Plaintiffs-appellants are former employees of the Dun & Bradstreet Corporation ("Dun & Bradstreet") who were terminated from the company when Dun & Bradstreet sold its "Receivables Management Services" operations, conducted in the United States, Canada, and Hong Kong, on April 30, 2001. Upon the sale, plaintiffs-appellants became employees of a new corporation, "Dun & Bradstreet Receivables Management Services," which resulted from the sale. Their change in employment did not qualify them to receive severance benefits under the "Career Transition Plan," a Dun & Bradstreet benefit plan. It also affected the retirement benefits that they could receive under another benefit plan, the "Master Retirement Plan," which on December 31, 2001 was replaced by the "Dun & Bradstreet Corporation Retirement Account Plan." The new pension plan established as the Dun & Bradstreet Corporation Retirement Account Plan created different retirement benefits but assumed the vested obligations of the superseded Master Retirement Plan, which is at issue in this appeal.

Plaintiffs-appellants, many of whom had nearly attained the age of 55 at the time of the sale of the Receivables Management Services operations, sued Dun & Bradstreet, the Dun & Bradstreet Corporation Retirement Account Plan, and the Dun & Bradstreet Career Transition Plan in the United States District Court for the District of Connecticut, seeking individual and class action relief. They alleged that they were wrongfully denied benefits under the Dun & Bradstreet Corporation Retirement Account Plan and the Dun & Bradstreet Career Transition Plan, contrary to the requirements of the Employee Retirement Income Security Act of 1974 ("ERISA"), 29 U.S.C. § 1001 et seq. The district court ruled against plaintiffs with respect to both benefit plans. McCarthy v. Dun & Bradstreet Corp., 372 F. Supp. 2d 694 (D.Conn.2005) (McCarthy II); McCarthy v. Dun & Bradstreet Corp., No. 03CV431, 2004 WL 2743569, 2004 U.S. Dist. LEXIS 23996 (D.Conn. Nov. 30, 2004) (McCarthy I).

Plaintiffs-appellants appeal the district court's rulings on three motions in favor of defendants-appellees: (1) the district court's grant of defendants' motion to dismiss, under Fed.R.Civ.P. 12(b)(6), plaintiffs-appellants' claim that the "Summary Plan Description" for the Master Retirement Plan violated ERISA by inadequately disclosing the method by which a benefit of the Master Retirement Plan (the "deferred vested retirement benefit") is reduced actuarially when paid to former employees of Dun & Bradstreet, such as plaintiffs-appellants, who elected to receive payments before reaching age 65; (2) the district court's grant of defendants-appellees' summary judgment motion to deny relief on plaintiffs-appellants' claim that the Master Retirement Plan used an unreasonably high discount rate of 6.75 percent to reduce actuarially the deferred vested retirement benefit that the Master Retirement Plan paid to such former employees; and (3) the district court's denial in part of plaintiffs-appellants' motion to amend their complaint to challenge as unlawful under ERISA the mortality table that the Master Retirement Plan used in the actuarial reduction. For the reasons discussed in this opinion, we affirm all three rulings of the district court.

The facts underlying this appeal, as summarized below, are undisputed. Plaintiffs-appellants ceased being employees of Dun & Bradstreet on April 30, 2001, the date on which the company sold its Receivables Management Services operations. As former employees of Dun & Bradstreet who were terminated before reaching the minimum early retirement age of 55, plaintiffs-appellants no longer qualified for the early retirement benefit that was available under the Master Retirement Plan to employees retiring directly from Dun & Bradstreet. As former employees whose pension benefits had vested by the accrual of a minimum of five years of credited service with Dun & Bradstreet, but who were separated from Dun & Bradstreet before reaching the age of 55, plaintiffs-appellants remained eligible to receive a deferred vested retirement benefit under the Master Retirement Plan. Under the terms of this deferred vested retirement benefit, pension-vested former employees such as plaintiffs-appellants could receive, upon reaching the normal retirement age of 65, the full retirement benefit for which they qualified under the plan.

The Master Retirement Plan calculated the full retirement benefit according to a formula based on a participant's years of credited service and earnings with Dun & Bradstreet, with a reduction designed to compensate for Dun & Bradstreet's contribution to the participant's Social Security retirement benefit (the "Social Security Offset"). The Social Security Offset is based on a percentage of the estimated annual retirement benefit the participant would be entitled to receive at age 65 under the Social Security program.

The Master Retirement Plan provided that former employees, i.e., employees who terminated their employment before reaching the age of 55, instead of receiving their deferred vested retirement benefit upon their reaching the age of 65, could choose to receive payments as early as age 55. Under this early payment option, a former employee's deferred vested retirement benefit was actuarially reduced from the amount that would have been paid at age 65 in two respects. First, to reflect the time value of money, the Master Retirement Plan reduced the benefit by a 6.75 percent discount rate for each year prior to the age of 65 that payments began. Second, the benefit was reduced by a mortality factor to adjust actuarially for the possibility that a participant might not live to the age of 65.

Unlike former employees such as plaintiffs-appellants who were eligible only for deferred vested retirement benefits, employees retiring directly from Dun & Bradstreet were eligible to receive an early retirement benefit under the Master Retirement Plan. The Master Retirement Plan provided this early retirement benefit to employees who accrued ten years of credited service with Dun & Bradstreet, retired directly from Dun & Bradstreet after reaching the age of 55, and chose to receive payments before reaching the age of 65. This early retirement benefit was a more desirable benefit than the deferred vested retirement benefit as actuarially reduced under the early payment option. Under the early retirement benefit, the accrued pension was reduced by only three percent for each year that payments began before the retiree reached the age of 65.

To apprise plan participants of the benefits available under the Master Retirement Plan, Dun & Bradstreet, as required by ERISA, provided plan participants with a summary plan description ("Summary Plan Description"). The Summary Plan Description contains both a "Vesting" section that explains the deferred vested retirement benefits available to pension-vested former employees and an "Early Retirement Benefit" section that discusses the early retirement benefits available to directly-retiring Dun & Bradstreet employees. Included in the Early Retirement Benefit section is a reduction table that illustrates the percentage of accrued retirement benefits a direct retiree would receive for each year that payments begin before age 65, based on the three percent annual reduction. There is no table or discussion in the Vesting section of the Summary Plan Description that sets forth the percentage by which the actuarial reduction will reduce the benefit of a pension-vested former employee who is terminated from employment with Dun & Bradstreet before reaching the age of 55 but elects to receive payments before the age of 65.

On March 12, 2003, plaintiffs sued in district court, claiming that the provision of the Master Retirement Plan that actuarially reduced benefits of former employees who elected to receive payments prior to attaining the age of 65 could not be enforced against them because, in their view, the Summary Plan Description was inadequate under ERISA. They maintained that, as a result of the deficiencies in the Summary Plan Description, they should be held to qualify for unreduced benefits or, alternatively, for the early retirement benefits they would have received had they retired directly from Dun & Bradstreet. The district court dismissed this count of plaintiffs' complaint under Fed.R.Civ.P. 12(b)(6) for failure to state a claim upon which relief can be granted. The district court concluded that the treatment of the actuarial reduction in the Summary Plan Description was satisfactory under ERISA. Plaintiffs-appellants raise the same issue on appeal.

Plaintiffs-appellants argue, as a second issue on appeal, that the district court erred in denying them the opportunity to amend their complaint to raise a challenge to the mortality table used in the Master Retirement Plan which, together with the 6.75 percent discount rate reduction, actuarially reduced the deferred vested retirement benefit payable to former employees choosing to receive payments before reaching age 65. The district court denied the motion, concluding that the amendment would constitute an entirely new claim that would have prejudiced defendants because the amendment was sought at a late stage of the litigation, after the close of discovery and after defendants had moved for summary judgment.

Plaintiffs-appellants also claimed in district court, and argue again on appeal, that the 6.75 percent discount rate that the Master Retirement Plan used to reduce actuarially the deferred vested retirement benefits of former employees renders the actuarial reduction unreasonable. This discount rate, in their view, "works a prohibited forfeiture of benefits under ERISA Section 203(a)." Am. Compl. ¶ 95. The district court awarded summary judgment to defendants-appellees, concluding that ERISA does not require a "zero-risk" discount rate and that no reasonable juror could find that the 6.75 percent discount rate was unreasonable. McCarthy II, 372 F.Supp.2d at 699 & n. 2.

A. The District Court Did Not Err in Dismissing the Claim that the Summary Plan Description Violates ERISA

Section 102 and related provisions of ERISA require that a summary plan description be furnished to all participants and beneficiaries of an employee benefit plan and that it reasonably apprise participants and beneficiaries of their rights and obligations under the plan. 29 U.S.C. §§ 1022(a), 1024(b) (2000). Before the district court, plaintiffs-appellants claimed in their amended complaint that Dun & Bradstreet violated ERISA Section 102 by "fail[ing] to include in the [Master Retirement Plan] summary plan description the actuarial assumptions and/or the reduction chart it intended to apply to early retirement for former employees . . . ." Am. Compl. ¶ 93. They sought as relief "unreduced benefits upon early retirement or, in the alternative, early retirement benefits reduced for former employees in the same manner as such benefits are reduced for current Dun & Bradstreet employees." Am. Compl. WHEREFORE Cl. ¶ 3. The district court, concluding that the Summary Plan Description satisfied the requirements of ERISA, granted defendants' motion to dismiss. McCarthy I, 2004 WL 2743569, at *5, 2004 U.S. Dist. LEXIS 23996, at *15.

We review de novo determinations of a district court that resolve a motion to dismiss a complaint. Miller v. Wolpoff & Abramson, L.L.P., 321 F.3d 292, 300 (2d Cir.2003). In reviewing a motion to dismiss under Fed.R.Civ.P. 12(b)(6) for failure to state a claim upon which relief can be granted, we accept as true all factual statements alleged in the complaint and draw all reasonable inferences in favor of the non-moving party. In re Tamoxifen Citrate Antitrust Litig., 429 F.3d 370, 384 (2d Cir.2005), amended by 466 F.3d 187, 200 (2d Cir.2006). In general, our review is limited to the facts as asserted within the four corners of the complaint, the documents attached to the complaint as exhibits, and any documents incorporated in the complaint by reference. Taylor v. Vt. Dep't of Educ., 313 F.3d 768, 776 (2d Cir.2002).

The Federal Rules of Civil Procedure require that a pleading contain "a short and plain statement of the claim showing that the pleader is entitled to relief." Fed.R.Civ.P. 8(a)(2). Under this simplified standard for pleading, "a court may dismiss a complaint only if it is clear that no relief could be granted under any set of facts that could be proved consistent with the allegations." Tamoxifen, 429 F.3d at 384 (quoting Swierkiewicz v. Sorema N.A., 534 U.S. 506, 514, 122 S. Ct. 992, 152 L. Ed. 2d 1 (2002) (quotation marks, citation, and alteration omitted)). We therefore must construe the complaint liberally to determine whether the district court erred in concluding that plaintiffs could prove no set of facts that would entitle them to relief on their claim that the Summary Plan Description violates Section 102 of ERISA. See generally Jaghory v. N.Y. State Dep't of Educ., 131 F.3d 326, 329 (2d Cir.1997). We find no error in the district court's grant of the motion to dismiss and agree with the underlying conclusion that the Summary Plan Description did not violate Section 102 of ERISA.

Section 102(a) of ERISA provides that a summary plan description "shall be sufficiently accurate and comprehensive to reasonably apprise such participants and beneficiaries of their rights and obligations under the plan." 29 U.S.C. § 1022(a). ERISA Section 102(b) lists specific information that must be included in every summary plan description, including the "circumstances which may result in disqualification, ineligibility, or denial or loss of benefits. . . ." Id. § 1022(b).

The disclosure requirements ERISA imposes on summary plan descriptions present two issues concerning the Summary Plan Description for the Master Retirement Plan. The first, and more general, issue is whether the Summary Plan Description, in describing the deferred vested retirement benefit, is sufficiently accurate and comprehensive to satisfy Section 102(a). Because plaintiffs do not claim that the Summary Plan Description is inaccurate, the question is whether the Summary Plan Description is insufficiently comprehensive to "reasonably apprise" plaintiffs of their rights because it does not disclose the method by which the deferred vested retirement benefit available to former employees choosing to receive payments before age 65 would be actuarially reduced. The second, and more specific, issue is whether the Summary Plan Description, in not disclosing that method of actuarial reduction, complies with the Section 102(b) requirement to disclose "circumstances which may result in disqualification, ineligibility, or denial or loss of benefits."

ERISA provides some guidance on the meaning of the requirement in Section 102(a) to "reasonably apprise" participants and beneficiaries by including a long list of specifically-required disclosures in Section 102(b). That statutory list does not include, specifically or by implication, the method of actuarial reduction at issue in this case. The Department of Labor has promulgated regulations that interpret and expand the statutory list of required disclosures and, in so doing, provide further guidance to drafters of summary plan descriptions on what disclosures are required to meet the general statutory requirement to reasonably apprise beneficiaries of plan benefits. See 29 C.F.R. §§ 2520.102-2-102-4. The regulations, like the statute, do not explicitly require disclosure of the method of actuarial reduction at issue here. This omission, while somewhat indicative, does not entirely resolve the issue before us. It can be argued that the method of actuarial reduction, even though not expressly required to be disclosed by the statute or the regulations, is important enough to a description of the deferred vested retirement benefit that any such omission results in a summary plan description that is insufficient under Section 102(a).

The Summary Plan Description for the Master Retirement Plan addressed in separate sections the normal retirement benefit, the early retirement benefit, and the deferred vested retirement benefit. From our review of the Summary Plan Description and of these three sections in particular, we conclude that the Summary Plan Description reasonably apprised plan participants and beneficiaries of their rights under the deferred vested retirement benefit and thereby satisfied Section 102(a) of ERISA. It did so by apprising participants and beneficiaries of the deferred vested retirement benefit in general and by specifically distinguishing that benefit from the early retirement benefit.

In a section under the heading "How the Retirement Plan Works," the Summary Plan Description explains that the normal retirement date under the Plan is a participant's 65th birthday, that payment of benefits normally begins the first full month thereafter, and that the retirement benefit is calculated based on credited service and earnings at separation from service with Dun & Bradstreet.1 The same section contains a reference to the possibility of retirement as early as age 55, if certain requirements are met. This early retirement option is discussed in more detail in the "Early Retirement Benefit" section of the Summary Plan Description, which explains that an employee with at least 10 years of vesting service may choose to retire as early as age 55. The section also explains that an early-retiring employee may choose to delay receiving payment until age 65, in which case the full accrued benefit would be paid. It further explains that an employee retiring early may choose to receive payments as early as age 55 but that, as a result, the accrued benefit will be reduced by three percent for each year that payments begin before age 65. The same section contains the aforementioned reduction table setting forth the percentage of accrued retirement benefits a direct retiree would receive for each year that payments begin before age 65, based on the reduction of three percent for each year that payments begin before the participant reaches the age of 65.2

In discussing the ordinary and early retirement benefits available to employees, the sections of the Summary Plan Description entitled How the Retirement Plan Works and Early Retirement Benefit do not expressly or impliedly refer to the situation of an employee who is separated from employment before reaching the minimum early retirement age of 55 and who chooses to receive payments before reaching age 65. Deferred vested retirement benefits are discussed in the separate section entitled Vesting, which appears later in the Summary Plan Description. The Vesting section, to which plaintiffs-appellants direct their principal argument that the Summary Plan Description is inadequate under Section 102 of ERISA, begins by defining the concept of vesting, explaining that "[v]esting means earning the right to receive a retirement benefit, at a future date — even if you leave the Company before you are eligible for retirement." Summ. Plan Description at 17. It adds that "[y]ou are fully vested in your accrued Retirement Plan benefits after you complete 5 years of vesting service." Id. The next paragraph describes the deferred vested retirement benefit in general, i.e., as it applies absent the early payment option, stating that "[i]f you terminate employment after becoming vested, you will be entitled to receive a deferred vested retirement benefit from the Plan" and that "[y]our deferred vested benefit is calculated in the same way as a normal retirement benefit assuming benefit payments begin at age 65." Id. Finally, in a third paragraph consisting of a single sentence, the Summary Plan Description discusses the consequence of electing early payment of the deferred vested retirement benefit. The sentence reads as follows: "If you choose, the payment of your deferred vested benefit can begin as early as age 55, but the amount of the benefit will be reduced actuarially, resulting in a lower Plan benefit than if the reduction table in the `Early Retirement Benefit' section was used." Id.

The Summary Plan Description might have been more informative in discussing the early payment option of the deferred vested retirement benefit. However, neither ERISA nor the Labor Department's regulations require a summary plan description to describe or illustrate every method by which a plan benefit may be limited under an early payment option or similar such limitation. The Labor Department's regulations expressly allow a Summary Plan Description to summarize, rather than describe in every detail, the benefits available under an employee pension benefit plan. "Such plan benefits shall be described or summarized." 29 C.F.R. § 2520.102-3(j)(1). For these reasons, we are unable to agree with plaintiffs-appellants' argument that the Summary Plan Description is inadequate under Section 102(a) of ERISA, 29 U.S.C. § 1022(a).

We turn next to the second issue presented, i.e., whether the Summary Plan Description complied with Section 102(b) of ERISA, 29 U.S.C. § 1022(b). As the district court observed, § 1022(b) "specifically says that the [Summary Plan Description] must set out `circumstances which may result in . . . loss of benefits.'" McCarthy I, 2004 WL 2743569, at *4, 2004 U.S. Dist. LEXIS 23996, at *12 (quoting 29 U.S.C. § 1022(b)) (emphasis added by district court). The Summary Plan Description, in the section entitled "Vesting," discloses the circumstances in which the actuarial reduction would occur, i.e., when a participant whose employment terminates after the participant's benefits become vested but before the participant becomes eligible for retirement chooses to receive payments before reaching the normal retirement age of 65. As did the district court, we decline to construe Section 102(b) of ERISA to require disclosure of more detail, e.g., the specific method of actuarial reduction, than the circumstances resulting in the reduced benefits.

The Labor Department's regulations expand on the statutory obligation of Section 102(b) to disclose in a summary plan description "circumstances which may result in disqualification, ineligibility, or denial or loss of benefits. . . ." 29 U.S.C. § 1022(b). The regulations, in this regard, require that the summary plan description disclose the "circumstances which may result in disqualification, ineligibility, or denial, loss, forfeiture, suspension, offset, reduction, or recovery (e.g., by exercise of subrogation or reimbursement rights) of any benefits that a participant or beneficiary might otherwise reasonably expect the plan to provide on the basis of the description of benefits required by paragraphs (j) and (k) of this section." 29 C.F.R. § 2520.102-3(l) (emphasis added). The Summary Plan Description at issue satisfies this requirement of the regulations, both by disclosing the circumstances in which the actuarial reduction will occur, and by distinguishing the early payment option of the deferred vested retirement benefit from the early retirement benefit. As the district court observed, "[t]here is simply no way that a former employee reading [the Vesting] section could be under the impression that he was to receive the same benefits as current employees." McCarthy I, 2004 WL 2743569, at *4, U.S. Dist. LEXIS 23996, at *13.

The Labor Department's regulations, in addressing the contents of a summary plan description, provide that

[t]he format of the summary plan description must not have the effect to [sic] misleading, misinforming or failing to inform participants and beneficiaries. Any description of exception [sic], limitations, reductions, and other restrictions of plan benefits shall not be minimized, rendered obscure or otherwise made to appear unimportant. Such exceptions, limitations, reductions, or restrictions of plan benefits shall be described or summarized in a manner not less prominent than the style, captions, printing type, and prominence used to describe or summarize plan benefits.

29 C.F.R. § 2520.102-2(b) (emphasis added). Here also, the Summary Plan Description does not run afoul of the regulatory requirements. The regulations permit a summary plan description to summarize a limitation on a benefit, so long as the other requirements of the regulations are observed.

Plaintiffs-appellants argue that the Summary Plan Description is inadequate because, in failing to disclose the method of actuarial reduction in the Vesting Section, it does not disclose "what their age 55 retirement benefits are." Br. of Pls.-Appellants 12. They argue further that the Summary Plan Description "misleads the plaintiffs by highlighting what Dun & Bradstreet says are the subsidized benefits of current employees and obscuring the stunning difference between subsidized (70 percent of normal retirement) and unsubsidized (38 percent of normal retirement) early retirement benefits," id., and "minimizes" the effect of benefit limitations and restrictions, id. at 5. They argue that the Summary Plan Description causes confusion by omitting discussion of the "fate" of terminated early retirees in the Early Retirement Benefit section in the Summary Plan Description and by discussing this type of former employee "only briefly" in a "vaguely titled" section called Vesting. Id. In their view, the Summary Plan Description should have included a reduction table, statement, or illustration to explain the extent of the actuarial reduction. Id. at 20.

We find no reason to conclude that the Vesting section of the Summary Plan Description confuses, misleads, or misinforms plan participants whose employment is terminated prior to their reaching the minimum early retirement age of 55 such that they would believe that they will receive the early retirement benefit. To the contrary, the Vesting section expressly informs the reader that a plan participant who leaves Dun & Bradstreet before becoming eligible for retirement and who receives the deferred vested retirement benefit prior to the age of 65 will not receive the early retirement benefit determined according to the reduction table in the Early Retirement Benefit section but instead, as a result of actuarial reduction, will receive a lower benefit. Moreover, because the Vesting section is sufficiently prominent within the context of the Summary Plan Description as a whole, we do not conclude that the text or format of the Summary Plan Description minimized, rendered obscure, or otherwise made to appear unimportant the limitation resulting under the early payment option of the deferred vested retirement benefit that was available to employees leaving Dun & Bradstreet before reaching the age of 55 and choosing to receive payments prior to age 65.

Plaintiffs-appellants maintain that the failure of the Summary Plan Description to disclose the size of the actuarial reduction violates ERISA as construed in Layaou v. Xerox Corp., 238 F.3d 205 (2d Cir.2001). We disagree that our holding in Layaou compels the conclusion that the Summary Plan Description at issue in this appeal violates ERISA. Layaou does not hold that to satisfy ERISA requirements a summary plan description invariably must describe or illustrate the method by which a specific retirement benefit is actuarially reduced in a particular circumstance, such as this case, where the employees separated before reaching the minimum early retirement age and elected to receive a vested benefit before reaching the ordinary retirement age.

The plaintiff Layaou, upon voluntarily leaving the employ of Xerox in 1983, had received under a retirement plan lump-sum distributions totaling $22,353.88. Layaou, 238 F.3d at 206 & n. 2. Layaou was re-employed by Xerox in 1987, began earning retirement benefits for this second employment period, and was laid off in 1994 during a reduction-in-force. Id. at 206. Each year, Layaou had received from Xerox a brochure to fulfill the ERISA obligation for a summary plan description as well as a form listing the estimated individual retirement benefits Layaou had earned to date. Id. at 206-07. The summary plan description brochure stated, "[t]he amount you receive may also be reduced if you had previously left the Company and received a distribution at that time." Id. at 210. The form issued to Layaou in 1994 estimated for Layaou a monthly retirement benefit of $924 as calculated under the Retirement Income Guarantee Plan guaranteed annuity calculation method ("RIGP method"), which was one of three methods used by the Xerox retirement plan to calculate retirement benefits; the Xerox retirement plan paid benefits upon retirement in an amount equal to the highest result of three different calculation methods. Id. at 206, 210. The $924 estimated monthly benefit was based on retirement at age 65. See id. at 206-07. As did the brochure, the form stated that the benefits as calculated under the RIGP method "may be reduced if you receive amounts before age 65 or receive amounts from another Xerox retirement plan." Id. at 207. The 1994 form notified Layaou that under the Cash Balance Retirement Account method ("CBRA method") of calculating his benefits, he would receive a lump sum payment of $18,403 and that under the Transitional Retirement Account method ("TRA method"), his lump sum benefit would be $9,244. Id.

When Layaou's retirement became effective in 1995, by which time Layaou had reached the age of 55, the plan administrator calculated Layaou's benefit as a lump sum and converted it to a monthly payment of $145; this amount was calculated not under the RIGP method but under the CBRA method, which under the plan administrator's calculation yielded the highest of the three benefit calculation methods. Layaou, 238 F.3d at 207-08. The final calculation of Layaou's monthly retirement benefit reflected a reduction for what Xerox referred to as a "phantom account" offset, under which earned benefits were reduced by the value of a hypothetical account containing the original distributed sum (in this case, $22,353.88) and an amount based on an estimate of what that distribution would have earned had it been invested. Id. at 206-07.

The brochure constituting the summary plan description did not inform Layaou about the "phantom account" offset other than by stating that "[t]he amount you receive may also be reduced if you had previously left the Company and received a distribution at that time." Id. at 210. The form containing the annual estimate, in referring to the benefit calculated under the RIGP method, alluded generally to the possibility of a reduction "if you . . . receive amounts from another Xerox retirement plan." Id. The form did not include such a qualification in presenting the estimated lump-sum distributions calculated under the CBRA and TRA methods.

We concluded in Layaou that the summary plan description contravened ERISA by "fail[ing] to provide notice to Layaou and other similarly situated employees that their future benefits would be offset by an appreciated value of their prior lump-sum benefits distributions." Id. We found that the summary plan description failed to satisfy Section 102 of ERISA and the Labor Department's regulations, noting that the summary plan description did not clearly identify the loss of benefits caused by a prior lump-sum distribution. Id. at 211 (citing 29 C.F.R. § 2520.102-3(l)).

In contrast to the summary plan description at issue in Layaou, the Vesting section of the Summary Plan Description for the Master Retirement Plan is definite in informing a participant that a reduction will occur under the early payment option and gives some information, albeit limited, about the method of reduction, stating that "the amount of the benefit will be reduced actuarially, resulting in a lower Plan benefit than if the reduction table in the `Early Retirement Benefit' section was used." Summ. Plan Description at 17. The information provided about the method of reduction, although presented only in brief summary form, is sufficient under Section 102 of ERISA and the Labor Department's regulations, which permit some details about a particular option associated with a particular benefit to be summarized. The Summary Plan Description reasonably apprises participants of their rights concerning the deferred vested retirement benefit provided by the Master Retirement Plan and discloses the circumstances under which that benefit will be reduced.

Plaintiffs-appellants point to dicta in Layaou in which we noted that a statement such as "`[a]ny future benefit will be 23 offset by the appreciated value of any prior distribution 24 assuming that amount remained in the plan'" would have sufficed to provide employees with sufficient notice of the plan's offset provision, and in which we indicated that a clarifying example calculating the benefits of an employee who had received a prior distribution could have provided adequate notice. Layaou, 238 F.3d at 211. We do not consider the dicta in the Layaou opinion to signify that ERISA imposes a blanket requirement under which a Summary Plan Description invariably must describe the method of calculating an actuarial reduction or must use a clarifying example to illustrate how a benefit is actuarially reduced when a participant who has vested rights to receive a particular plan benefit chooses to receive payments before reaching normal retirement age.

Plaintiffs-appellants' reliance on various other precedents is also misplaced. Plaintiffs-appellants argue that in Feifer v. Prudential Insurance Co. of America, 306 F.3d 1202 (2d Cir.2002), this court refused to allow a plan sponsor to reduce disability plan benefits by the amount of participants' social security benefits where the reduction was not properly disclosed in a summary plan description. Id. at 1212. Feifer, however, does not support this argument. In Feifer, the employer had distributed a "Program Summary" with an accompanying booklet announcing a new benefits plan that did not exist in written form at the time the Program Summary was distributed. Id. at 1205. We concluded that the Program Summary and the booklet, at the time they were distributed, constituted the actual retirement plan for ERISA purposes and that no summary plan description of the retirement plan existed at that time. Id. at 1209-10. As a result, the Program Summary controlled the amount of permissible reductions to an employee's benefits. Id. Feifer did not involve the question of the adequacy of a disclosure of a benefit reduction in a summary plan description associated with a retirement plan and therefore has no bearing on the issue before us.

Plaintiffs-appellants also rely on Burke v. Kodak Retirement Income Plan, 336 F.3d 103 (2d Cir.2003). They argue that pursuant to the holding in Burke, an employer may not enforce a plan requirement where that requirement was not clearly set forth in the section of the summary plan description that dealt with the benefits at issue. However, Burke is distinguishable because it involved a conflict between the employer's summary plan description and the retirement plan. See id. at 110-11. In Burke, a plaintiff sued for survivor income benefits under a retirement plan that conditioned eligibility for receipt of such benefits on the filing of an affidavit. Id. at 106. The "Survivor Income Benefits" section of the summary plan description omitted any reference to the affidavit requirement, to which the summary plan description made reference in sixteen other sections. Id. Accordingly, we held that the summary plan description violated ERISA, applying the well-established principle that "[w]here the terms of a plan and the [summary plan description] conflict, the [summary plan description] controls." Id. at 110. Plaintiffs-appellants are not alleging a conflict between Dun & Bradstreet's Summary Plan Description and the Master Retirement Plan.

Plaintiffs-appellants argue that the common-law principle of Gediman v. Anheuser Busch, Inc., 299 F.2d 537 (2d Cir.1962), a pre-ERISA case, requires us to reject a summary plan description that conceals the size of a benefit reduction. We do not find this argument persuasive. Gediman involved benefits owed on behalf of a deceased beneficiary of a pension plan who previously had received negligent advice from an employer's pension consultants. Id. at 541. H. James Gediman, the executor of an estate, brought the action on behalf of the deceased former employee, James Barsi, to recover amounts allegedly due under the employer's pension plan. Id. at 538-39. Barsi, who had arranged for an early retirement date and had elected to receive deferred cash benefits instead of an annual pension benefit, died as a result of a car accident prior to receiving the payments under the deferred cash benefit option. Id. at 540-41. Just before he elected to receive the deferred cash benefits, Barsi wrote a letter to his employer, seeking advice regarding his retirement benefit options. Id. He received written advice in the form of a memorandum from the employer's pension consultants that failed to inform him that, as a result of an election to receive the cash benefits, the value of his benefits would be greatly reduced in the event of his death before the deferral date for the cash payments. Id. at 545. The employer was held liable in tort for the negligent advice of the pension consultants. Id. at 547-48.

Gediman is distinguishable from this case in two ways. First, because the case did not arise out of ERISA, it does not involve the statutory and regulatory requirements imposed on a summary plan description. Instead, the case involved the application of common-law principles regarding the fiduciary duty of care that arose when the pension consultants voluntarily undertook to give advice to Barsi. Second, the facts of Gediman are inapposite. In Gediman, the court held that the defendant misinformed Barsi as to the consequences of the election that he made upon retirement. Id. at 539. The opinion explains that the memorandum from the pension consultants failed to disclose that the retirement plan would provide a greatly reduced benefit if Barsi should die before rather than after his deferral date and also failed to disclose that the retirement plan, in that event, provided a benefit under a "wholly different regime." Id. at 545 ("[T]he `death benefit' described in paragraph 3 of their memorandum differed from that in paragraph 2 not just in degree but in kind."). The court even went so far as to conclude that the defendants had misled Barsi. Id. at 547.

In contrast to the situation in Gediman, the Summary Plan Description at issue here did not misinform or mislead the plaintiffs-appellants. It disclosed the circumstances that would result in a reduction of their benefits and, as set forth above, was not required by statute or regulation to disclose the specifics of how the reduction would occur.

Plaintiffs-appellants also direct our attention to Wilkins v. Mason Tenders District Council Pension Fund, 445 F.3d 572 (2d Cir.2006), which was decided after briefing and oral argument in this appeal. Plaintiffs-appellants argue that the holding in Wilkins supports their claim that the Summary Plan Description violates ERISA because it fails to disclose relevant information regarding the size of benefits due to former employees electing to receive early payment of deferred vested retirement benefits. We disagree. Wilkins involved the failure of a summary plan description to disclose "`circumstances which may result in disqualification, ineligibility, or denial or loss of benefits.'" Id. at 580-81 (quoting 29 U.S.C. § 1022(b)).

The plaintiff in Wilkins was a union employee who, over a period of thirty years, worked in the construction industry for several different employers. Id. at 575. The employers were required by collective bargaining agreements with the union to contribute to the union pension fund based on their employees' covered employment. Id. In Wilkins's case, there were significant discrepancies between the earnings that the employers reported to the pension fund and those the employers reported to the Social Security Administration. Id. at 575-76. Following his receipt of a lump sum benefit in 1999, Wilkins claimed additional benefits based on work that was not reflected in the records of the fund but was reflected in his Social Security Administration statement of earnings. Id. at 576. The pension fund maintained a policy that employees seeking benefits based on work that was not reported by employers must submit "proof of covered employment as a condition of receiving the benefits to which they are entitled under the terms of the plan. . . ." Id. at 584. Social Security earning statements did not suffice under the policy. Id. at 576-77. Additionally, this policy was not set forth in the summary plan description. Id. at 581. Because Wilkins did not produce proof of covered employment, his claim was denied. Id. at 576-77.

The district court denied relief on other grounds. Id. at 577-78. On appeal, Wilkins argued that his benefits were wrongfully denied due to the failure of the summary plan description to comply with 29 U.S.C. § 1022(b), and we agreed. Id. at 584. "It seems to us obvious that the Policy, by erecting an additional, mandatory prerequisite to the receipt of promised benefits, may result in disqualification, ineligibility, or a denial or loss of benefits. It must, therefore, be disclosed in the [summary plan description]." Id. Because "no provision of the [summary plan description] even arguably gives notice of the Policy," the summary plan description violated ERISA. Id. at 582.

Unlike the summary plan description at issue in Wilkins, the Summary Plan Description for the Master Retirement Plan adequately discloses the circumstances under which the actuarial reduction will occur. As we stated previously, the relevant circumstances are those of a participant whose employment terminates after the participant becomes vested but before the participant becomes eligible for retirement, and who chooses to receive payments before reaching the normal retirement age of 65.

B. The District Court Did Not Abuse its Discretion in Denying in Part Plaintiffs-Appellants' Motion to Amend the Complaint to Challenge the Mortality Table

Before the district court, plaintiffs moved under Fed.R.Civ.P. 15(a) to amend their previously amended complaint to add, inter alia, a claim that the mortality table used by the Master Retirement Plan to calculate the actuarial reduction for deferred vested retirement benefits is outdated and unreasonable when combined with the 6.75 percent discount rate. Br. of Pls.-Appellants 29, 32. The district court denied the motion in part, declining to allow plaintiffs to add the claim concerning the mortality table, which the district court considered to be an entirely new claim that was being raised at a late stage in the litigation, i.e., after discovery had been completed and after defendants had moved for summary judgment. McCarthy II, 372 F.Supp.2d at 700-01.

We review the determination of a district court to deny a party leave to amend the complaint under Fed.R.Civ.P. 15(a) for abuse of discretion. Grochowski v. Phoenix Constr., 318 F.3d 80, 86 (2d Cir.2003). We find that the district court did not abuse its discretion in denying the motion in part and thereby disallowing the claim pertaining to the mortality table.

Although Rule 15(a) of the Federal Rules of Civil Procedure provides that leave to amend "shall be freely given when justice so requires," it is within the sound discretion of the district court to grant or deny leave to amend. See Zahra v. Town of Southold, 48 F.3d 674, 686 (2d Cir.1995) (upholding the denial of a motion to amend a complaint that was filed two and one-half years after the commencement of the action and three months prior to trial); see also Ansam Assocs., Inc. v. Cola Petroleum, Ltd., 760 F.2d 442, 446 (2d Cir.1985) (upholding the denial of a motion to amend a complaint when discovery already had been completed and the non-movant had already filed a motion for summary judgment). A district court has discretion to deny leave for good reason, including futility, bad faith, undue delay, or undue prejudice to the opposing party. See Foman v. Davis, 371 U.S. 178, 182, 83 S. Ct. 227, 9 L. Ed. 2d 222 (1962). However, "[o]utright refusal to grant the leave without any justifying reason for the denial is an abuse of discretion." Jin v. Metro. Life Ins. Co., 310 F.3d 84, 101 (2d Cir.2002).

Plaintiffs filed the original complaint in this action on March 12, 2003 and amended it on July 9, 2003. McCarthy II, 372 F.Supp.2d at 699. They moved to amend the complaint a second time on December 21, 2004, more than two months after discovery was completed and more than a year and a half after the filing of the original complaint. Id. at 700. The district court originally granted the motion, believing it unopposed. Id. Defendants moved to vacate the order granting the motion to amend. Id. Defendants did not object to most of plaintiffs' proposed amendments but opposed the amendment that would add a claim concerning the reasonableness of the mortality table used in the Master Retirement Plan's actuarial reduction. Id.

In denying plaintiffs' second motion to amend, the district court noted that plaintiffs' complaint "specifically alleged an unreasonable interest rate" but "did not allege, in general, an improper actuarial reduction, which might encompass a number of factors, including the mortality table used." Id. at 701. The district court noted that the first amended complaint "did not claim that the `application of an unreasonable actuarial reduction' worked a forfeiture, and it certainly did not claim that the `application of an unreasonable mortality table' worked a forfeiture." Id.; see Am. Compl. ¶ 95. The district court concluded that "plaintiffs' motion to amend seeks to add a new claim." McCarthy II, 372 F.Supp.2d at 700. The district court further concluded that "[i]f the amendment is allowed, merits discovery will need to be reopened and the litigation will, in essence, start over — the same experts will likely need to produce new reports and be re-deposed." Id. at 701.

Plaintiffs became aware of the need to consider a possible claim directed to the mortality table more than seven months before moving to amend their complaint. Their own expert had provided, by April 30, 2004, a declaration disclosing his position that the mortality table used by the Master Retirement Plan raised an issue. See Claude Poulin Decl. dated Apr. 30, 2004, ¶ 20. His declaration stated that "the mortality table used by the Plan in the calculation of the actuarial reduction factors is an old table that overestimates the mortality rates currently applicable to the affected plan participants." Id. ¶ 18. On May 27, 2004, the same expert, during a deposition, again identified a potential issue with the mortality table, testifying that the mortality tables used by the plan were outdated and led to a skewed actuarial reduction. Claude Poulin Dep. dated May 27, 2004, at 122.

Plaintiffs-appellants argue that defendants were not prejudiced by an amendment because the April 2004 declaration and May 2004 deposition of plaintiffs' actuarial expert gave defendants full and fair notice that the mortality table "significantly contributed to the ERISA violation alleged in the original complaint." Br. of Pls.-Appellants 29-30. As the district court correctly noted, however, the amended complaint challenged specifically the discount rate used in the actuarial reduction, not the actuarial reduction method itself. McCarthy II, 372 F.Supp.2d at 701. A complaint provides a defendant with "notice of what the plaintiff's claim is and the grounds upon which it rests." See Swierkiewicz, 534 U.S. at 512-14, 122 S. Ct. 992 (quoting Conley v. Gibson, 355 U.S. 41, 47, 78 S. Ct. 99, 2 L. Ed. 2d 80 (1957)) (quotation marks omitted). Having received such notice, a defendant may conduct his trial preparation accordingly and is not required, based on the plaintiff's subsequent conduct in litigation, to anticipate future claims that a plaintiff might intend to pursue. Thus, when plaintiffs' counsel attempted to question defendants' expert about mortality assumptions during an October 6, 2004 deposition, defendants' counsel objected, stating that "[a]t some point I have [to move for] a protective order if you turn it into a deposition not about the opinion the witness has been retained to testify on, but on a separate issue that is not mentioned in the complaint, not mentioned at the motion to dismiss stage that led to this round of briefing, and is not in the case." Edward W. Brown Dep. dated Oct. 6, 2004, at 74.

Plaintiffs sought to amend their complaint after an inordinate delay. By that time, discovery had closed, defendants had filed for summary judgment, and nearly two years had passed since the filing of the original complaint. In light of this record, we conclude that the district court did not exceed its discretion in denying plaintiffs' leave to amend.

C. The District Court Did Not Err in Granting Summary Judgment on the Lawfulness of the 6.75 Percent Discount Rate

We review de novo a district court's grant of summary judgment. Miller, 321 F.3d at 300. Summary judgment is awarded when there are no genuine issues of material fact and the moving party is entitled to judgment as a matter of law. Fed.R.Civ.P. 56(c). In ruling on a summary judgment motion, the district court must "`resolve all ambiguities, and credit all factual inferences that could rationally be drawn, in favor of the party opposing summary judgment'" and determine whether there is a genuine dispute as to a material fact, raising an issue for trial. Kessler v. Westchester County Dep't of Soc. Servs., 461 F.3d 199, 206 (2d Cir.2006) (quoting Cifra v. Gen. Elec. Co., 252 F.3d 205, 216 (2d Cir.2001)). A fact is "material" when it "`might affect the outcome of the suit under governing law.'" Jeffreys v. City of N.Y., 426 F.3d 549, 553 (2d Cir. 2005) (quoting Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 248, 106 S. Ct. 2505, 91 L. Ed. 2d 202 (1986)). An issue of fact is "genuine" if "`the evidence is such that a reasonable jury could return a verdict for the nonmoving party.'" Id. (quoting Anderson, 477 U.S. at 248, 106 S. Ct. 2505). Unless the nonmoving party offers "`some hard evidence showing that its version of the events is not wholly fanciful[,]'" summary judgment is granted to the moving party. Id. at 554 (quoting D'Amico v. City of N.Y., 132 F.3d 145, 149 (2d Cir.1998)).

Before the district court and again on appeal, plaintiffs-appellants argued that one component of the Master Retirement Plan's actuarial reduction, the 6.75 discount rate, violated ERISA because the discount rate was unreasonable and "[t]he application of an unreasonable rate of interest works a prohibited forfeiture of benefits under ERISA Section 203(a)." Am. Compl. ¶ 95 According to plaintiffs-appellants, a reasonable discount rate is "a long-term rate" based on "relatively risk-free investments," namely the thirty-year Treasury Bond, that would "`yield the kind of investment return retiring plan participants would experience in the marketplace.'" Br. of Pls.-Appellants 8-9 (quoting Claude Poulin Dep. dated May 27, 2004, at ¶ 14).

The district court granted summary judgment to defendants, concluding as a matter of law that ERISA does not mandate the use of a zero-risk discount rate. McCarthy II, 372 F.Supp.2d at 699. The district court saw no genuine issue of material fact, considering the rate chosen by the Plan to be "one that no reasonable juror could find unreasonable. . . ." Id.

We agree with the district court that ERISA does not require a plan to use in the actuarial reduction a zero-risk discount rate or a rate that is practically risk-free. We see no error in the district court's finding that the actuarial reduction used in the Master Retirement Plan was not unreasonable solely for using a 6.75 percent discount rate. We therefore affirm the grant of summary judgment to defendants-appellees.

Section 206(a) of ERISA requires employers offering an early retirement benefit to current employees to offer an equivalent, although actuarially reduced, early retirement benefit to qualifying employees who have separated from service prior to satisfying the age requirement for early retirement. 29 U.S.C. § 1056(a).3 The benefit the separated employee receives upon satisfying the age requirement for early retirement must be "not less than the benefit to which he would be entitled at the normal retirement age, actuarially reduced under regulations prescribed by the Secretary of the Treasury." Id.

Section 206(a), among other sections of ERISA, has a counterpart in the Internal Revenue Code, which contains provisions allowing favorable tax treatment to qualifying retirement plans. Section 401(a)(14) of Title 26 contains the parallel provision to ERISA Section 206(a) in providing that a qualified defined benefit pension plan must afford early retirement benefits that are "not less than the benefit to which [the participant] would be entitled at the normal retirement age, actuarially, reduced under regulations prescribed by the Secretary [of the Treasury]." 26 U.S.C. § 401(a)(14) (2000).

The Secretary of the Treasury has promulgated regulations to construe Internal Revenue Code § 401(a)(14). These regulations provide that under a qualifying plan the "reduced normal [i.e., early] retirement benefit is the benefit to which the participant would have been entitled under the plan at normal retirement age, reduced in accordance with reasonable actuarial assumptions." 26 C.F.R. § 1.401(a)-14(c)(2) (emphasis added).

We conclude, as did the district court, that the regulations do not specify a rate or range of discount rates that qualify as "reasonable actuarial reductions" for payment of early retirement benefits. McCarthy II, 372 F.Supp.2d at 696. The parties are also in agreement on this point. See Edward W. Brown Report dated Aug. 4, 2004, at 4 (stating that "[n]either the IRS [n]or any actuarial organization has published guidance on what constitutes a reasonable interest rate for determining early retirement payments"); Claude Poulin Decl. dated Apr. 30, 2004, ¶ 20 (stating that "there are no prescribed interest rate or mortality table assumptions for the calculation of early retirement reduction factors . . . ."). We further conclude that by failing to specify a discount rate, the regulations provide benefit plans with a degree of discretion in setting discount rates to achieve a reduction according to reasonable actuarial assumptions.

The question of whether the discount rate qualifies as a reasonable rate for purposes of ERISA is a mixed question of law and fact. "Because statutory terms are at issue, their interpretation is a question of law, and it is the court's duty to define the appropriate legal standard." Chandris, Inc. v. Latsis, 515 U.S. 347, 369, 115 S. Ct. 2172, 132 L. Ed. 2d 314 (1995). However, a question of fact exists if reasonable persons applying the proper legal standard could differ on whether the reduction was accomplished according to actuarial assumptions that were reasonable as a result of the discount rate used. See id. Mixed questions of law and fact are reviewed under the de novo standard. Beth Israel Med. Ctr. v. Horizon Blue Cross and Blue Shield of New Jersey, Inc., 448 F.3d 573, 580 (2d Cir.2006).

In determining whether the Master Retirement Plan was reasonable in its use of the 6.75 percent discount rate for the actuarial reduction, the district court found that "a plan has met its ERISA obligations with respect to calculation of early benefit payments if it selects a discount rate that is reasonably calculated to be representative of its participants' average discount rate," McCarthy II, 372 F.Supp.2d at 698, i.e., the average of the rates of return desired by the participants, which would vary according to such factors as degree of risk and duration of investment, see id. at 697. The court then considered the assumptions a plan can make with regard to the average discount rate of its participants. The court noted that in selecting a discount rate, a plan could assume that its participants have a zero tolerance for risk or could instead focus on a plan's rate of return. The court determined that the investment characteristics of a plan and a plan's rate of return are instructive because the rate of return controls the amount of defined benefit a plan will offer. Id. The district court considered the discount rate used in the Master Retirement Plan not to be unreasonable because that rate, although above the zero-risk rate on thirty-year government securities that plaintiffs proposed, was well below the approximate 8-10 percent rate of return on the Master Retirement Plan's assets. Id. at 698-99.

Plaintiffs-appellants submit that the rate is unreasonable, arguing that employer contributions, not plan returns, control the amount of defined benefits that a plan is able to offer in the first place. Br. of Pls.-Appellants 24. They consider it unreasonable to use a plan's investment experience when calculating deferred vested retirement benefits because investment in the equities market is volatile, future projections of a plan's investment returns are self-interested, and allowing a plan sponsor to rely on investment returns assumes that past returns are relevant to the analysis of long-term future investment returns. Id. at 25-26.

The court finds no error in the district court's conclusion that the actuarial reduction method was not unreasonable solely for its use of a 6.75 percent discount rate. The rate was significantly lower than the approximately 8-10 percent rate of return earned on the assets of the Master Retirement Plan, the 6.75 discount percent rate was below the 7.37 and 6.88 percent average interest rates on thirty-year government securities that existed around the time the plan was created, and plaintiffs-appellants' own expert did not testify that the 6.75 percent discount rate was presumptively unreasonable as an actuarial matter when used in a calculation for deferred vested retirement benefits.

A plan's experience in the market, i.e., the actual rate of return on the plan's investments, is relevant to determining whether an actuarial rate is reasonable. In 2002, the Master Retirement Plan's actuary estimated, for funding purposes, that the plan's projected rate of return would be 8.25 percent. McCarthy II, 372 F.Supp.2d at 698. The Master Retirement Plan's investment experience in the equities market yielded relatively consistent results: "Over the past two years, the Plan assets have earned a rate of return of 9.63%; over the last year, 15.91%; over the past 10 years, 10.78%; and over the past 15 years, 10.27%." Id. at 696. The 6.75 percent discount rate used by the Master Retirement Plan for purposes of the actuarial reduction was thus below both the estimated rate of return and the actual rate of return achieved by the assets of the plan.

A discount rate chosen by a plan may be suspect where a plan projects inordinately high returns or experiences unusually high investment success and bases its actuarial discount rate on this high rate. There is no indication here, however, that the Master Retirement Plan sought to link the discount rate with its projected return on investment. The fact that the discount rate selected by the Master Retirement Plan to calculate actuarial reductions fell well below that rate, which was projected to be 8.25 percent but actually yielded an average over 10 percent, is a further indication that the actuarial assumptions are not unreasonable solely because of the use of the 6.75 percent discount rate. Nor is there any indication in the record that the Master Retirement Plan based its portfolio of investments on high-risk equities yielding volatile returns.

Additionally, the Master Retirement Plan selected and maintained a discount rate that was, at the time, comparable to the interest rate on thirty-year government securities. The Master Retirement Plan was amended and restated in 1994, in which year the average interest rate for thirty-year government securities was 7.37 percent. See Fed. Reserve Statistical Release: Selected Interest Rates: Historical Data: 30-year Treasury Bill, available at http://www. federalreserve.gov/releases/h15/data.htm. In 1995, at the time the Internal Revenue Service ("IRS") reviewed the plan for compliance with the trust qualification requirements of 26 U.S.C. § 401(a), the average interest rate for thirty-year government securities was 6.88 percent, a rate comparable to but still higher than the Plan's 6.75 percent rate.4 Id.; Br. of Pls.-Appellants 10 (stating that the 6.75 percent fixed rate ten years ago approximated the rate of the thirty-year Treasury Bond). By selecting a discount rate that was lower than the average interest rate set for thirty-year government securities, the Master Retirement Plan applied a discount rate that was at that time more favorable to participants in the plan than would have been the thirty-year interest rate on government securities. In summary, the district court's finding that no juror could have found on this record that the use of the 6.75 percent discount rate was unreasonable is further supported by the average rate of return on the Master Retirement Plan's investments, which was substantially higher than the discount rate, and the rate of return on thirty-year government securities around the time the plan was created, which was comparable to the discount rate.

Plaintiffs-appellants argue that although application of the 6.75 percent discount rate may have been reasonable in 1995, it is not reasonable in today's low interest rate environment.5 Essentially, plaintiffs-appellants advocate for "periodic" adjustment of the rate used to determine actuarial equivalence. Reply Br. of Pls.-Appellants 18 (arguing that "nothing prevents the company from periodically reviewing its rate and changing it as needed"). ERISA does not specifically require that retirement plans periodically adjust their actuarial interest rates. If a plan were required to do this, an employer potentially could manipulate the benefits provided to a participant, particularly in a year in which interest rates were extraordinarily high. The court recognizes the concern expressed in the relevant provisions of Title 26, Title 29, and the related regulations, that employers should not be able to manipulate actuarial assumptions to their benefit and to the detriment of employees. See, e.g., 26 U.S.C. § 401(a)(25) (requiring, in order for a defined benefit plan to be treated as providing definitely determinable benefits, that "whenever the amount of any benefit is to be determined on the basis of actuarial assumptions, such assumptions [be] specified in the plan in a way which precludes employer discretion").

Plaintiffs' expert, Claude Poulin, prepared a declaration and testified at deposition on the unreasonableness of the actuarial discount rate.6 Notably, he did not testify that the 6.75 percent discount rate was presumptively unreasonable or that it failed to comply with industry standards. Instead, he testified that he had seen discount rates both lower and higher than that used by the Master Retirement Plan. Claude Poulin Dep. dated May 27, 2004, at 49. He concluded that "the interest rate in conjunction with the mortality tables [was] unreasonable in determining actuarial equivalency." Id. at 122 (emphasis added). The essence of Mr. Poulin's testimony was that the discount rate adopted by the Master Retirement Plan became unreasonable when it was used in connection with what he considered to be an outdated mortality table. Id. at 48, 52. Mr. Poulin testified that "it is possible to generate or create a mortality table that combined with a 6.75 percent interest rate would produce a reasonable actuarial equivalent benefit." Id. at 132. The fact that plaintiffs' own expert did not characterize the 6.75 percent discount rate as presumptively unreasonable but testified that "many plan rates are lower or maybe slightly higher" supported the district court's conclusion. Id. at 49 (emphasis added).

Plaintiffs' expert further stated that "the rates used for the calculation of lump sums give an indication of what ERISA and the Internal Revenue Code prescribe as reasonable actuarial assumptions for the purpose of determining actuarial equivalence in general." Claude Poulin Decl. dated Apr. 30, 2004, ¶ 20. The statute, 26 U.S.C. § 417(e)(3)(A)(ii)(II), formerly required that qualified retirement plans use the annual interest rate yield on thirty-year Treasury securities in determining certain distributions.7 We note significant differences between lump sum distributions and deferred vested retirement benefits. Although use of the thirty-year Treasury rate may create a strong presumption that a plan complies with 26 C.F.R. § 1.401(a)-14(c)(2), neither the Internal Revenue Code nor any regulations require use of the rate on thirty-year Treasury securities to determine the actuarial equivalent of a deferred vested retirement benefit.

For the reasons stated in the foregoing, the district court's grant of defendants' motion to dismiss the count of the complaint that challenged the Summary Plan Description, the district court's denial in part of plaintiffs' motion to amend the complaint to disallow a claim relating to the mortality table, and the district court's award of summary judgment in favor of defendants on the issue of the use by the Master Retirement Plan of the 6.75 percent discount rate in the actuarial reduction, are AFFIRMED.