In the
 United States Court of Appeals
              For the Seventh Circuit
                        ____________

No. 02-3674
DAVID BERGER and GERRY TSUPROS,
 on behalf of themselves
 and others similarly situated,
                                              Plaintiffs-Appellees,
                               v.

XEROX CORPORATION RETIREMENT
 INCOME GUARANTEE PLAN,
                                            Defendant-Appellant.
                        ____________
           Appeal from the United States District Court
                for the Southern District of Illinois.
           No. 00-584-DRH—David R. Herndon, Judge.
                        ____________
       ARGUED APRIL 9, 2003—DECIDED AUGUST 1, 2003
                        ____________


  Before FLAUM, Chief Judge, and POSNER and KANNE,
Circuit Judges.
  POSNER, Circuit Judge. 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 con-
tract—we use the word in both senses and trust to context
to disambiguate) is what is called a “cash balance” plan.
2                                                 No. 02-3674

It is a defined benefit plan rather than a defined contribu-
tion 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 ac-
count, the employer makes no contributions to an em-
ployee 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
No. 02-3674                                                  3

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 retire-
ment 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,” 

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. 

In the case of a defined contribution plan
(the benefits of which, incidentally, vest immediately),
that benefit is simply the amount in his retirement ac-
count when he leaves the company’s employment. 

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
4                                                  No. 02-3674

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, contend 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., 

, 600 (7th Cir. 2002); Esden v. Bank of Boston, 

,
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
No. 02-3674                                                5

method of equating them is the application of a dis-
count rate to the future value. There is no single actu-
arial 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 receiv-
ing $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 be-
tween 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 pres-
ent 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 employ-
ment—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 distribu-
tion) 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.
6                                                  No. 02-3674

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 en-
titlement (a future value, obviously, since we are deal-
ing with employees who leave Xerox before reaching
retirement age) the plan must add the credits to the em-
ployee’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 em-
ployee. The Xerox plan computed the lump sum differ-
ently. Instead of adding future interest credits to the
departing employee’s cash balance at the plan’s future
interest credit rate of the T-bill rate plus 1 percent, it added
interest at a rate exactly equal to the discount rate pre-
scribed 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 bal-
ance 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 pro-
duces a lower number than would the one-year T-bill
rate plus 1 percent, the interest rate that is used to com-
pute the future interest credits. Thus, even if the accrued
pension must include those credits, as the plaintiffs
No. 02-3674                                                7

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 alterna-
tive 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 para-
graph, 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 lump-sum 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.
8                                               No. 02-3674

   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 abso-
lute, 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 dis-
tribution. 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 distri-
bution, 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 re-
tirement 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 retire-
ment age “receives a distribution” then, and thus his
accrued benefits include future interest credits to that
No. 02-3674                                                9

date. Any distribution that he receives earlier is the com-
mutation 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 contribu-
tion 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 con-
gressional policy of requiring that a lump-sum distribu-
tion 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
10                                               No. 02-3674

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 entitle-
ments of employees who choose cash balance plan bene-
fits 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 discount-
ing, 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, 

, 143-44 (7th
Cir. 1994); Smith v. Local 819 I.B.T. Pension Plan, 

, 238 (2d Cir. 2002); Esden v. Bank of 

, 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
retirement age.
No. 02-3674                                                  11

  The Internal Revenue Service’s Notice 96-8, cited earlier,
is an authoritative interpretation of the applicable stat-
utes and regulations for reasons explained in Esden v. Bank
of 

, 229 F.3d at 168-69, and it defines front-
loaded 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 inte-
rest credits are in the nature of accrued benefits . . . and
thus, once accrued, must become nonforfeitable.” A forfei-
ture 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 pen-
sion benefit to which the plan entitles employees who leave
their money in the plan until they reach their normal re-
tirement 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 (pen-
sion at age 65 rather than lump sum now), which is pre-
cisely what the law forbids. We conclude, in agreement
with the Second Circuit which considered a materially
12                                                No. 02-3674

identical plan in the Esden case, that the Xerox plan’s
method of computing the plaintiffs’ lump-sum entitle-
ments 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 com-
mon 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, 

, 209-10 (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, 

,
116-18 (1989); Southern Illinois Carpenters Welfare Fund
v. Carpenters Welfare Fund of Illinois, 

, 922-23
No. 02-3674                                                 13

(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. 

, 534 U.S. at 213-14;
Honolulu Joint Apprenticeship & Training Committee v. Foster,

, 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 suspi-
cious 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 estab-
lished the right of each of the class members, and the
computation of the damages due each followed mechani-
14                                                   No. 02-3674

cally, as in Allison v. Citgo Petroleum Corp., 

, 414-
15 (5th Cir. 1998); see also Jefferson v. Ingersoll Int’l Inc., 

, 898-99 (7th Cir. 1999).
  Regarding damages, Xerox complains that the district
judge refused to discount the pension benefit by the proba-
bility that the employee would actually live till age 65. This
complaint, typical of many of the arguments made in
scattershot 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),
No. 02-3674                                               15

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 independ-
ent 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.

A true Copy:
       Teste:

                          _____________________________
                          Clerk of the United States Court of
                            Appeals for the Seventh Circuit




                    USCA-02-C-0072—8-1-03