SAMUEL H. MAYS, JR., District Judge.
Plaintiffs James Szoke and eighteen fellow employees1 appeal the judgment of the district court granting summary judgment to Defendant United Parcel Service of America, Inc. (“UPS America”) on their claims under the Employee Retirement Income Security Act of 1974 (“ERISA”), 29 U.S.C. § 1132(a)(1)(B) and the Age Discrimination in Employment Act (“ADEA”), 29 U.S.C. §§ 621 et seq. Appellants argue that the district court erred by 1) finding that ERISA did not bar UPS America from switching Appellants from one pension plan to another, 2) refusing to allow Appellants to amend their Amended Complaint to add United Parcel Service, Inc. (“UPS Ohio”) as a defendant, and 3) granting summary judgment to UPS America on their ADEA claim. For the following reasons, we AFFIRM the judgment of the district court.
I.
Appellants all work or worked as delivery center clerks for UPS Ohio and began working for the company between 1959 and 1989. (Amended Compl., Dkt. No. 14, ¶¶ 12-31.) Since 1974, the International Brotherhood of the Teamsters, Local 407 has represented all of UPS Ohio’s clerical employees. (Compl., Dkt. No. 1, ¶ 2.) A series of collective bargaining agreements has governed Appellants’ terms of employment with UPS Ohio, including their pension benefits. Because Appellants are Ohio-based employees, both the Teamsters’ national agreement with UPS Ohio and a local agreement, known as the “Ohio Rider,” govern Appellants’ pension benefits. (See, e.g., Administrative Record at 26.) (“Admin.Rec.”) All UPS Ohio clerks began to participate in the UPS Retirement Plan in 1976. (Admin. Rec. at 147-263.) The Retirement Plan guaranteed that Appellants would receive a set monthly pension based on their number of years with UPS Ohio. It also capped Appellants’ maximum monthly benefits. The Teamsters and UPS Ohio negotiated the maximum pension amount and raised the cap periodically. (See Admin. Rec. at 24 (noting that the cap increased from $1,000 per month to $1,100 per month under the agreement for the period beginning August 1,1993).)
On September 1, 1995, Appellants ceased accruing additional benefits under the Retirement Plan and transferred to the UPS Pension Plan. (Admin. Rec. at 53.) That transfer occurred in the middle of the period covered by the collective bargaining agreements for August 1, 1993 [148]*148to July 31, 1997. (Id. at 24.) Although no document dated September 1, 1995, reflects that the parties agreed to a transfer from the Retirement Plan to the Pension Plan, on October 13, 1995, all UPS Ohio clerks were invited to attend a presentation that would explain their new benefits. (Id. at 299-317.) The presentation highlighted what UPS Ohio viewed as improvements to Appellants’ benefits. Specifically, the maximum monthly pension benefit increased from $1,100 to $1,500 under the Pension Plan. (Id. at 309.) The presentation also noted that “your bargaining representatives and numerous Teamster employees have made it known that they wanted to see UPS play a bigger role in helping you provide for your retirement.” (Id. at 300.) To accommodate this request by union representatives and employees for better benefits, UPS Ohio agreed “to allow Ohio Teamsters to participate in the UPS Pension Plan instead of the UPS Retirement Plan.” (Id.)
On December 21, 1995, the board of directors of UPS America, a subsidiary of UPS Ohio that serves as the plan sponsor for both the Retirement and Pension Plans, formally adopted an amendment reflecting the transfer to the Pension Plan. (Id. at 145.) The resolution noted that the effective date for the change was September 1, 1995, and that UPS America acted “to allow full-time employees represented for purposes of collective bargaining by the International Brotherhood of the Teamsters — Ohio Rider to participate in the [Pension] Plan.” (Id.) The Teamsters signed an agreement with UPS Ohio on January 19, 1996, recognizing that “[e]mployees will remain in a United Parcel Service Health and Welfare and Pension Plan unless dictated otherwise by contract language (including the Ohio Rider).” (Id. at 28A.)2 The collective bargaining agreement for the period from August 1,1997 to July 31, 2002, specifically referred to the “UPS Pension Plan” and noted that the parties, through negotiation, had agreed to raise the maximum monthly pension benefit to $1,750 from its previous cap of $1,500. (Id. at 33.) Employees also received individual notice of these enhanced benefits under the Pension Plan. (See id. at 44 (letter to Plaintiff Cecelia Miller).)
Beginning in 1998, some of the Ohio clerks became unhappy with their pension benefits. (See id. at 48.) The union acknowledged that it had “over-looked” the clerks in prior contract negotiations, but urged them to “stay mad until the next contract is negotiated.” (Id. at 47-48.) When the time approached to negotiate the collective bargaining agreement and Ohio Rider for August 1, 2002 to July 31, 2007, the UPS Ohio clerks wrote their union representatives and urged them to negotiate a better pension benefit that would not be reduced based on the employees’ receipt of Social Security benefits. (Id. at 48-51.) Unsatisfied with the results of the negotiations and convinced that they would have received a larger benefit had they remained in the UPS Retirement Plan, Appellants filed suit against UPS America in the United States District Court for the Northern District of Ohio. Appellants alleged that UPS America had violated ERISA by switching their pension benefits without their knowledge or their union’s consent. (Amended Compl. ¶¶ 39-44.) Appellants asked the district court to declare that they were never lawfully enrolled in the UPS Pension Plan and to calculate their benefits under the Retirement Plan. (Id. ¶¶ 49-50.) Appellants also alleged that the effect of the change in plan was to discriminate against [149]*149older employees, in violation of the ADEA.3 (Id. ¶¶ 53-59.)
The district court decided that only one of the Appellants, Cecelia Miller, had retired from UPS Ohio and consequently was due benefits currently. The parties agreed that the benefit calculation for Miller “would be representative of all retirees, present or future.” Szoke v. UPS of Am., Inc., No. L03CV1628, 2006 WL 2792161, at *1, 2006 U.S. Dist. LEXIS 69325, at *4 (N.D.Ohio Sept. 26, 2006). The district court, therefore, had the parties submit Miller’s claim for additional benefits to the plan administrator so that she could exhaust her administrative remedies. The administrator rejected her claim that it should determine her benefits under the Retirement Plan and denied her subsequent administrative appeal of that decision. (Admin. Rec. at 1-3, 53-55.) After the conclusion of the administrative review process, the district court affirmed the administrator’s determination, finding that its benefit calculation was not arbitrary or capricious. Szoke, 2006 WL 2792161, at *6-7, 2006 U.S. Dist. LEXIS 69325, at *17-20. The district court later granted summary judgment to UPS America on the remaining Appellants’ ERISA claims because the same analysis applied to the other eighteen Appellants. (Order, Dkt. No. 94, at 9.) The district court also granted summary judgment to UPS America on Appellants’ ADEA claims because UPS America was not Appellants’ employer and no identity of interest existed between UPS America and the actual employer, UPS Ohio. (Id. at 18-22.) Finally, the district court rejected Appellants’ effort to amend their Amended Complaint to state a claim against UPS Ohio. It found that Appellants had unduly delayed; the amendment would cause substantial prejudice to the Defendant; and Appellants had failed to cure their Amended Complaint’s deficiency although Appellants had known for years that UPS America was not their employer. (Id. at 22-25.) Appellants timely appealed. (Notice of Appeal, Dkt. No. 96.)
II.
A.
Appellants initially argue that the district court erred in finding that the plan administrator’s benefit determination was not arbitrary and capricious. Appellants make three primary arguments. First, they argue that the district court improperly limited its review to the administrative record considered by the plan administrator. Appellants argue that it was inappropriate for the district court to limit its consideration to the administrative record for the claims of employees other than Miller. (Appellants’ Br. at 26-30.) Appellants next assert that a separate section of the collective bargaining agreement — not contained within the administrative record — forbids the change in pension plans that occurred. (Id. at 27-28.) Finally, Appellants assert that the record does not support the administrator’s decision and that the administrator “cherry-picked” the record for evidence that would support the denial of benefits. (Id. at 26-27, 30-31.)
We review a district court’s grant of summary judgment de novo. Wilkins v. Baptist Healthcare Sys., Inc., 150 F.3d 609, 613 (6th Cir.1998). We also review a plan administrator’s denial of benefits de novo. Moon v. Unum Provident Carp., 405 F.3d 373, 378 (6th Cir.2005). Howev[150]*150er, where a plan “vests the administrator with complete discretion in making eligibility determinations, such determinations will stand unless they are arbitrary and capricious.” Id. (citation omitted). “[W]hen it is possible to offer a reasoned explanation, based on the evidence, for a particular outcome, that outcome is not arbitrary and capricious.” Williams v. Int’l Paper Co., 227 F.3d 706, 712 (6th Cir.2000) (internal quotation marks and citation omitted). The parties do not dispute that the plan administrator had complete discretion. (See Appellants’ Br. at 25; Appellee’s Br. at 22.)
1.
A federal court’s review of a plan administrator’s benefit determination is limited to the record as it existed on the date the administrator made its decision. Moon, 405 F.3d at 378-79. Neither the text nor “the legislative history [of ERISA] suggests that Congress intended that federal district courts would function as substitute plan administrators, a role they would inevitably assume if they received and considered evidence not presented to administrators concerning an employee’s entitlement to benefits.” Perry v. Simplicity Eng’g, 900 F.2d 963, 966 (6th Cir.1990). The district court, therefore, properly limited its review to the administrative record considered by the plan administrator. We shall do the same and consequently will not consider the additional evidence outside the administrative record on which Appellants seek to rely.4 Further, because Miller’s benefit claim was representative of the potential claims of all Appellants, the district court properly restricted its review to the administrative record when considering the remaining eighteen Appellants’ claims. See Szoke, 2006 WL 2792161, at *1-2, 2006 U.S. Dist. LEXIS 69325, at *4.
2.
Appellants argue that the administrative record does not support the plan [151]*151administrator’s determination that Appellants’ benefits should be calculated under the UPS Pension Plan. (Appellants’ Br. at 80-31.) Appellants are correct that there is no signed document dated September 1, 1995, reflecting the switch from the Retirement Plan to the Pension Plan. However, the record as a whole supports the administrator’s determination that the initial calculation of Appellants’ benefits under the Pension Plan was correct.
The presentation made to clerical employees on October 13, 1995, supports the administrator’s decision. It reflects that the switch from the Retirement Plan occurred on September 1, 1995, and notes that the switch happened because Teamster “representatives and numerous Teamster employees have made it known that they wanted to see UPS play a bigger role in helping [employees] provide for [their] retirement.” (Admin. Rec. at 300, 304.) This slide presentation took place less than sixty days after the effective date of the switch. Similarly, the resolution enacted by UPS America’s board of directors making the change official states that the change occurred to benefit “full-time employees represented for purposes of collective bargaining by the International Brotherhood of Teamsters — Ohio Rider.” (Id. at 145.) Appellants received notification of the change along with updates about their current eligibility for benefits. (Id. at 44 (letter to Cecelia Miller).)
The record further reflects that Appellants were aware of the change to the Pension Plan well before filing suit in 2004. In April and May 2001, Appellants complained of being “over-looked” in prior pension negotiations and asked their union to improve their benefits in future contract negotiations. (Id. at 47-48.) Appellant
Szoke wrote and signed a letter on behalf of all clerical employees from Local 407 and noted specifically that they were currently “under the UPS Pension Plan.” (Id. at 48.) Szoke attached three sheets containing the signatures of the other Local 407 clerical employees, including all named Appellants. (Id. at 49-51.) Notably, the letter did not complain that the 1995 change to the Pension Plan occurred without notice or without collective bargaining by the union. (Id. at 48.) Appellants complained instead that the union had failed to negotiate the best possible agreement on their behalf. (Id.)
The September 15, 1997, Letter of Understanding, made a part of the collective bargaining agreements for the period from 1997 to 2002, also supports the administrator’s decision. The letter required that the maximum monthly benefit under the “Pension Plan” increase from $1,500 to $1,750. (Id. at 33.) The maximum benefit had risen to $1,500 after the switch to the Pension Plan. (See id. at 316.) Under the prior Retirement Plan and the original language of the collective bargaining agreements for the period from 1993-1997, the maximum benefit was $1,100. (Id. at 24.) The Teamsters’ acknowledgment of the $1,500 cap and the negotiated agreement with UPS Ohio to raise that cap to $1,750 shows at a minimum that the Teamsters, through collective bargaining, ratified the pension changes.5
Appellants also assert that the plan administrator “cherry-picked” the record to support its initial decision to deny additional benefits. (Appellants’ Br. at 26-27); see Metro. Life Ins. Co. v. Conger, 474 F.3d 258, 266 (6th Cir.2007) (finding a plan administrator’s decision arbitrary and ca[152]*152pricious where it cherry-picked the record for evidence to support its denial of benefits). The record does not support this assertion. Between August 30, 2004, and June 2, 2005, the plan administrator sent four letters to Appellants’ counsel asking him to supplement the administrative record with evidence supporting his contentions. (Admin. Rec. at 79-97.) The final letter warned Appellants’ counsel that, if he did not provide further documentation, “the Committee will have no option other than to consider your failure to respond in making its determination.” (Id. at 97.) Appellants’ counsel failed to provide the requested documentation supporting the request for additional benefits. (See id. at 53 (plan administrator’s decision denying appeal).)
Because the administrative record supports the administrator’s determination that Appellants are to receive benefits under the Pension Plan and that their union bargained for those benefits in contract negotiations, we affirm the judgment of the district court finding that the plan administrator’s benefits determination was not arbitrary or capricious.
B.
Appellants make two arguments to support their assertion that the district court erred in granting summary judgment in favor of UPS America on their ADEA claims. First, they argue that the district court abused its discretion when it denied them leave to amend their Amended Complaint to reflect that their claim should lie against their employer, UPS Ohio, rather than plan sponsor, UPS America. They argue that, at a minimum, the district court should have allowed additional time for discovery so that they could review UPS’ corporate structure and determine who their actual employer was. (Appellants’ Br. at 31-35.) Alternatively, Appellants argue that UPS America and UPS Ohio share an identity of interest that would allow Appellants to pursue their claims against UPS America without formally naming it in the EEOC charge. (Reply Br. at 14-23.)
We review a district court’s decision denying a motion to amend for abuse of discretion. Wade v. Knoxville Utils. Bd., 259 F.3d 452, 459 (6th Cir.2001). A district court abuses its discretion when it fails to give a reason for denying the motion, applies an incorrect legal standard, misapplies the correct legal standard, or relies on clearly erroneous findings of fact. Riverview Health Inst., LLC v. Medical Mut. of Ohio, 601 F.3d 505, 512 (6th Cir. 2010); Schenck v. City of Hudson, 114 F.3d 590, 593 (6th Cir.1997). We review a district court’s grant of summary judgment de novo. Wilkins, 150 F.3d at 613.
Appellants filed an Amended Complaint on October 27, 2003. (See Dkt. No. 14.) The Amended Complaint named UPS America as the Defendant and alleged that it “was the employer of all Plaintiffs during the relevant period of time.” (Amended Compl. ¶ 32.) UPS America filed its Answer on January 30, 2004. (See Dkt. No. 42.) It specifically denied that it was Appellants’ employer. (Answer ¶ 32.) It also “affirmatively state[d]” that all Appellants are or were “employee[s] of United Parcel Service, Inc., an Ohio corporation.” (See, e.g., id. ¶ 13.) It repeated that information nineteen times, once for each Appellant. (Id. ¶¶ 13-31.) Appellants did not file their Motion to Amend until February 22, 2007, after the district court had granted summary judgment on Appellant Miller’s ERISA claims and while motions for summary judgment were pending on all remaining claims of the Amended Complaint. (See Dkt. No. 84.)
[153]*153When considering whether to grant a motion to amend under Federal Rule of Civil Procedure 15(a), district courts must consider a number of factors, among them “[u]ndue delay in filing, lack of notice to the opposing party, bad faith by the moving party, repeated failure to cure deficiencies by previous amendments, undue prejudice to the opposing party, and futility of amendment.” Wade, 259 F.3d at 458 (citing Head v. Jellico Housing Autk, 870 F.2d 1117,1123 (6th Cir.1989)). “Delay by itself is not sufficient reason to deny a motion to amend.” Id. (citation omitted). Notice and substantial prejudice are two of the “critical factors.” Id. at 458-59 (citation omitted). When a party seeks to amend its complaint at a late stage of the litigation, “there is an increased burden to show justification for failing to move earlier.” Id. at 459 (citing Duggins v. Steak ‘N Shake, Inc., 195 F.3d 828, 834 (6th Cir. 1999)).
Appellants waited more than three years after UPS America first filed its Answer denying that it was Appellants’ employer before filing their Motion to Amend. Contrary to their assertions, Appellants did not need discovery to determine who their employer was. The Answer stated that UPS Ohio was Appellants’ employer. (Answer ¶¶ 13-31.) Appellants were on notice that they might have named the wrong defendant even before UPS America filed its Answer. In their January 29, 2004, Response to UPS America’s Motion to Dismiss, Appellants explained that there was a “variance” between the name on the EEOC charge and the party named as a defendant in the lawsuit. (Dkt. No. 39, at 7.) Appellants then explained it was their intention to argue that there was an identity of interest between UPS Ohio and UPS America. (Id. at 7-8.) Appellants failed to act with diligence in seeking to amend their Amended Complaint. See United States v. Midwest Suspension & Brake, 49 F.3d 1197, 1202 (6th Cir.1995) (“[A] party must act with due diligence if it intends to take advantage of [Rule 15(a)’s] liberality.” (citation omitted)).
By seeking permission to amend their Amended Complaint, add a new defendant, and change their legal argument at such a late stage of the litigation, Appellants deprived either UPS entity of notice of the claims against which it would need to defend. We have held that a defendant suffers substantial prejudice when a plaintiff waits until after the filing of a summary judgment motion to file a motion to amend. Coming v. Nat’l Union Fire Ins. Co., 257 F.3d 484, 496-97 (6th Cir.2001) (motion to amend denied where it “suddenly appeared]” after defendant had moved for summary judgment); see also Wade, 259 F.3d at 459. Here, not only was a summary judgment motion pending, but the district court already had granted a prior motion for partial summary judgment. Because Appellants’ three-year delay in seeking to amend their Amended Complaint was unjustified, deprived the Defendant and UPS Ohio of notice, and prejudiced the Defendant and UPS Ohio, we hold that the district court did not abuse its discretion in denying Appellants’ Motion to Amend.
Appellants’ second argument is that there is an identity of interest between the party named in their EEOC charge, UPS Ohio, and the party they have actually sued, UPS America. (Reply Br. at 14-23.) A party may only sue an entity for violating civil rights statutes such as Title VII or the ADEA if it named the same entity in its prior EEOC charge. See Knafel v. Pepsi-Cola Bottlers of Akron, Inc., 899 F.2d 1473, 1480-81 (6th Cir.1990). There is a limited exception to this general rule when the unnamed party in the EEOC [154]*154charge has a “clear identity of interest” with the party actually sued. Id. at 1481 (citation and internal quotation marks omitted). We have adopted two separate tests to determine when an identity of interest exists. See Alexander v. Local 496, Laborers’ Int’l Union, 177 F.Sd 394, 411-412 (6th Cir.1999). Under either test, the named and unnamed parties must be “virtual alter egos.” Knafel, 899 F.2d at 1481. Merely showing that they are parent and subsidiary is not sufficient. See id.
The first test, known as the Seventh Circuit test, requires that a party demonstrate that “the unnamed party possessed] sufficient notice of the claim to participate in voluntary conciliation proceedings” before the EEOC. Alexander, 177 F.3d at 411; see also Eggleston v. Chicago Journeyman Plumbers’ Local Union No. 130, 657 F.2d 890, 905 (7th Cir.1981). We have required that the unnamed party have actual notice of the claim. See, e.g., Alexander, 177 F.3d at 412 (finding the test satisfied when a local union official against whom plaintiff filed discrimination charges informed the national union and forwarded copies of the charges); Jackson v. Fed. Express Corp., No. 04-2470 Ma/A, 2006 WL 181964, at *3-4, 2006 U.S. Dist. LEXIS 5060, at *8-9 (W.D.Tenn. Jan. 18, 2006) (EEOC directly contacted unnamed party, and it responded as though charge filed against it). Although Appellants note that UPS America received all details of the charge when they filed suit in federal court, (see Reply Br. at 19-20), the purpose of the Seventh Circuit test is to allow claims to proceed only against those unnamed parties who had an opportunity to attempt voluntary conciliation before the EEOC. Alexander, 177 F.3d at 411; see also Eggleston, 657 F.2d at 905 (the unnamed party must have had the opportunity to settle the charge in voluntary conciliation); Weatherspoon v. N. Oakland Gen. Hosp., No. 04-40184, 2006 WL 126615, at *3, 2006 U.S. Dist. LEXIS 2803, at *8 (E.D.Mich. Jan. 17, 2006) (“Mere notice of the EEOC investigation ... is insufficient to satisfy the test.”). UPS America did not have an opportunity to settle the claim voluntarily. Therefore, we find that Appellants have not satisfied the Seventh Circuit test.
The second test we have adopted for determining whether an identity of interest exists is known as the Third Circuit test. Alexander, 177 F.3d at 411; Glus v. G.C. Murphy Co., 562 F.2d 880, 888 (3d Cir.1977). The four factors to consider under that test are:
(1) Whether the role of the unnamed party could through reasonable effort by the complainant be ascertained at the time of the filing of the EEOC complaint;
(2) Whether, under the circumstances, the interests of a named [party] are so similar as the unnamed party’s that for the purpose of obtaining voluntary conciliation and compliance it would be unnecessary to include the unnamed party in the EEOC proceedings;
(3) Whether its absence from the EEOC proceedings resulted in actual prejudice to the interests of the unnamed party;
(4) Whether the unnamed party has in some way represented to the complainant that its relationship with the complainant is to be through the named party.
Romain v. Kurek, 836 F.2d 241, 246 (6th Cir.1987) (citation omitted). These factors consider the relationship between the named and unnamed party when Appellants filed their initial EEOC charge. Alexander, 177 F.3d at 411.
At the time Appellants filed their initial EEOC charge against UPS Ohio, they could easily have determined that UPS [155]*155America was their plan sponsor. The Retirement Plan summary, given to all eligible UPS employees, clearly states “The Plan is sponsored by United Parcel Service of America, Inc.,” and is followed by UPS America’s mailing address. (Admin. Rec. at 278.) Because reasonable efforts would have led Appellants to discover UPS America’s potential role in their age discrimination claim, the first factor weighs against Appellants.
UPS Ohio and UPS America would have different interests in voluntary conciliation proceedings. UPS America has no employees, serves solely as the Retirement and Pension Plans’ sponsor, and did not participate in negotiations with the national Teamsters or Appellants’ Local 407. UPS Ohio and UPS America are also legally separate entities, and the existence of a parent-subsidiary relationship is not enough to satisfy the identity of interest test. See Knafel, 899 F.2d at 1481. Because UPS America did not have the opportunity to participate in conciliation and did not have actual notice of the charge against UPS Ohio, it suffered prejudice. Cf. Alexander, 177 F.3d at 412 (holding that, when the national union did have actual notice of the pending EEOC charge and therefore could have participated in any conciliation proceedings, the third factor supports finding that an identity of interest exists); Weatherspoon, 2006 WL 126615, at *3-4, 2006 U.S. Dist. LEXIS 2803, at *10 (separate institutions with separate interests require separate notice). Therefore, the second and third factors also weigh against finding that there is an identity of interest between UPS Ohio and the unnamed party in the charge, UPS America.
UPS America did not hide its role in administering the Retirement and Pension Plans or suggest that UPS Ohio was actually the party administering the plans. As noted above, the plan documents, including the summary provided to Appellants, unambiguously stated that UPS America was the plan sponsor. (Admin. Rec. at 278.). All four factors of the Third Circuit test weigh against finding that there is an identity of interest. Because neither test adopted by this circuit favors finding that the unnamed party in the EEOC charge, UPS America, shares an identity of interest with UPS Ohio, we affirm the district court’s grant of summary judgment to UPS America on Appellants’ ADEA claims.
III.
For the foregoing reasons, we AFFIRM the judgment of the district court in its entirety and hold that 1) the plan administrator’s decision denying Appellants additional benefits was not arbitrary and capricious; 2) the district court did not abuse its discretion in denying Appellants’ motion to amend; and 3) there is no identity of interest between UPS America and UPS Ohio.