
127 F.Supp.2d 192 (2001)
ISB LIQUIDATING COMPANY and Kidde Industries, Inc., Petitioners-Plaintiffs,
v.
DISTRICT NO. 15 MACHINISTS' PENSION FUND, by its BOARD OF TRUSTEES, I. Michael Bracco, Richard Hubert, John Scarfi, Jerome Freedman, William Henry and Alan Stern, Respondents-Defendants.
No. CV 96-0731.
United States District Court, E.D. New York.
January 3, 2001.
*193 Barry N. Saltzman, Richards & O'Neil, New York City, for petitioners-plaintiffs.
Patricia McConnell, Vladeck, Waldman, Elias & Engelhard, P.C., New York City, for respondents-defendants.

MEMORANDUM & ORDER
DEARIE, District Judge.
ISB Liquidating Company[1] and Kidde Industries, Inc.[2] (the "Employers") bring this action to vacate an arbitration award upholding the withdrawal liability assessed by the District No. 15 Machinists' Pension Fund (the "Fund") under the Multiemployer Pension Plan Amendments Act of 1980 ("MPPAA"), 29 U.S.C. §§ 1381 et seq.
For the reasons set forth below, the Court denies the Employers' motions to vacate the arbitration award and for summary judgment. The Fund's cross-motion to confirm the arbitration award is granted. *194 The Fund's application for costs and attorney's fees is denied.

Background
The following material facts are undisputed. The Fund is a multiemployer pension plan within the meaning of Section 2 of ERISA, 29 U.S.C. § 1002, and the provisions of the MPPAA. Until February of 1991, the Employers contributed monthly to the Fund on behalf of their covered employees pursuant to successive collective bargaining agreements between the Employers and the Fund. On February 8, 1991, the Employers withdrew from the Fund within the meaning of the MPPAA. The Fund assessed withdrawal liability against the Employers in the amount of $2,023,901 using the direct attribution method. The Employers filed for arbitration of the Fund's assessment on March 24, 1992 with the American Arbitration Association. Arbitrator Maurice C. Benewitz (the "Arbitrator") rendered an Opinion and Award, dated January 22, 1996, finding that the Fund's assessment of $2,023,901 in withdrawal liability against the Employers was correct as a matter of fact and law. This action followed.

The Fund's Method for Calculating Withdrawal Liability
Under the MPPAA, "[w]hen an employer withdraws from a multiemployer plan, the plan sponsor ... shall (1) determine the amount of the employer's withdrawal liability, (2) notify the employer of the amount of the withdrawal liability, and (3) collect the amount of the withdrawal liability from the employer." 29 U.S.C. § 1382. To determine the amount of liability, the plan sponsor must use one of four methods provided for by statute or any alternative method approved by the Pension Benefit Guaranty Corporation ("PBGC"). 29 U.S.C. § 1391. The presumptive method applies unless a fund elects one of the other methods provided for by statute or an approved alternative method. Id.
Employers withdrawing from the Fund after September 25, 1980, were assessed withdrawal liability under a hybrid method. Under the hybrid method, an employer was assessed liability equal to the higher of the assessment using (a) the presumptive method and (b) a variant of the direct attribution method. The direct attribution method, like the presumptive method, is one of the four statutorily permitted methods for determining withdrawal liability. The PBGC approved the Fund's adoption of this alternative hybrid method.
In 1984, certain employers initiated a class action against the Fund, Cummings-Landau Laundry Machinery Co. v. District No. 15 Machinists Pension Fund, 84-CV-5530 (S.D.N.Y.Keenan, J.) ("Cummings-Landau"), seeking to invalidate the amendment to the Fund's trust agreement adopting the hybrid method. Plaintiffs contended that the Fund's use of its approved "higher of two" hybrid method violated the MPPAA in that a single method, as contemplated by the statute, was not applied uniformly to compute the liability of each withdrawing employer. The class was defined as
consisting of all employers (a) who made contributions to [the Fund], (b) who thereafter withdrew from [the Fund] or will during the pendency of this action withdraw from [the Fund], and (c) whose withdrawal liability was computed by [the Fund] using the method chosen by its Trustees, which computation resulted in the imposition of a withdrawal liability in an amount in excess of that computed using the method prescribed in Section 4211(b) of ERISA, 29 U.S.C. § 1391(b) [the presumptive method].
(Stipulation and Order for Class Action Certification in Cummings-Landau, Record, Fund Ex. 2 at p. 2).[3] The Employers were not members of the class.
*195 During the pendency of Cummings-Landau, the PBGC issued proposed regulations which, if approved, would invalidate the use of hybrid methods, including that used by the Fund. Under the proposed regulations, until a plan that had been using a hybrid method was amended to adopt a valid method, its method would be deemed to be the presumptive method. See Allocating Unfunded Vested Benefits, 50 Fed.Reg. 36603, 36610 (1985) (to be codified at 29 C.F.R. § 2642) (proposed September 9, 1985).[4] Thereafter, on December 9, 1985, before the regulations were approved, the trustees of the Fund voted to adopt the presumptive method for calculating withdrawal liability for all employers withdrawing on or after January 1, 1986. (Record, Joint Ex. E). The final PBGC regulations, published October 26, 1987, and effective November 25, 1987, did prohibit plans from assessing liability under hybrid methods and deemed the method of such plans to be the presumptive method pending the adoption by plan amendment of a different valid method. 29 C.F.R. § 2642.14 (1988).[5]
On January 15, 1986, Fund counsel proposed to settle the Cummings-Landau case, offering to reduce the assessed withdrawal liability of members of the class by 85% of the difference between their liability calculated under the Fund's hybrid method and their liability had it been calculated using the presumptive method. Fund counsel further proposed "commencing January 1, 1986, ... to compute the withdrawal liability of all withdrawing employers under the presumptive method." (Record, Empl.Ex. 3). The Cummings-Landau parties entered into a Stipulation of Settlement on January 22, 1986 (the "Stipulation"). The Stipulation provided the following:
In full and complete settlement of the claims asserted in this class action and subject to the terms and conditions of this Stipulation, the withdrawal liability to defendant of each class member, as computed and assessed by defendant in accordance with the method adopted and applied by defendant's Trustees to calculate the liability of employers withdrawing from defendant between September 27, 1980 and December 31, 1985, shall be reduced an amount equal to eighty five percent (85%) of the difference between the liability so computed and the liability as computed under the "presumptive method" prescribed in Section 4211(b) of ERISA, 29 U.S.C. § 1391(b). As to all employers withdrawing from defendant on or after January 1, 1986, the defendant shall compute and assess withdrawal liability under said "presumptive method."
(emphasis added) (Record, Empl.Ex. 11 at ¶ 3). The Stipulation was approved by court order dated December 29, 1986.
The Fund assessed withdrawal liability against all employers withdrawing between January 1, 1986 and February 28, 1989 using the presumptive method. Beginning in March of 1989, pursuant to an *196 amendment to the plan,[6] the Fund began assessing the liability of withdrawing employers using the direct attribution method set forth in MPPAA Section 4211(c)(4), 29 U.S.C. § 1391(c)(4). This method was used to calculate the withdrawal liability of $2,023,901 against the Employers for their withdrawal on February 8, 1991.

The Fund's CalculationThe "Last Employer" Assumption
In calculating the Employers' withdrawal liability using the direct attribution method, the Fund attributed all of the service credits of two employees to the withdrawing Employers, their "last employer," although some of the plan service credits were earned by those employees while employed elsewhere. According to the Employers, as a result of the incorporation of this "last employer" assumption in the direct attribution calculation, the Employers' withdrawal liability was improperly increased by about $25,000.

The Arbitration
Before the Arbitrator, the Employers' challenged the Fund's assessment of withdrawal liability on the grounds that the Fund's use of the direct attribution method violated the court-ordered Cummings-Landau Stipulation, which according to the Employers, bound the Fund to use in perpetuity the presumptive method for calculations on or after January 1, 1986. In April of 1995, during the course of the arbitration, the record was reopened at the Employers' request to allow a challenge to the Fund's use of the "last employer" assumption in the calculation made under the already challenged direct attribution method.
The Arbitrator found that he was precluded from considering the issue of whether the Cummings-Landau Stipulation required the use of the presumptive method because in an unrelated action, captioned Sigmund Cohn Corp. and District No. 15 Machinists Pension Fund, 14 EBC 1031 (Sands, Arb.1991), in which the same Cummings-Landau issue was raised, another arbitrator declined to address it on the grounds that it was outside his statutory authority to decide and would be more properly addressed to a court in proceedings to enforce, vacate or modify the arbitration award. Moreover, the Arbitrator "fe[lt] doubly bound to observe [the Sigmund Cohn arbitrator's] findings [that construction of the Cummings-Landau Stipulation was outside his authority] ... because a district court confirmed the Sigmund Cohn award."[7] (Opinion and Award of Arbitrator, Pet'r Mem. of Law, Ex. A at p. 27). The Arbitrator also found "that in any case, the outcome would not be clear if he did consider it proper to construct Cummings-Landau and apply it to th[e] disagreement." (Id. at p. 25). Accordingly, the Arbitrator dismissed the challenge to the Fund's use of the direct attribution method.
The Arbitrator also dismissed the Employers' challenge to the Fund's use of the "last employer" assumption on two grounds. First, the Arbitrator held that because the Employers' asserted at the first arbitration hearing that their challenge was to the use of the direct attribution method, and not to the amount calculated, the calculation itself could not be challenged in the arbitration proceeding. Second, the Arbitrator held that the challenge would nonetheless fail on the grounds that the "last employer" assumption was an appropriate use of statistical methodology under MPPAA Section *197 4213(a), 29 U.S.C. § 1393(a), for determining attributable benefits under the direct attribution method set forth in MPPAA Section 4211, 29 U.S.C. § 1391.

Discussion

Arbitrability of the Employers' Cummings-Landau Defense
As noted above, citing the arbitration decision in Sigmund Cohn Corp. and District No. 15 Machinists Pension Fund and this Court's confirmation in Sigmund Cohn Corp. v. District No. 15 Machinists Pension Fund, 804 F.Supp. 490 (E.D.N.Y. 1992), Arbitrator Benewitz found that he was precluded from interpreting the Cummings-Landau Stipulation and applying it to this case. In Sigmund Cohn Corp., Arbitrator Sands stated:
I have not considered and do not determine Cohn's arguments that the Cummings-Landau court order prevented any departure from the presumptive method and that the principles of equitable estoppel bar the Fund from assessing maximum withdrawal liability to which it is statutorily entitled to do. As I read MPPAA, nothing in my statutory mandate authorizes me as arbitrator to decide issues that do not arise under ERISA Sections 4201 - 4219 and 4225. These arguments fall outside that mandate, and they are more properly addressed to a court in proceedings to enforce, vacate or modify....
(Pet'r Mem. of Law, Ex. C at p. 14-15). Because this Court agreed with Arbitrator Sands' decision that as of the time of Sigmund Cohn's withdrawal the Fund had not effectively adopted the attributable method, and therefore was required to use the statutory presumptive method, this Court also did not address the Cummings-Landau arguments. See Sigmund Cohn Corp., 804 F.Supp. at 490.
Under MPPAA Section 4221(a)(1), 29 U.S.C. § 1401(a)(1), "[a]ny dispute between an employer and the plan sponsor of a multiemployer plan concerning a determination made under sections 1381 through 1399 [MPPAA Sections 4201 through 4219] ... shall be resolved through arbitration." The Employers argue that because the dispute over the meaning of the Cummings-Landau Stipulation concerns the Fund's use of the direct attribution method instead of the presumptive method in calculating withdrawal liability, methods appearing in MPPAA Section 4211, 29 U.S.C. § 1391, the question falls squarely within the jurisdiction of the Arbitrator. Because the Arbitrator did not decide the issue, the Employers contend that his Opinion and Award should be vacated. The Fund contends that adjudication of the Cummings-Landau defense has been appropriately left to this Court.
As an initial matter, the question to be resolved with respect to the Stipulation is whether it requires the use of the presumptive method in perpetuity. This question is not akin to the factual issues that must be resolved in order to actually calculate withdrawal liability and the timing of payments under 29 U.S.C. §§ 1381 through 1399.[8] Rather, it is a question of whether the Stipulation affects which method of calculation must be applied. In the Court's view, the only provision for which Congress has specified an arbitral resolution under which construction of the Stipulation could fall is the broad introductory provision of 29 U.S.C. § 1382(1), requiring *198 the plan sponsor to "determine the amount of ... withdrawal liability." Construction of the Stipulation literally "determine[s] the amount" of withdrawal liability because it determines whether the presumptive or attributable method applies. However, such an expansive reading of 29 U.S.C. § 1382 would "moot the exhaustive list of arbitrable questions because every issue in a MPPAA case ultimately impacts the existence or amount of ... withdrawal liability." Bd. of Tr. of Trucking Empl. Pension Fund v. Centra, 983 F.2d 495, 507 (3d Cir.1992).
Moreover, as set forth in T.I.M.E.-DC, Inc. v. Management-Labor Welfare & Pension Funds, 756 F.2d 939, 945 (2d Cir.1985), the arbitration requirement set forth in 29 U.S.C. § 1401 does not constitute a bar to federal jurisdiction. See ILGWU Nat. Retirement Fund v. Levy Bros. Frocks, Inc., 846 F.2d 879, 886 (2d Cir.1988). Exceptions to the arbitral exhaustion doctrine have been recognized by courts when the doctrine's policies, including the application of the administrative body's superior expertise, promotion of judicial economy, and deference to the statutory scheme, are not implicated. T.I.M.E.-DC, 756 F.2d at 945. In cases, as here, where the parties would likely seek judicial review of any decision an arbitrator might reach, judicial economy is not promoted by requiring arbitration. Id. Moreover, the issue of the interpretation of the Cummings-Landau Stipulation and its implications for non-class members is not one for which an arbitrator skilled in pension and labor matters would have superior expertise to offer.[9] Finally, as set forth above, Congress has not provided for an arbitral resolution under the statutory scheme for the interpretation of settlement agreements.
Indeed, the Employers ultimately contend that the error committed by the Arbitrator in failing to address the Cummings-Landau defense is now moot because the Employers seek a decision from this Court, by summary judgment, on the merits of the issue. They agree that no further benefit would be derived from remanding the issue of the Cummings-Landau defense to the Arbitrator for decision because any decision would result in the parties returning to this Court again with applications to confirm or vacate.
For these reasons, the Court now addresses the merits of the Cummings-Landau defense.

The Employers' Cummings-Landau Defense
The Employers, not members of the Cummings-Landau class, urge this Court to interpret the Stipulation to bind the Fund in perpetuity to assess withdrawal liability using the presumptive method. They argue that because the Stipulation sets forth that "[a]s to all employers withdrawing from defendant on or after January 1, 1986, the defendant shall compute and assess withdrawal liability under said `presumptive method'," the Fund must assess withdrawal liability using the presumptive method for all future employers and cannot validly adopt another method. The Fund contends that the phrase "all employers withdrawing from defendant on or after January 1, 1986" refers to a subgroup of the plaintiff class of employers, namely those who withdrew between January 1, 1986 and the conclusion of the action. According to the Fund's interpretation, the other sub-group consists of those employers who withdrew from September 27, 1980 through December 31, 1985 and were subject to the hybrid method. Thus, the Fund argues, the Stipulation does not *199 bind it to use the presumptive method to calculate the liability of all future withdrawing employers. Rather, it binds the Fund to use the presumptive method for class members who withdrew on or after January 1, 1986, while the action remained pending.
Although the Court agrees with the Fund's interpretation of the Stipulation as not requiring the Fund to apply the presumptive method in perpetuity to employers withdrawing on or after January 1, 1986, the Court does not agree that the employer class was split into two groups by the Stipulation. More precisely, the plaintiff employer class was closed by the Fund trustees' agreement to adopt the presumptive method beginning January 1, 1986.
The plaintiff class, as set forth above, was defined to include employers who withdrew from the Fund prior to the termination of the lawsuit whose liability was calculated using the hybrid method. The lawsuit concluded on December 29, 1986, when the Stipulation was approved and the complaint was dismissed. As noted above, on December 9, 1985, the trustees of the Fund agreed to use the presumptive method for calculating withdrawal liability for all employers withdrawing on or after January 1, 1986. Thus, at the time the Stipulation was filed with the Court for approval on January 22, 1986, employers withdrawing on or after January 1, 1986 and before the conclusion of the action were subject to withdrawal liability using the presumptive method. A close reading of the class definition reveals that such employers fell outside of the defined class because class members must have both withdrawn from the Fund and have been subject to withdrawal liability in excess of that which would have been assessed using the presumptive method. Because the trustees agreed to adopt the presumptive method during the pendency of the action, the plaintiff class effectively closed as of December 31, 1985.
This Court, essentially in agreement with the Fund, finds that the language in the Stipulation clarifies that those employers that withdrew during the pendency of the lawsuit but were taken outside of the class because of the intervening agreement by the trustees to adopt the presumptive method would have their liability calculated under the newly adopted presumptive method and not the hybrid method subject to reduction by formula. Further, it constitutes an agreement to abandon the controversial hybrid method for calculating withdrawal liability in the future in addition to the Fund's agreement to reduce the previously calculated assessments under the hybrid method by a formula amount. At the time the trustees agreed to revert to the presumptive method, the PBGC regulations disallowing the use of their hybrid method were not final. In fact, the regulations did not become effective until November 25, 1987, nearly two years later. Thus, during the pendency of the Cummings-Landau action, the Fund was not required to abandon its use of the hybrid method. However, in light of the lawsuit and the proposed regulations, it voluntarily reverted to the presumptive method, the method which applies if no other valid method is adopted by amendment. Thus, the provision of the Stipulation referring to "all employers" indeed benefits all employers withdrawing from the Fund after January 1, 1986 in that, in the context of the Stipulation, it is a commitment to abandon in perpetuity the challenged hybrid method from that date forward. Nothing, including the trustees' agreement to adopt the presumptive method at the December 9, 1985 meeting, otherwise would have prevented the Fund from adopting the hybrid method again for withdrawals prior to November 25, 1987.[10] However, it does not, as the *200 Employers contend, bind the Fund to use the presumptive method to calculate withdrawal liability forevermore. The Fund remained free to amend its method of computing withdrawal liability with respect to later withdrawals to another valid allocation method other than the hybrid method, subject to the rules and limitations imposed by ERISA and its plan documents.
To the extent that the Stipulation may be ambiguous, this Court's reading of the Stipulation is consistent with contemporaneous extrinsic evidence.[11] An examination of the minutes of the December 9, 1985 meeting reveals that the trustees were apprised that the proposed regulations made it clear that the PBGC would no longer approve the Fund's hybrid method and that, in the absence of any other approved method, the presumptive method would apply. The minutes specifically note that legal counsel "recommended that for future withdrawals the [t]rustees consider a different calculation method." (emphasis added). (Record, Joint Ex. E at ¶ 3(b)). A motion was then made and seconded "to adopt the presumptive method of calculating withdrawal liability for all employers which withdraw on and after January 1, 1986." Id. Thus, the language of the minutes referring to "all employers which withdraw on and after January 1, 1986" essentially tracks that of the Stipulation referring to "all employers withdrawing from defendant on or after January 1, 1986." It is clear from the minutes that the trustees contemplated a future change to the calculation method, and to interpret the Stipulation as forever binding the Fund to use the presumptive method would contradict this essentially contemporaneous evidence.
Moreover, the Cummings-Landau plaintiffs' submissions in support of the Stipulation, cited by the Employers, are entirely consistent with this Court's determination that the Stipulation does not bind the Fund to use the presumptive method in perpetuity. Each of those submissions essentially restates the terms of the Stipulation and merely reflects the Fund's agreement to abandon the hybrid method and revert, as required by statute and regulation in the absence of the adoption of a valid alternative, to the presumptive method. They do not suggest that the Fund has undertaken an obligation to apply the presumptive method in perpetuity. Thus, the fact that statements made in plaintiffs' submissions regarding the Stipulation were not challenged by the Fund is not surprising, and it is certainly not dispositive in the Employers' favor, as they contend.
For example, the Cummings-Landau plaintiffs' brief in support of the Stipulation describes the provision at issue as follows:
in a provision that does not affect the class but will benefit employers who withdraw from the [Fund] in the future, the [Fund] has agreed to abandon its method of computing withdrawal liability *201 in favor of the [presumptive] method plaintiff claims should be applied.
(Record, Empl.Ex. 6 at p. 4). Put another way, with respect to employers who withdraw in the future, the Fund agreed to abandon the hybrid method challenged by plaintiffs and revert to the method that applies in the absence of a valid alternative. Nothing states, or even implies, that an alternative method, other than the challenged and ultimately invalidated hybrid method, may not be adopted in the future. The accompanying affidavit of Mr. Nelson provides further support. It states that the Fund
has in essence agreed to the declaratory and injunctive relief sought by stipulating to abandon its "higher of two" [hybrid] method and prospectively compute withdrawal liability under the statutory Presumptive Method for employers withdrawing from defendant on or after January 1, 1986.... This provision does not affect class members, but benefits employers withdrawing from [the Fund] ... in the future.
(Record, Empl.Ex. 7 at p. 8). The relief sought in the complaint was a judgment:
1. Declaring that the amendment to [the Fund's] Trust Agreement adopting the "higher of two" [hybrid] method for computing employers' withdrawal liability is in contravention of MPPAA and is invalid;
2. Permanently enjoining [the Fund] from computing withdrawal liability in accordance with the method adopted by the amendment to [the Fund's] Trust Agreement;
3. Directing [the Fund] to recompute the withdrawal liability of plaintiff and each class member in accordance with the method prescribed in the absence of a valid amendment to the Trust Agreement, namely, the Presumptive Method set forth in section 4211(b) of ERISA, 29 U.S.C. § 1391(b).
4. Directing [the Fund] to make restitution to each class member that has paid a withdrawal liability to [the Fund] in an amount in excess of that authorized under section 4211(b) of ERISA, 29 U.S.C. § 1391(b).
(Record, Empl.Ex.1). Thus, the declaratory and injunctive relief sought in paragraphs one and two above amount to a declaration that the hybrid method is invalid, resulting in invalidation of the amendment to the trust agreement adopting such method and, consequently, reversion by law, to the presumptive method applicable in absence of a valid amendment, and an injunction permanently prohibiting the Fund from applying the hybrid method. This fully comports with the Court's interpretation of the Stipulation as requiring the Fund to abandon the hybrid method in perpetuity without requiring it to apply the presumptive method forevermore.[12]
At the meeting of the trustees on March 28, 1986, the Stipulation was summarized. The minutes provide that, "[g]iven the unfavorable impact the [proposed] regulations would have, the suit was settled" such that "the Fund would use the presumptive method hereafter as its method for computing withdrawal liability." (Record, Empl.Ex.14). This, too, comports with the Court's interpretation in that there is no suggestion that the Fund would not be able to change its method in the future and in that, as reported, the settlement merely brought the Fund's practices in line with the anticipated regulation.[13]
*202 Moreover, the Court's interpretation is consistent with the trustees' fiduciary obligation to use the latitude afforded by the statute in allowing various methods of calculating withdrawal liability to ensure the viability of the Fund. Accordingly, the Employers' Cummings-Landau defense to the application of the direct attribution method for determining their withdrawal liability is unavailing.

The Fund's Last Employer Assumption
The direct attribution method is set forth in MPPAA Section 4211(c)(4), 29 U.S.C. § 1391(c)(4). It provides, in pertinent part:
(A) The amount of the unfunded vested benefits allocable to an employer under this paragraph is equal to the sum of
(i) the plan's unfunded vested benefits which are attributable to participants' service with the employer (determined as of the end of the plan year preceding the plan year in which the employer withdraws), and
(ii) the employer's proportional share of any unfunded vested benefits which are not attributable to service with the employer or other employers who are obligated to contribute under the plan in the plan year preceding the plan year in which the employer withdraws (determined as of the end of the plan year preceding the plan year in which the employer withdraws).
(B) The plan's unfunded vested benefits which are attributable to participants' service with the employer is the amount equal to the value of nonforfeitable benefits under the plan which are attributable to participants' service with such employer (determined under the plan rules not inconsistent with regulations of the [PBGC]) decreased by the share of plan assets determined under subparagraph (C) which is allocated to the employer as provided under subparagraph (D).
(emphasis added). Thus, unfunded vested benefits which are directly attributable to the service of employees with the employer and a share of the unfunded vested benefits not attributable to any contributing employer are added to determine withdrawal liability. The PBGC, the parties agree, has not issued any regulations pertaining to the attribution of vested benefits to participants' service with a withdrawing employer under Section 4211(c)(4)(B), 29 U.S.C. § 1391(c)(4)(B).
By amendment to its plan dated May 22, 1989, the Fund adopted the direct attribution method for assessing withdrawal liability and rules providing that in the absence of reliable records, for the purpose of determining the value of vested benefits which are attributable to participants' service with an employer, participants' service would be attributed to the employer using a "last employer" assumption. Specifically, Section 12.03(d) of the plan states:
(II)(A) The Plan's unfunded vested benefits which are attributable to Participants' service with the Employer is the amount equal to the value of vested benefits under the Plan which are attributable to Participants' service with such Employer (determined under subsection *203 (c)(I) above) decreased by the share of Plan Assets determined under subsection (d)(III) below which is allocated to the Employer as provided under subsection (d)(IV) below.
(emphasis added) (Record, Joint Ex. G at p. 12). Section 12.03(c)(I) provides, in pertinent part:
(A) The actuarial value of vested benefits attributable to service with the Employer shall be determined on the basis of Fund records or, in the event detailed employment records of a Participant are not available in the Fund office, then on the basis of records submitted by the Employer deemed satisfactory by the Trustees.
(B) In the absence of said reliable records establishing employment (or non-employment) to the contrary, the following service shall be attributable to the Employer:
(1) All pension credits and years of vesting service of pensioners and vested inactives last employed by the Employer, and
(2) All pension credits and years of vesting service of Employees employed by the Employer on the date of the Employer's withdrawal.
(Resp't Mem. of Law at p. 15) (quoting Record, Joint Ex. G at p. 10-11; exhibit submitted is missing p. 11). The Fund's trust agreement was amended in June of 1989 to reflect this change. (Record, Joint Ex. H). The trustees reaffirmed their adoption of the "last employer" assumption at their October 2, 1989 meeting. (Record, Fund Ex. 7). Pursuant to these changes, if existing employment records are inadequate to determine the value of vested benefits attributable to participants' service with a withdrawing employer, the "last employer" assumption is applied whereby all employees employed by that employer at the time of the withdrawal are deemed to have accrued all of their credited service with that employer.
According to the Fund, the "last employer" assumption was adopted because of deficiencies in the Fund's computerized participant data prior to January 1, 1987. Computerized data concerning participants' service before 1987 summarized past service without indicating either the employers or the years of service attributable to employment with a given employer. (See Record, Aff. of Albert Cardillo at ¶ 2, November 8, 1995). Moreover, manual compilation of the data not available from the computerized records would be so time-consuming as to make calculation of the vested service credits of all participants employed by a given employer not feasible. (Id. at ¶¶ 4, 9). The Fund actuary recommended the adoption of the "last employer" assumption on the ground that, according to the Fund, it was extremely rare for a participant to be employed by more than one contributing employer, and that, if a participant left a contributing employer, it would be highly unusual for such participant to then work for another contributing employer.[14] (Id. at ¶ 7). The actuary concluded that the "last employer" assumption was a reasonable assumption to be used in the absence of adequate service records, and, therefore, was permissible under MPPAA Sections 4211(c)(4) and 4213(a), 29 U.S.C. §§ 1391(c)(4) and 1393(a), the sections setting forth the direct attribution method and the providing for the use of actuarial assumptions.
As a result of the "last employer" assumption, the Fund attributed all of the service credits of two employees to the Employers in determining withdrawal liability, even though some the their service credits were earned while they were employed by other contributing employers. As a result, the Employers contend, their *204 withdrawal liability was increased by approximately $25,000.[15]
The Fund contends MPPAA Section 4213(a), 29 U.S.C. § 1393(a), permits the use of reasonable actuarial assumptions and methods in calculating withdrawal liability. That section provides:
The [PBGC] may prescribe by regulation actuarial assumptions which may be used by a plan actuary in determining the unfunded vested benefits of a plan for purposes of determining an employer's withdrawal liability under this part. Withdrawal liability under this part shall be determined by each plan on the basis of
(1) actuarial assumptions and methods which, in the aggregate, are reasonable (taking into account the experience of the plan and reasonable expectations) and which in combination, offer the actuary's best estimate of anticipated experience under the plan, or
(2) actuarial assumptions and methods set forth in the [PBGC's] regulations for purposes of determining an employer's withdrawal liability.
MPPAA Section 4213(b), 29 U.S.C. § 1393(b) provides, in pertinent part:
In determining unfunded vested benefits of a plan for purposes of determining an employer's withdrawal liability under this part, the plan actuary may
....
(2) in the absence of complete data, rely on the data available or on data secured by sampling which can reasonably be expected to be representative of the status of the entire plan.
MPPAA Section 4213(c), 29 U.S.C. § 1393(c) further provides:
For purposes of this part, the term "unfunded vested benefits" means with respect to a plan, an amount equal to
(A) the value of nonforfeitable benefits under the plan, less
(B) the value of the assets of the plan.
In contrast, the Employers construe these provisions as expressly limiting the use of actuarial assumptions to the determination of "unfunded vested benefits" of a plan. They argue that using actuarial assumptions, reasonable or otherwise, for attributing a participant's service with other employers to the Employers is impermissible in that it does not relate to the determination of "unfunded vested benefits" of the plan. The amount of unfunded vested benefits of the plan are the same regardless of the allocation of that amount among employers based on participants' service. Use of the "last employer" assumption, they contend, converts the Fund's method of calculating withdrawal liability from one that is statutorily permissible under 29 U.S.C. § 1391(c)(4) into an unapproved alternative method. Moreover, the Employers argue that the service data is available and that the use of actuarial assumptions is, therefore, inappropriate under MPPAA Section 4213(b)(2), 29 U.S.C. § 1393(b)(2). They suggest that the Fund has the information regarding one employee in hand and that the other employee, who is currently receiving checks from the Fund, could be contacted to gather the information regarding her service with her previous employer. See n. 15, supra.
The Fund cites two decisions in other circuits in support of its reading of the *205 statute. In Huber v. Casablanca Industries, Inc., 916 F.2d 85 (3d Cir.1990), cert. dismissed, 506 U.S. 1088, 113 S.Ct. 1070, 122 L.Ed.2d 497 (1993), as in this case, the fund allocated unfunded vested benefits using the direct attribution method and a "last employer" assumption. Also as in this case, the employer argued that use of the "last employer" assumption transformed the statutorily permissible direct attribution method into an alternative method that required PBGC approval under 29 U.S.C. § 1391(c)(5). The Third Circuit did not reach the issue. Rather, it accepted
the Arbitrator's finding that, given the unrebutted testimony of extremely low employee interchange between the [only] two [contributing] employers, one may view the last employer assumption as a reasonable simplifying assumption by the Fund actuary. See 29 U.S.C. § 1393(a)(1).
Huber, 916 F.2d at 107.[16] Similarly, in Artistic Carton Co. v. Paper Industry Union-Management Pension Fund, 971 F.2d 1346 (7th Cir.1992), the parties disputed whether pursuant to the parenthetical language in MPPAA Section 4211(c)(4)(B), 29 U.S.C. § 1391(c)(4)(B) (setting forth the direct attribution method),[17] a plan using the direct attribution method could attribute service with one employer, in that case a predecessor company, to another. The plan's trust agreement provided that "[s]ervice with an Employer shall include all service ... credited to the Employees ... for whom it was the last contributing Employer." Id. at 1352. It further provided that "[s]ervice with a predecessor shall be taken into account as service with the withdrawing Employer, and contributions by and withdrawal liability assessed against such predecessor shall be treated as contributions of the withdrawing Employer." Id. The court observed that "[i]nstead of forbidding clauses such as [that in the plan's trust agreement], ERISA gives pension funds the power to attribute service to particular employers" and noted that according to the arbitrator below in that case, attribution of service is "common to attributable rule plans." Id. at 1353.[18] The court acknowledged that "[p]erhaps [the employer] is right to say that one parenthetical phrase in § 4211(c)(4)(B) is a slight foundation for so muscular a provision," but found that the fund in that case did not depend on ERISA for its authority. Rather, it found that the trust agreement was a contract that the employer had agreed to be bound by, including the provision incorporating the "last employer" assumption. Id. at 1353-54. The MPPAA, the court said, establishes mandatory liability; it does not forbid employers from agreeing to pay more. Id. at 1353. Accordingly, the calculation of withdrawal liability was affirmed.[19]
In countering, the Employers cite H.C. Elliott, Inc. and Carpenters Pension Trust Fund, 13 EBC 1962, 1965-66 (Kagel, Arb. 1991). In that case, the parties argued over the calculation of employer contributions and its impact on withdrawal liability. *206 The arbitrator distinguished permissible actuarial assumptions from the sum of employer contributions, a "readily verifiable" figure. The Employers contend that the determination of participants' service, like the compilation and addition required to calculate employer contributions in H.C. Elliott, is simply a matter of fact available in Fund records or by contacting participants and should not be subject to actuarial assumptions.
Although the cases cited by the Fund are not factually identical to the case at hand in that one dealt with a fund in which there were only two contributing employers and one dealt with the liability assessed against a successor employer, the Court finds the reasoning of those cases persuasive and applicable to this case. They support the proposition that the "last employer" assumption may be employed by a fund allocating withdrawal liability using the direct attribution method, either as a simplifying actuarial assumption that is reasonable under the particular circumstances and therefore permitted under 29 U.S.C. § 1393(a) or as a permissible plan rule under 29 U.S.C. § 1391(c)(4)(B) which an employer may agree to be bound by under general contracting principles. Indeed, in this case, Arbitrator Benewitz recognized that because the Fund's computerized records do not reflect participants' complete service histories and a survey of pension applications supported the assertion that an insignificant number of employees had service with more than one employer, the "last employer" assumption was a reasonable actuarial assumption. Moreover, he characterized the actuary's statement that
[d]epending upon the size of the Employers' work force and the rate of employee turn-over, it is equally likely that the use of the "last employer" assumption would result in a lower withdrawal liability than would a calculation based upon a manual review of the Fund records
(See Record, Aff. of Albert Cardillo at ¶ 2, November 8, 1995) as a correct statement of a statistical presumption. (Opinion and Award of Arbitrator, Pet'r Mem. of Law, Ex. A at p. 3). The Arbitrator ultimately concluded that "the `last employer' rule is a proper use of statistical methodology and that the [Employers'] challenge could not stand even if the opening statement of counsel [asserting that the challenge was not to the calculation of withdrawal liability itself and, therefore, requiring dismissal] had not been made." Id.
Arbitrator's findings of fact are entitled to a presumption of correctness. See 29 U.S.C. § 1401(c); Sigmund Cohn, 804 F.Supp. at 490. With respect to decisions on matters of law in withdrawal liability disputes under the MPPAA, the Second Circuit has assumed, without ruling, that de novo review is the appropriate standard. See Bowers v. Andrew Weir Shipping, Ltd., 27 F.3d 800, 804-805 (2d Cir. 1994), cert. denied, 513 U.S. 1000, 115 S.Ct. 511, 130 L.Ed.2d 418 (1994) (noting that all other circuits that have considered the issue have so decided). Given Arbitrator Benewitz's findings and the case law presented, this Court concludes that the award should be confirmed.

Attorney's Fees
The Fund seeks costs and attorney's fees pursuant to MPPAA Section 4301(e), 29 U.S.C. § 1451(e). Five factors are considered in determining whether an award of attorney's fees is appropriate. They are:
(1) the degree of the offending party's culpability or bad faith, (2) the ability of the offending party to satisfy an award of attorney's fees, (3) whether an award of fees would deter other persons from acting similarly under like circumstances, (4) the relative merits of the parties' positions, and (5) whether the action sought to confer a common benefit on a group of pension plan participants.
Anita Foundations, Inc. v. ILGWU Nat. Retirement Fund, 902 F.2d 185, 188 (2d. Cir.1990); see also Sigmund Cohn, 804 *207 F.Supp. at 496. Although this Court confirms the arbitration award, the Employers have not exhibited culpability or bad faith. Indeed, because the Arbitrator determined that he lacked jurisdiction to entertain the Employers' Cummings-Landau defense, further litigation was required for the Employers to assert their claim. Moreover, although this Court ultimately finds them unpersuasive, the Employers' arguments are not without foundation, nor are they, as the Fund contends, "exceedingly strained." (See Resp't Ans. Mem. of Law at p. 37). Accordingly, the Court declines to award attorney's fees.

Conclusion
For the reasons set forth above, the arbitration award in the Fund's favor is confirmed. The Employers' motions to vacate the arbitration award and for summary judgment that the Fund must reassess their withdrawal liability using the presumptive method are denied. The Fund's application for costs and attorney's fees is denied.
SO ORDERED.
NOTES
[1]  ISB Liquidating Company is the successor to Bright Star Industries, Inc.
[2]  Kidde Industries, Inc. is the successor to Tose-Fowler, Inc.
[3]  The Record of the Arbitration Proceeding annexed to the Fund's cross-petition will be referred to as "Record." Joint exhibits will be referred to as "Record, Joint Ex. ___", the Fund's exhibits will be referred to as "Record, Fund Ex. ___" and the Employers' exhibits will be referred to as "Record, Empl.Ex. ___".
[4]  The supplementary information describing proposed regulation 29 C.F.R. § 2642.14 explains that "[if] a plan sponsor of a plan that has been using [a "higher of two" allocation method] does not amend the method before the regulation's effective date, the plan will be deemed to have the allocation method that would be applicable under ERISA if the plan had never been amended, i.e. the presumptive method." 50 Fed.Reg. 36603, 36606 (September 9, 1985).
[5]  Specifically, the final regulation provides:

A plan may not apply to any employer withdrawing on or after November 25, 1987, an allocation method approved by the PBGC before that date that allocated to the employer the greater of the amounts of unfunded vested benefits determined under two different allocation rules. Until a plan that has been using such a method is amended to adopt a valid allocation method, its allocation method shall be deemed to be the statutory allocation method that would apply if it had never been amended.
29 C.F.R. § 2642.14 (1988).
[6]  In an unrelated action, it was found that the Fund had not effectively amended its plan and trust agreement until May 22 and June 5, 1989, respectively. Sigmund Cohn Corp. and District No. 15 Machinists Pension Fund, 14 EBC 1031 (Sands, Arb.1991), conf'd, Sigmund Cohn Corp. v. District No. 15 Machinists Pension Fund, 804 F.Supp. 490 (E.D.N.Y.1992).
[7]  The Sigmund Cohn Opinion and Award was confirmed by Memorandum and Order of this Court. See Sigmund Cohn, 804 F.Supp. at 490.
[8]  As stated in Refined Sugars, Inc. v. Local 807 Labor-Management Pension Fund, 580 F.Supp. 1457, 1461 (S.D.N.Y.1984), Sections 1381 through 1399

involve questions of whether an employer has totally, partially or not withdrawn from a plan and what the amount, if any, of its consequent liability should be. These determinations are made by reference to and by interpretation of the Act, which has detailed provisions as to when withdrawal has occurred, whether such withdrawal is total or partial, whether the employer is liable for payment of withdrawal liability after a withdrawal has taken place and how that liability is to be computed.
Id. at 1461 (internal quotations and citation omitted).
[9]  The Employers point to Judge Keenan's order to arbitrate a dispute concerning the calculation of withdrawal liability for B & J Spring Equipment Co., a member of the plaintiff class in Cummings-Landau, under the Stipulation as support for their contention that issues concerning the Stipulation are arbitrable. However, the Stipulation explicitly set forth that disputes between class members and the Fund would be resolved through arbitration. The Employers are not class members.
[10]  Under the Court's interpretation, the commitment to abandon the hybrid method constitutes binding consideration. As the Fund contends, it had a pre-existing duty to apply the presumptive method because of the trustees' December 1985 agreement. However, in absence of the provision in the Stipulation, it could have elected at a later date to re-adopt the hybrid method.

Indeed, the trustees voted to adopt the presumptive method on December 9, 1985. However, from the record, it does not appear that the plan and trust agreement were ever formally amended to reflect the adoption of the presumptive method. Effective November 25, 1987, the PBGC prohibited use of the hybrid method, and pursuant to 29 C.F.R. § 2642.14, the plan was deemed to have adopted the presumptive method. According to the Fund, written instruments amending the plan and trust agreement to adopt the direct attribution method were executed in 1989. (See Record, Joint Stipulation at ¶¶ 20, 23, 29-30; see also n. 6, supra).
[11]  The Stipulation of Settlement is a contract, the meaning of which is ordinarily discerned within its "four corners." To the extent that it is ambiguous, it is appropriate to consider evidence and circumstances surrounding its negotiation. See, e.g., Canterbury Belts Ltd. v. Lane Walker Rudkin, Ltd., 869 F.2d 34, 38 (2d Cir.1989); U.S. v. American Soc. of Composers, Authors and Publishers, 782 F.Supp. 778, 787-89 (S.D.N.Y.1991).
[12]  In addition, paragraphs three and four correspond to the provisions of the Stipulation requiring partial restitution to class members whose assessed withdrawal liability exceeded the liability that would have been assessed had the presumptive method been applied.
[13]  Fund counsel's advice rendered in January of 1989 is also consistent with the Court's interpretation. Counsel states:

The Cummings-Landau settlement does not preclude an amendment applicable to future withdrawals.... We do not believe the order bars a plan amendment made in accordance with a PBGC regulation issued nearly one year after the lawsuit was settled.
We have also been asked to comment on whether the Fund may revert to its former allocation method. Based upon the PBGC regulation, it does not appear possible to reinstate that method.... On December 29, 1986 the court approved a settlement which provided, inter alia, that the withdrawal liability allocated to employers withdrawing on or after January 1, 1986 would be calculated using the presumptive method only. Furthermore, the PBGC, in its regulation effective November 25, 1987, prohibited plans from using "higher-of-the-two" allocation method [sic] approved by the PBGC prior to that date. Under this rule, the Fund would now be unable to use the alternative allocation method approved by the PBGC in 1981 even if there was no Cummings-Landau order.
(Record, Empl.Ex.15). Thus, according to Fund counsel, both the final PBGC regulation and the Cummings-Landau Stipulation preclude re-adoption of the hybrid method.
[14]  Participants provide complete employment histories on their pension applications. By sampling 270 pension applications, the actuary confirmed that 3 of the 270 applicant participants, a statistically insignificant 1%, had service with more than one contributing employer. (See Record, Aff. of Albert Cardillo at ¶ 8, November 8, 1995).
[15]  Specifically, Fund records available in 1995 indicated that employee Williams Spears worked at Linden Motor Freight for thirteen years, from January 1975 to December 1988. All of his eighteen years of service shown in the Fund's records were attributed to the Employers, where he worked for two years, under the "last employer" assumption. In addition, employee Anna A. Stelmach was previously employed by New Era Manufacturing. The dates of her service there were not available in Fund records. According to the participant data used to compute the withdrawal liability, she is currently receiving checks from the Fund. (Pet'r Mem. of Law, Ex. E, Letter from Patricia McConnell to Jonathan A. Kenter dated August 10, 1995).
[16]  The arbitrator's award was reported as Casablanca Industries, Inc. and UFCW Local 23Giant Eagle Pension Fund, 7 EBC 2705 (Jaffe, Arb.1986).
[17]  Specifically, the statute refers to "benefits under the plan which are attributable to participants' service with such employer (determined under plan rules not inconsistent with regulations of the [PBGC])." 29 U.S.C. § 1391(c)(4)(B); see also p. 202, supra (full text).
[18]  The arbitration award confirmed in Artistic Carton is not reported.
[19]  The court did not decide the question presented of whether use of the "last employer" assumption transformed the fund's method for calculating withdrawal liability into an "alternative method" requiring PBGC approval or whether the assumption was just a rule elaborating the direct attribution method of 29 U.S.C. § 1391(c)(4)(B), which under the parenthetical expression takes effect unless the PBGC objects. The argument was not made before the arbitrator or the district court. See Artistic Carton, 971 F.2d at 1354.
