit is brought by a fiduciary, because ERISA fiduciaries may sue under ERISA only for equitable relief. 29 U.S.C. § 1132(a)(1)(3); Great-West Life & Annuity Ins. Co. v. Knudson, 534 U.S. 204, 209-10, 122 S. Ct. 708, 151 L. Ed. 2d 635 (2002). But the suit here is by plan participants suing "to recover benefits." 29 U.S.C. § 1132(a)(1)(B). The plan defines a participant as anyone who has a claim to benefits, and anyway ERISA defines "participants" to include former participants with a colorable claim to benefits. 29 U.S.C. § 1002(7); Firestone Tire & Rubber Co. v. Bruch, 489 U.S. 101, 116-18, 109 S. Ct. 948, 103 L. Ed. 2d 80 (1989); Southern Illinois Carpenters Welfare Fund v. Carpenters Welfare Fund of Illinois, 326 F.3d 919, 922-23 (7th Cir.2003). The relief sought is indeed not equitable, but it is declaratory. What is sought is a declaration that Xerox's method of computing the lump sums to which withdrawing employees are entitled is unlawful. That is a ground common to all the members of the class.

True, the declaration sought and obtained was merely a prelude to a request for damages (incorrectly described by the plaintiffs as a request for restitutionary relief equitable in nature — the monetary relief sought is not restitutionary, and if it were it would not be equitable, Great-West Life & Annuity Ins. Co. v. Knudson, supra, 534 U.S. at 213-14, 122 S. Ct. 708; Honolulu Joint Apprenticeship & Training Committee v. Foster, 332 F.3d 1234, 1237-38 (9th Cir.2003)). But a declaratory judgment is normally a prelude to a request for other relief, whether injunctive or monetary; so there is nothing suspicious about the characterization of the suit as one for declaratory relief. The hope that motivates casting a request for relief in declaratory terms is that if the declaration is granted, the parties will be able to negotiate the concrete relief necessary to make the plaintiffs whole without further judicial proceedings. No one wants an empty declaration. As long as the concrete follow-on relief that is envisaged will if ordered (that is, if negotiations for relief consistent with the declaration break down) be the direct, anticipated consequence of the declaration, rather than something unrelated to it, the suit can be maintained under Rule 23(b)(2).

The reason for allowing opting out in other types of class action is that even though one class member's claim may overlap another's (common issues), it may be different in respects that makes him want to bring his own suit. There is nothing like that here. The declaration established the right of each of the class members, and the computation of the damages due each followed mechanically, as in Allison v. Citgo Petroleum Corp., 151 F.3d 402, 414-15 (5th Cir.1998); see also Jefferson v. Ingersoll Int'l Inc., 195 F.3d 894, 898-99 (7th Cir.1999).

Regarding the scope of that right, Xerox complains that the district judge refused to discount the pension benefit by the probability that the employee would actually live till age 65. This complaint, typical of many of the arguments made in scatter-shot fashion in Xerox's briefs, is unfathomable, since the plan provides that if the employee dies before reaching retirement age his spouse or other designated beneficiary steps into his shoes and is entitled to his entire pension benefit.

Xerox also complains about the discount rate used by the district judge to compute the lump sums to which the class members are entitled. We said that the discount rate applicable to plans of this vintage is prescribed by the PBGC but, actually there are two discount rates prescribed, the higher of which, and hence the one Xerox wants to use (since the higher the discount rate the smaller the present-value lump sum), is applicable to vested benefits of $25,000 or more. 29 U.S.C. § 1053(e)(2) (1993). (The idea behind this distinction is presumably that the greater the employee's retirement assets, the less need there is to protect him from accepting an inadequate lump-sum distribution.) But remember that the employee gets his choice between the defined contribution benefit to which the Xerox plan entitles him and the defined benefit (cash balance) benefit. Suppose that for a particular employee the former is $50,000 and the latter is $60,000, in which event he would take the latter amount. Xerox argues that because that amount exceeds $25,000, the higher discount rate is applicable. The judge, however, decided that since the employee would in any event be entitled to $50,000 (that being the value of his defined contribution benefit), the incremental value of his defined benefit is only $10,000 and so the lower discount rate must be used.

This example may seem plausible, but only because of the modest sums involved. The logic of the judge's method would apply to a case in which the employee's defined contribution account was worth $1 million and his cash-balance entitlement was worth $1,010,000, which doesn't make any sense that we can see. More fundamentally, the entitlement conferred by the cash balance plan, including the discount-rate rules applicable to the plan, is independent of other entitlements that the employee might have — especially an entitlement (to the balance in his defined contribution plan) that he voluntarily forgoes. So this part of the judgment must be modified to provide that only members of the class whose cash balance plan entitlement is less than $25,000 are entitled to the lower discount rate. In all other respects the judgment is affirmed.

MODIFIED AND AFFIRMED.