Plaintiffs brought this action pursuant to the Age Discrimination in Employment Act, 29 U.S.C. § 621, et seq. (ADEA). Plaintiffs alleged that their former employer, Lib-bey-Owens-Ford Company (LOF) discharged them because of their age. Following a trial in district court, the jury returned a verdict for the plaintiffs, and awarded damages to both plaintiffs. Defendants have appealed the judgment, asserting that the district court should have granted either their motion for summary judgment, or their motions for directed verdict. Defendants also assert that the district court erred in admitting the testimony of plaintiffs’ statistical expert. Plaintiffs have cross-appealed, claiming that the district court abused its discretion in decreasing their awards by the amount of retirement benefits received. Plaintiffs also assert that it was an error for the district, court to deny their post-trial motion for prejudgment interest.
Upon review of the record in this case, we find that the district court correctly denied LOF’s motions for summary judgment and directed verdict. We also find no merit in LOF’s assertion that the testimony of plaintiffs’ statistical expert should not have been admitted. Additionally, we find no abuse of discretion in the district court’s decision to decrease plaintiffs’ awards by the amount of retirement benefits received, and in the denial of prejudgment interest. Accordingly, we affirm the judgment of the district court.
I.
This court has before it a lengthy record following a six-day trial, and extensive briefs in which facts are still bitterly contested. We will briefly summarize the facts viewing contested facts in a light more favorable to the plaintiffs, since LOF is appealing the denial of a summary judgment motion and directed verdict motions for the defense.
Plaintiff John McMahon was hired by LOF in 1958. He was employed there continuously until January 29, 1982, when he was notified that his employment with LOF was being terminated, effective immediately. During his tenure with LOF, McMahon held several supervisory positions, with numerous titles, such as “Chief Analyst of the Clerical Work Measurement Department,” “Corporate Director of Office Services and Cost Reduction” and “Group Manager of Office Services and Records Retention.” Although his job titles changed, McMahon’s positions generally entailed responsibilities over telephone operations, the mail room, microfilm operations, switchboard operators, and word processing. When McMahon was discharged, he was fifty-nine years old. Most of his job duties were reassigned to Robert Sherman, age thirty-five, who was recently appointed to a newly created position entitled “Manager of Telecommunications Operations.”
Plaintiff Jack Anteau commenced work with LOF in 1941 while still in high school. He was employed at LOF continuously, except for a two-year period of service in the armed forces during World War II, until January 29, 1982, at which time he was also discharged from LOF. Anteau held several positions at LOF with titles such as “Assistant Office Services Manager” and “Office Services Analyst.” He had various responsibilities, but basically he helped supervise switchboard operators, mail room personnel, and the print shop. He also had responsibilities over furniture and equipment acquisitions. Anteau was fifty-seven years old when he was discharged. Following Anteau’s termination, many of his responsibilities were divided and assumed by the aforementioned Robert Sherman, William Thomas and Larry Wno-zowski, who were all under age forty.
*1076LOF agrees that both plaintiffs were long-term, competent employees. In contrast to plaintiffs’ claims that they were discharged because of their age, LOF asserts that plaintiffs were discharged because of corporate reorganization and budget cuts. LOF claimed at trial that the division’s decreased profitability and the threat of a hostile takeover necessitated the budget cuts and reorganization. LOF also asserts that Robert Sherman was given the position of “Manager of Telecommunications” because he was knowledgeable in data communications, a skill needed for the updating of the department in which both plaintiffs worked. LOF claimed at trial that because of the updating and reorganization, plaintiffs’ job responsibilities were mostly eliminated or greatly altered, and consequently their positions were no longer needed.
It appears from the record that LOF’s planning for corporate reorganization began in 1981. In June 1981, Howard Sel-land, age thirty-eight, became vice president of planning and administrative systems. Plaintiff McMahon reported directly to Mr. Selland, and plaintiff Anteau was another step down the hierarchial flow chart. Mr. Selland created a new tier of managerial functions between himself and plaintiff McMahon, and hired five directors in the early fall of 1981, at an annual salary cost of $250,000. Burton Jones, age thirty-one, the new director between Sel-land and plaintiff McMahon, proceeded to reorganize the department. At some point during the latter half of 1981, Selland and Jones were informed that they would need to cut their budget, and by January 1982, the decision was made to lay off a few employees, including both plaintiffs, which resulted in an approximate cost savings of $170,000.
Plaintiffs filed separate ADEA complaints post-termination, and the cases were subsequently consolidated for discovery and trial. After a six-day jury trial in April 1987, the jury returned a verdict in favor of McMahon for the sum of $180,000 and in favor of Anteau for the sum of $101,000. Attorney fees, costs, and interest were added to these awards. LOF filed a motion to amend or alter the judgments, asking the trial court judge to decrease the awards for various reasons, the only one relevant to this appeal being the request for a decrease due to retirement benefits received by the plaintiffs since termination. The district court granted this request, and decreased McMahon’s award by $32,641 and Anteau’s award by $21,830. Plaintiffs requested post-trial to be awarded prejudgment interest on the back pay awards, but the trial court judge denied the request. Defendant now appeals, and plaintiffs cross-appeal.
II.
LOF’s first issue on appeal is that the district court erred in denying LOF’s motions for summary judgment, and for a directed verdict at the close of plaintiffs’ evidence. LOF asserts that plaintiffs failed to present a prima facie case that they were discharged on the basis of age discrimination, and that therefore summary judgment or a directed verdict should have been granted. LOF’s second issue on appeal is that the district court erred in denying a directed verdict for the defense at the close of all the evidence. Here LOF claims that there was insufficient evidence upon which a jury could base a finding that LOF discriminated against plaintiffs because of their age. Because these two issues are so similar, we will discuss them together.
This court has addressed, on several occasions, the issue of the amount of evidence needed to establish a prima facie case of age discrimination. Rose v. National Cash Register Corp., 703 F.2d 225 (6th Cir.), cert. denied, 464 U.S. 939, 104 S.Ct. 352, 78 L.Ed.2d 317 (1983); Blackwell v. Sun Electric Corp., 696 F.2d 1176 (6th Cir.1983); Ackerman v. Diamond Shamrock Corp., 670 F.2d 66 (6th Cir.1982); Laugesen v. Anaconda Co., 510 F.2d 307 (6th Cir.1975). We have refused to adopt rigid guidelines for establishing a prima facie case, and instead have opted for a case-by-case approach. Here plaintiffs, both over forty years of age and therefore members of the protected class in age dis*1077crimination actions, provided evidence that they were discharged, that their performance evaluations were consistently above average, and that some if not all of their job responsibilities were given to employees under forty years of age. The plaintiffs also offered statistical data on employees terminated and those remaining in their department, and data concerning ages of all employees terminated from LOF during 1982. When considering a motion for directed verdict in an age discrimination case, we have held that
[ejvidence is sufficient to preclude granting a motion for directed verdict when, in reviewing the evidence in the light most favorable to the non-moving party, it would permit a reasonable jury to find in favor of that party.
Rose, 703 F.2d at 227, citing Coffy v. Multi County Narcotics Bureau, 600 F.2d 570, 579 (6th Cir.1979). Therefore, if a plaintiff presents evidence which would permit a reasonable jury to find that he was discharged because of his age, he has survived a defendant’s directed verdict motion.
However, LOF contends that plaintiffs failed to establish a prima facie case of age discrimination as set forth in La Grant v. Gulf & Western Mfg. Co., 748 F.2d 1087 (6th Cir.1984). In La Grant we only held that when there is a corporate reorganization or reduction in forces, the “mere termination of a competent employee when an employer is making cutbacks due to economic necessity is insufficient to establish a prima facie case of age discrimination.” La Grant, 748 F.2d at 1090. All La Grant required was that the plaintiff come forward with additional direct, circumstantial, or statistical evidence that age was a factor in his termination.
In the case before us plaintiffs have come forward with additional evidence and dispute LOF’s claim of reduction in forces due to economic necessity. Plaintiffs assert that these reasons are pretext, and they have come forward with evidence such as the cost savings of employees discharged compared to recent increases in salaried personnel, and that LOF’s corporate headquarters had a net reduction in personnel in 1982 of only eleven employees out of four hundred nineteen. Plaintiffs also offer evidence of LOF’s profits and continued dividend payments to stockholders, and evidence of raises given to employees in 1982, such as Mr. Selland, who was the vice president of the plaintiffs’ department which was allegedly in a state of economic crisis. Plaintiffs also offered as evidence the testimony of a statistical expert, who stated that based on his analysis of data relating to the ages of employees who were terminated, hired, or continued to work at LOF, he believed that age was a consideration in the termination and selection of personnel at LOF in 1982. Finally, plaintiffs dispute LOF’s claim that their jobs were eliminated, and instead offer evidence that job titles were changed, and that their responsibilities were divided and assumed by employees who were under forty years of age.
LOF also argues that they were entitled to a directed verdict because plaintiffs voluntarily retired, citing Ackerman v. Diamond Shamrock Corp., 670 F.2d 66 (6th Cir.1982). In Ackerman, the plaintiff, age fifty-nine, was offered an early retirement package which was more generous than he would have received had he been terminated. Ackerman considered the retirement offer for a month before signing it. He then brought an ADEA claim, which was dismissed on summary judgment on the basis that the plaintiff offered no evidence of age discrimination. Ackerman, 670 F.2d at 70. We do not believe that Ackerman is applicable to this case. Both plaintiffs McMahon and Anteau were terminated abruptly on January 29, 1982, and neither were offered any more retirement benefits than they would have received had they waited additional years to retire. Just because they were entitled to retirement benefits does not mean that they elected an early retirement package and therefore were not terminated. The evidence at trial clearly indicates that plaintiffs were involuntarily discharged and we therefore find no merit in LOF’s claim of entitlement to a directed verdict on this issue.
*1078We find that plaintiffs offered enough evidence to permit a reasonable jury to find that age was a determining factor in their discharge, thereby establishing a prima fa-cie case. The trial judge correctly denied LOF’s motions for summary judgment, and for a directed verdict at the close of plaintiffs’ evidence. The burden then shifted to LOF to produce a legitimate, nondiscriminatory reason for the decision to discharge plaintiffs. Fite v. First Tennessee Production Credit Ass’n, 861 F.2d 884 (6th Cir.1988); Blackwell, 696 F.2d at 1180. LOF offered the reasons of corporate reorganization and economic necessity. Plaintiffs countered with evidence of why these reasons were pretextual. The district court correctly denied LOF’s request for a directed verdict at the close of all the evidence because the plaintiffs presented enough evidence of pretext for a reasonable jury to find in favor of the plaintiffs.
III.
LOF also asserts on appeal that the district court erred in admitting the testimony of plaintiffs’ statistical expert, Dr. Kart. LOF made no objection at trial to Dr. Kart’s qualifications as an expert. LOF claims now that the testimony should not have been admitted because “the basis for the testimony was flawed.”
Our review of the admission of testimony by a trial court is limited to the abuse of discretion standard. The determination of whether evidence should be admitted based on considerations of relevance and materiality is vested in the broad discretion of the trial court. Consolidated Grain & Barge Co. v. Marcona Conveyor Corp., 716 F.2d 1077, 1083 (5th Cir.1983).
Dr. Kart testified as to his statistical analysis of various sets of age groups of terminated employees compared to all LOF employees grouped into various age groups. He also compared new hirees at LOF to terminated employees. Terminated employees included only those employees discharged or laid off; it did not include those who retired on left for other reasons. When comparing new hirees and employees transferred to LOF from other divisions with those terminated, Dr. Kart found statistically significant values leading him to conclude that age influenced LOF personnel decisions. LOF disagreed with Dr. Kart’s testimony, specifically his comparison of the ages of new hirees to terminated employees on the basis that the ages of those in the applicant pool would control the ages of the new hirees. LOF had full opportunity to impeach Dr. Kart on cross-examination, and did question him on his use of the applicant pool. LOF also presented their own statistical expert, Dr. Wiersma. The jury evidently chose to credit Dr. Kart’s testimony. Since this testimony was relevant and material to the issue of whether LOF discharged plaintiffs because of their age, we cannot say that it was an abuse of discretion for the trial judge to admit the testimony. Walker v. Pettit Constr. Co., 605 F.2d 128, 131-32 (4th Cir.1979).
IV.
The plaintiffs assert in their cross-appeal that the district court abused its discretion in granting LOF’s request to have the awards decreased by the amount of retirement benefits received. Plaintiff McMahon’s award was decreased by $32,641, the amount of benefits he received from discharge until the month of trial. Plaintiff Anteau’s award was decreased by $21,830, the amount he received from discharge until January 1986, the month testimony indicated he would have elected disability retirement.
The granting of a motion to amend a judgment under Fed.R.Civ.P. 59(e) is within the sound discretion of the trial court.1 McCarthy v. Manson, 714 F.2d 234, 237 (2d Cir.1983). Our standard of review entails whether the district court abused its discretion in granting LOF’s motion. Huff v. Metropolitan Life Ins. Co., *1079675 F.2d 119, 122, n. 5 (6th Cir.1982). At trial, plaintiffs offered the testimony of an economic expert, Dr. Leo Navin, who provided detailed loss calculations. Plaintiffs argued to the jury that these amounts, less $15,000 each for severance pay received, should be awarded as back pay damages. The jury then awarded these requested amounts rounded to the nearest thousand. Since Dr. Navin stated that he had not subtracted retirement benefits from his back pay calculations, the district court judge found that he could clearly delineate the composition of the jury awards, and concluded that plaintiffs were not entitled to a back pay award which included a retirement benefit they would not have received had they remained employed.
The purpose of a back pay award is “to restore the employee to the status quo he would have enjoyed if the discriminatory discharge had not taken place.” McCann Steel Co. v. NLRB, 570 F.2d 652, 656 (6th Cir.1978) (citations omitted). In other words, “back pay must be limited to actual damages and proved with reasonable certainty.” Blackwell, 696 F.2d at 1192, citing EEOC v. Detroit Edison Co., 515 F.2d 301, 314-16 (6th Cir.1975). Here the district court judge deducted retirement benefits from the back pay awards. Plaintiffs argue that this was an abuse of discretion because the testimony of Dr. Navin explained to the jury why the retirement benefits should not be subtracted from back pay. However, Dr. Navin’s reasoning appears quite speculative. See Hagelthorn v. Kennecott Corp., 710 F.2d 76, 86-87 (2d Cir.1983). We find no abuse of discretion in the district judge’s decision that the jury’s failure to deduct these amounts lacked both legal and factual justification.
V.
Plaintiffs also assert in their cross-appeal that the district court abused its discretion in denying their motion for prejudgment interest. In an ADEA case, prejudgment interest can be awarded. The district court is empowered “to grant such legal or equitable relief as may be appropriate to effectuate the purposes of this chapter_” 29 U.S.C. § 626(b). Prejudgment interest is designed to compensate a plaintiff for loss of the use of his wages wrongfully withheld through a discriminatory discharge. Reichman v. Bonsignore, Brignati & Mazzota, P.C., 818 F.2d 278, 281 (2d Cir.1987). However, whether to award prejudgment interest is within the discretion of the district court judge. Heiar v. Crawford County, 746 F.2d 1190, 1201 (7th Cir.1984), cert. denied, 472 U.S. 1027, 105 S.Ct. 3500, 87 L.Ed.2d 631 (1985). We are unable to conclude that the district judge abused his discretion in holding that the awards compensated plaintiffs in a manner appropriate to effectuate the purposes of the Act. Therefore we affirm the denial of prejudgment interest.
Based on the foregoing reasons, we AFFIRM the judgment of the district court.
. Rule 59(e) provides:
A motion to alter or amend the judgment shall be served not later than 10 days after entry of the judgment.