
549 F.3d 666 (2008)
Ronald L. MADDEN, Plaintiff-Appellee,
v.
CHATTANOOGA CITY WIDE SERVICE DEPARTMENT, Defendant-Appellant.
No. 08-5082.
United States Court of Appeals, Sixth Circuit.
Argued: October 21, 2008.
Decided and Filed: November 25, 2008.
*669 ARGUED: Kenneth O. Fritz, Nelson, McMahan & Noblett, Chattanooga, Tennessee, for Appellant. Randall D. Larramore, Paty, Rymer & Ulin, Chattanooga, Tennessee, for Appellee. ON BRIEF: Kenneth O. Fritz, Michael A. McMahan, Nelson, McMahan & Noblett, Chattanooga, Tennessee, for Appellant. Randall D. Larramore, Paty, Rymer & Ulin, Chattanooga, Tennessee, for Appellee.
Before: MOORE, GRIFFIN, and BRIGHT, Circuit Judges.[*]

OPINION
KAREN NELSON MOORE, Circuit Judge.
Defendant-Appellant Chattanooga City Wide Service Department ("CWS") appeals the district court's entry of judgment following a bench trial awarding Plaintiff-Appellee Ronald L. Madden ("Madden") back pay, front pay, and compensatory damages on his claim that CWS terminated his employment in violation of Title VII of the Civil Rights Act of 1964 ("Title VII"), 42 U.S.C. § 2000e-2, and the Tennessee Human Rights Act ("THRA"), TENN.CODE ANN. § 4-21-101 et seq. Madden, who is African-American, worked as a crew worker for CWS until he was fired following an incident on March 22, 2006, in which he set off firecrackers at a work site and was reported by his white supervisor to senior managers. White employees had set off firecrackers or similar devices in the presence of supervisors without facing discipline. On appeal, CWS argues that (1) the district court erred in finding that CWS intentionally discriminated against Madden, (2) the district court erred in failing to toll the award of back pay because Madden refused an offer of reinstatement, and (3) the district court erred by awarding excessive front pay. Because the district court did not clearly err in finding intentional discrimination and did not abuse its discretion in awarding damages, we AFFIRM the district court's judgment for Madden.

I. BACKGROUND
Madden began working as a crew worker for the Street Maintenance Section of CWS on November 25, 2003. On March 20, 2006, Madden was reassigned from his previous duties to a crew supervised by Keith Templin ("Templin"), who had worked as a crew supervisor for around five years.
Two days later, on March 22, 2006, the crew to which Madden was newly assigned was dispatched to clean a ditch in a rural area in Chattanooga, Tennessee. Upon arrival, the crew parked its trucks and crew cabs in a cul-de-sac off of the main road. While the other workers stayed near the trucks off the main road, Templin and an equipment operator walked a couple hundred feet down a smaller side road, where the ditch was located, to survey the site before moving the trucks into place. As he began walking down the road, Templin heard a single pop back near the trucks. Believing this was a backfire, Templin went back to talking with his operator. Templin then heard a series of pops, which sounded like firecrackers, so *670 he yelled back toward the trucks to "cut it out" if any of his crew members were responsible. After then hearing another series of pops, Templin started walking back to the trucks and yelled back for the person setting off fireworks to meet him halfway. Madden admitted to Templin that he set off the firecrackers.[1]
After the incident, Templin called his supervisor and told him that he "had instructed him to quit throwing the firecrackers and they persisted and that I was sending him in for him to deal with." J.A. at 172 (Trial Tr. at 102). Templin then called a truck driver to pick Madden up from the work site and return him to CWS. J.A. at 172-73 (Trial Tr. at 102-03).
Templin's report of Madden prompted an immediate investigation of the incident by senior managers at CWSTony Boyd ("Boyd"), CWS's construction manager, and James Templeton ("Templeton"), Director of CWS. Boyd, who received the call from Templin, instructed Templin to send Madden back to CWS for an investigation. J.A. at 174 (Trial Tr. at 104). According to Boyd, when Madden was asked why he set off the firecrackers, Madden responded that he was just joking and did not mention the presence of a dog at the work site. J.A. at 175 (Trial Tr. at 105). Both Boyd and Templeton testified at trial that no other incidents involving employee use of firecrackers had been brought to their attention. J.A. at 175 (Trial Tr. at 105); J.A. at 179 (Trial Tr. at 109). Following the investigation, Templeton made a recommendation that Madden's employment be terminated. J.A. at 179 (Trial Tr. at 109). At trial, Templeton explained that he considered it a safety issue, given the "close proximity of other employees" and "people coming out from their residences, concerned about what was going on." Id.
Templeton forwarded his recommendation that Madden be terminated to Steven C. Leach ("Leach"), Administrator of Public Works for the City of Chattanooga. Based on information about the incident provided by Templeton, Leach followed the recommendation and decided to terminate Madden's employment. At trial, Leach testified that his decision was based on concerns for the safety of other employees and the fact that the incident occurred in a public place. Like Boyd and Templeton, Leach testified that no other incidents involving employee use of firecrackers had ever been brought to his attention. J.A. at 157 (Trial Tr. at 87). Upon questioning by the court, Leach further testified that he had never been made aware of the specific incidents of firecracker use by employees described at trial by Madden's witnesses. J.A. at 160-63 (Trial Tr. at 90-93). On March 23, 2006, Leach informed Madden that his employment was terminated effective March 27, 2006, because of the firecracker incident. Mot. to Supplement (Ex. A at 1; Trial Tr. at 24); J.A. at 104 (Trial Tr. at 25).
Madden's termination was affirmed by the Chattanooga City Council following an administrative appeal by Madden. J.A. at *671 156 (Trial Tr. at 86). At the time he was fired, Madden earned an annual salary of $21,106 at an hourly rate of around $10 per hour. Mot. to Supplement (Ex. A at 1; Trial Tr. at 24). Madden then filed complaints with the Equal Employment Opportunity Commission ("EEOC") on February 15, 2006, and June 7, 2006, and with the Tennessee Human Rights Commission ("THRC"). Madden was issued an EEOC right to sue letter on February 13, 2007.
On October 4, 2006, Madden, proceeding pro se, filed the present suit against CWS, various city employees, and an EEOC investigator. Madden alleged three violations of Title VII:(1) wrongful termination based on his race, (2) racial harassment creating a hostile work environment, and (3) retaliation for his participating in an investigation under Title VII. J.A. at 16-26 (Complaint); J.A. at 73 (Summ. J. Mem. Op. at 5). Madden also brought claims under 42 U.S.C. §§ 1981, 1983, state-law claims under the THRA, and claims under the United States and Tennessee Constitutions. J.A. at 80-81 (Summ. J. Mem. Op. at 12-13). The district court dismissed all of Madden's claims except those against CWS. J.A. at 72 (Summ. J. Mem. Op. at 4).
On August 14, 2007, CWS moved for summary judgment on all of Madden's claims. J.A. at 67 (Mot. for Summ. J.). On October 22, 2007, the district court granted summary judgment on Madden's Title VII hostile-work-environment and retaliation claims, but denied summary judgment as to the wrongful-termination claim. J.A. at 73-80 (Summ. J. Mem. Op. at 5-12). Applying the burden-shifting framework of McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973), as modified by Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 252-53, 101 S.Ct. 1089, 67 L.Ed.2d 207 (1981), the district court found that Madden had established a prima facie case of discrimination, that CWS had put forth a legitimate nondiscriminatory reason for Madden's discharge, and that Madden had then provided sufficient evidence of pretext. J.A. at 73-78 (Summ. J. Mem. Op. at 5-10). Concluding that Madden's § 1981 and THRA claims would be analyzed under the same framework as his Title VII claims, the district court similarly granted summary judgment with respect to those hostile-work-environment and retaliation claims but denied summary judgment with respect to wrongful-termination claims under these statutes. J.A. at 80-81 (Summ. J. Mem. Op. at 12-13). Finally, the district court granted summary judgment as to Madden's constitutional claims because they failed to state cognizable claims. J.A. at 81 (Summ. J. Mem. Op. at 13).
The district court held a bench trial on November 13, 2007, and December 17, 2007, on Madden's wrongful-termination claims under Title VII and the THRA. J.A. at 51 (Mem. & Order at 1). Proceeding pro se at trial, Madden introduced evidence of at least two specific incidents in which white employees set off firecrackers or similar devices without facing discipline. Madden also introduced evidence that such firecracker use was common among CWS workers. This evidence was established through the testimony of William Brown ("Brown"), a former employee of CWS who left for a better job, Christopher Dossett ("Dossett"), an employee of CWS for nearly sixteen years, and Alonzo Lewis ("Lewis"), an employee of CWS for nearly four years.
The first incident occurred on the week of July 4, 2005, during work hours. It took place in an area called the "smoke hole," an outdoor smoking area adjacent to the building housing CWS's administrative offices where workers often waited to be dispatched to jobs. J.A. at 85-86 (Trial *672 Tr. at 5-6). Both Brown and Dossett testified that they witnessed Dana Young, a white employee of CWS, throw firecrackers or similar devices in the smoke hole. According to Brown, Young threw actual firecrackers. J.A. at 85 (Trial Tr. at 5). According to Dossett, Young threw "poppers," which are small, gunpowder-filled items that explode when thrown to the ground. J.A. at 96 (Trial Tr. at 16). Both Brown and Dossett testified that Templinthe supervisor who reported Madden's incident the following yearwas present at the smoke hole during this incident. J.A. at 87 (Trial Tr. at 7); J.A. 96-97 (Trial Tr. at 16-17). Dossett further testified that he saw both Young and Templin throw poppers at another CWS employee named James Morgan. J.A. at 96-97 (Trial Tr. at 16-17). In addition, Brown testified that during this incident, Wayne Wilkerson ("Wilkerson"), who manages CWS's street construction division and is white, came out of the CWS administration building to the smoke hole and said, "Okay, guys. Knock off the horseplay." J.A. at 89 (Trial Tr. at 9).[2]
In the second incident, a white employee threw firecrackers into the window of a moving work truck carrying African-American employees, causing them to jump from the truck. J.A. at 106 (Trial Tr. at 29). Alonzo Lewis, who witnessed the incident, testified that employees present who saw the incident laughed and viewed the incident as humorous. J.A. at 106-07 (Trial Tr. at 29-30). According to Lewis, "everybody laughed, so it wasn't no big deal out of it." J.A. at 106 (Trial Tr. at 29). Lewis further testified that Wilkerson was among those present. Id.
Madden also introduced evidence that such incidents were not isolated but were commonplace at CWS. Lewis testified that he had "seen or heard firecrackers being played plenty times." J.A. at 106 (Trial Tr. at 29). Lewis further testified that during the period surrounding the Fourth of July the use of firecrackers at CWS "used to be just a regular thing." J.A. at 108 (Trial Tr. at 31). In contrast to such testimony by Madden's witnesses, Wilkerson, Templin, and Young each denied witnessing anyone at CWS use firecrackers on the job.
Following the bench trial, on December 20, 2007, the district court found that Madden was terminated by CWS because of his race in violation of Title VII and the THRA. J.A. at 56-57 (Mem. & Order at 6-7). In its findings of fact, the district court stated that it credited the testimony of Madden's witnesses that the two incidents described above had occurred, and that it found the "blanket denials by defense witnesses ... not creditable in light of Plaintiff's evidence." J.A. at 54 (Mem. & Order at 4). The court stated that it also credited the testimony of CWS senior managers-Boyd, Templeton, Leach, and Donald Norris, deputy administrator for public works-that they had no knowledge of the other incidents involving firecrackers. Id. However, the court concluded that because firecracker use at CWS was so common, the senior managers "should have known that fireworks were being used" and "therefore attribute[d] knowledge to them." J.A. at 55 (Mem. & Order at 5). In concluding that Madden's termination was the result of intentional discrimination, the district court reasoned as follows:
While white employees used firecrackers without fear of discipline from supervisors or managers, Plaintiff's use of a *673 firecracker led to him being sent home and then terminated. Although there is no evidence any of Defendant's senior managers had actual knowledge of other incidents where employees set off firecrackers, the use of fireworks was widespread enough and was done openly so that these supervisors and managers should have known. Moreover, these managers are responsible for the information supplied to them by their subordinates. The Court concludes there was discrimination in what information was presented to them. In such a case, there must be a "causal nexus" between the discriminatory actions and the neutral decisionmaker. Christian v. Wal-Mart Stores, Inc., 252 F.3d 862, 876 (6th Cir.2001). That causal nexus exists here, where racial discrimination [a]ffected the decision to inform senior management about Plaintiff's firecracker incident, while not informing senior management about white employees who had used firecrackers during work.
J.A. at 56-57 (Mem. & Order at 6-7).
The district court awarded Madden a total of $120,000.50 in damages consisting of the following: (1) back pay of $36,935.50 based on an annual salary of $21,106 for the twenty-one months Madden was out of work; (2) compensatory damages of $30,300; and (3) front pay for two-and-one-half years of $52,765 (i.e., 2.5 x $21,106). In so doing, the court rejected CWS's argument that Madden failed to mitigate damages by failing diligently to seek alternate employment. CWS timely appealed.

II. ANALYSIS

A. THRA Claims
The district court's judgment was based on Madden's claims under both Title VII and the THRA. See J.A. at 57 (Mem. & Order at 7). The district court analyzed these claims in tandem, presumably because the analysis of Madden's wrongful-termination claim is the same under both Title VII and the THRA. See Newman v. Fed. Express Corp., 266 F.3d 401, 406 (6th Cir.2001); Graves v. Circuit City Stores, Inc., No. 03A01-9501-CH-00012, 1995 WL 371659, at *2 (Tenn.Ct.App. June 21, 1995) (unpublished opinion). CWS incorrectly states that the district court "narrowed the issue for trial in this matter to a Title VII wrongful termination case." CWS Br. at 7. Further, CWS fails to make any arguments in its briefs as to Madden's THRA claims, not even to state that it would consolidate its argument because the analysis under the THRA mirrors that under Title VII.
Under the general rule, "[a]n appellant waives an issue when he fails to present it in his initial briefs before this court." Marks v. Newcourt Credit Group, Inc., 342 F.3d 444, 462 (6th Cir.2003). However, we have recognized an exception, holding "that where an argument advanced in an appellant's opening brief applies to and essentially subsumes an alternative basis for affirmance not separately argued therein, the appellant does not waive that alternative basis for affirmance." United States v. Goforth, 465 F.3d 730, 737 (6th Cir.2006) (citing Stambaugh v. Corrpro Co., 116 Fed.Appx. 592, 596-97 (6th Cir. 2004)). Because the analysis of Madden's claims is the same under both Title VII and the THRA, we believe that CWS's arguments with respect to the THRA claims are sufficiently subsumed within its arguments on the Title VII claims for this exception to apply. Accordingly, we conclude that CWS did not waive its argument as to the THRA claims.

B. Intentional Discrimination Claim
On appeal from a judgment following a bench trial, a district court's findings of *674 fact "must not be set aside unless clearly erroneous, and the reviewing court must give due regard to the trial court's opportunity to judge the witnesses' credibility." Fed.R.Civ.P. 52(a)(6). "When findings are based on determinations regarding the credibility of witnesses, Rule 52(a) demands even greater deference to the trial court's findings; for only the trial judge can be aware of the variations in demeanor and tone of voice that bear so heavily on the listener's understanding of and belief in what is said." Anderson v. City of Bessemer City, 470 U.S. 564, 575, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). Thus, "when a trial judge's finding is based on his decision to credit the testimony of one of two or more witnesses, each of whom has told a coherent and facially plausible story that is not contradicted by extrinsic evidence, that finding, if not internally inconsistent, can virtually never be clear error." Id. We review de novo a district court's legal conclusions following a bench trial. Pressman v. Franklin Nat'l Bank, 384 F.3d 182, 185 (6th Cir.2004).
Title VII of the Civil Rights Act of 1964 provides in relevant part than an employer may not "discharge any individual, or otherwise... discriminate against any individual with respect to his compensation, terms, conditions, or privileges of employment, because of such individual's race." 42 U.S.C. § 2000e-2(a)(1).[3] CWS argues that the district court erred in finding that it intentionally discriminated against Madden on the basis of race. First, CWS argues that Madden could not satisfy the fourth prong of the prima facie case for discrimination: that he was treated differently than similarly situated, non-protected employees. Second, CWS argues that the district court erred in finding that Madden met his burden of showing that CWS's legitimate nondiscriminatory reason for terminating Madden was a pretext for discrimination. Finally, CWS argues that the district court erred in attributing the knowledge of lower-level supervisors of firecracker use by white employees at CWS to senior managers as a basis for finding that Madden's termination was discriminatory.
We have explained that "[w]hen reviewing the facts of a discrimination claim after there has been a full trial on the merits, we must focus on the ultimate question of discrimination rather than on whether a plaintiff made out a prima facie case." Barnes v. City of Cincinnati, 401 F.3d 729, 736 (6th Cir.), cert. denied, 546 U.S. 1003, 126 S.Ct. 624, 163 L.Ed.2d 506 (2005). As the Supreme Court has explained, when a discrimination claim is "fully tried on the merits," the question on appeal is not whether the plaintiff "made out a prima facie case," but rather "the ultimate question of discrimination vel non." U.S. Postal Serv. Bd. of Governors v. Aikens, 460 U.S. 711, 713-14, 103 S.Ct. 1478, 75 L.Ed.2d 403 (1983). This is because "[w]here the defendant has done everything that would be required of him if the plaintiff had properly made out a prima facie case, whether the plaintiff really did so is no longer relevant." Id. at 715, 103 S.Ct. 1478. Thus, this court's "duty, given Aikens, is simply to determine whether [the plaintiff] produced sufficient evidence to support the [factfinder's] finding of intentional discrimination." Noble v. Brinker Int'l, Inc., 391 F.3d 715, 721 (6th Cir.2004), cert. denied, 546 U.S. 821, 126 S.Ct. 353, 163 L.Ed.2d 62 (2005). At the same time, however, "the evidentiary underpinnings of a plaintiff's prima facie *675 case are not irrelevant or insulated from our examination to aid our determination whether the evidence is sufficient to support a finding of intentional discrimination." Barnes, 401 F.3d at 736.
"The ultimate question in every employment discrimination case involving a claim of disparate treatment is whether the plaintiff was the victim of intentional discrimination." Reeves v. Sanderson Plumbing Prods., Inc., 530 U.S. 133, 153, 120 S.Ct. 2097, 147 L.Ed.2d 105 (2000). A plaintiff may attempt to prove intentional discrimination through either direct or indirect evidence. See, e.g., Noble, 391 F.3d at 721. With respect to the indirect method of proof, the Supreme Court has held that "a plaintiff's prima facie case, combined with sufficient evidence to find that the employer's asserted justification is false, may permit the trier of fact to conclude that the employer unlawfully discriminated." Reeves, 530 U.S. at 148, 120 S.Ct. 2097. Referring to its holding in St. Mary's Honor Center v. Hicks, 509 U.S. 502, 511, 113 S.Ct. 2742, 125 L.Ed.2d 407 (1993), the Court in Reeves explained:
There we held that the factfinder's rejection of the employer's legitimate, nondiscriminatory reason for its action does not compel judgment for the plaintiff. [St. Mary's Honor Ctr.,] 509 U.S. at 511, 113 S.Ct. 2742. The ultimate question is whether the employer intentionally discriminated, and proof that "the employer's proferred reason is unpersuasive, or even obviously contrived, does not necessarily establish that the plaintiff's proferred reason ... is correct." Id. at 524, 113 S.Ct. 2742. In other words, "[i]t is not enough ... to dis believe the employer; the factfinder must believe the plaintiff's explanation of intentional discrimination." Id. at 519, 113 S.Ct. 2742.
In reaching this conclusion, however, we reasoned that it is permissible for the trier of fact to infer the ultimate fact of discrimination from the falsity of the employer's explanation.
Reeves, 530 U.S. at 146-47, 120 S.Ct. 2097 (case name added). Accordingly, in the instant case, the question is whether Madden produced sufficient evidence from which the district court, as trier of fact, could reasonably find that CWS's "proferred explanation is unworthy of credence." Id. at 143, 120 S.Ct. 2097 (internal quotation marks omitted).
A plaintiff may establish that an employer's explanation is not credible by demonstrating "either (1) that the proferred reasons had no basis in fact, (2) that the proferred reasons did not actually motivate his discharge, or (3) that they were insufficient to motivate discharge." Manzer v. Diamond Shamrock Chems. Co., 29 F.3d 1078, 1084 (6th Cir. 1994) (internal quotation marks omitted); see also Tisdale v. Fed. Express Corp., 415 F.3d 516, 529 (6th Cir.2005) (applying Manzer factors); Gray v. Toshiba Am. Consumer Prods., Inc., 263 F.3d 595, 600 (6th Cir.2001) (same).
Applying these principles to this case, we believe that Madden introduced sufficient evidence from which a reasonable factfinder could find that CWS's proffered explanation for his termination was not credible under the third Manzer factor. The first factor is not at issue because there is no dispute that Madden set off firecrackers while working on March 22, 2006, and that this was the proffered reason for his discharge. We believe that Madden's theory of the case is inconsistent with a showing under the second Manzer factor. Under the second factor, the plaintiff admits that "such conduct could motivate dismissal" but nonetheless argues "that the sheer weight of the circumstantial *676 evidence of discrimination makes it `more likely than not' that the employer's explanation is a pretext, or coverup." Manzer, 29 F.3d at 1084. Madden's theory at trial, however, was that setting off fireworks was a routine practice among workers at CWS that had never been the basis for punishment. Madden never admitted that such conduct could justify outright dismissal, but instead pressed senior managers in questioning at trial to explain why they had not proceeded under CWS's disciplinary proceduresincluding verbal and written warningsprior to terminating him.
Turning to the third Manzer factor, we believe that a reasonable factfinder could find that CWS's proffered reason was insufficient to motivate Madden's discharge. A plaintiff's showing under this factor "ordinarily[] consists of evidence that other employees, particularly employees not in the protected class, were not fired even though they engaged in substantially identical conduct to that which the employer contends motivated its discharge of the plaintiff." Id. First, Madden offered evidence that white employees were not firedor disciplined whatsoeverdespite engaging in substantially identical conduct to the conduct for which Madden was fired. Both Brown and Dossett testified that Dana Young, a white employee, threw firecrackers or similar devices during work hours at the "smoke hole," an area adjacent to the CWS administrative building where CWS employees often congregated. J.A. at 85 (Trial Tr. at 5); J.A. at 96 (Trial Tr. at 16). Both Brown and Dossett also testified that this incident was witnessed by Templin, the white supervisor whose report of Madden the following year led to his termination. J.A. at 87 (Trial Tr. at 7); J.A. 96-97 (Trial Tr. at 16-17). Moreover, Dossett testified that he witnessed both Young and Templin throw poppers at another CWS employee. J.A. at 96-97 (Trial Tr. at 16-17). In addition, Brown testified that another white manager, Wilkerson, came out of the CWS administration building during the incident and merely told the employees to "[k]nock off the horseplay." J.A. at 89 (Trial Tr. at 9). Madden also offered evidence of a second incident on CWS property, in which an unnamed white employee threw firecrackers into the window of a moving work truck carrying black employees, leading them to jump out of the truck. J.A. at 106 (Trial Tr. at 29). This incident was also witnessed by Wilkerson, who again did not pursue any disciplinary action against those involved. J.A. at 106-07 (Trial Tr. at 29-30).
CWS argues that Madden did not establish that he was treated less favorably than similarly situated, non-protected employees, because the incidents involving other employees did not involve misconduct of comparable seriousness. However, Madden introduced substantial evidence that the other incidents involved comparable or even more serious misconduct. CWS contends that the other incidents, if they took place, involved the use of "poppers," rather than actual firecrackers. But the testimony on this was contradictory. As to the first incident, whereas Dossett testified that it involved poppers, J.A. at 96 (Trial Tr. at 16), Brown testified that it involved actual firecrackers, J.A. at 85 (Trial Tr. at 5). As to the second incident, Lewis testified that a white employee threw "firecrackers" into the window of the truck carrying black employees, J.A. at 106 (Trial Tr. at 29), though he later testified that he was not sure whether it involved actual firecrackers or poppers, J.A. at 109-10 (Trial Tr. at 32-33). CWS further argues that Madden's incident differed because it was at a "work location around heavy operating equipment." CWS Br. at 14. Madden testified that the incident took place in a rural, non-residential area, J.A. *677 at 124 (Trial Tr. at 47), where the principal concern similarly would have been the safety of other employees rather than the public. CWS does not explain why the concerns about the dangers of fireworks to other employees would be any greater at such a work site than they would be when employees congregated outside the CWS building awaiting dispatch or when the employees were in a truck. In sum, CWS fails to show how the other incidentsparticularly throwing firecrackers or similar devices into a moving truck carrying employeesare any less hazardous than the incident for which Madden was terminated.
Second, Madden offered evidence that the use of firecrackers was commonplace at CWS. Lewis testified that he had "seen or heard firecrackers being played plenty times." J.A. at 106 (Trial Tr. at 29), and that around the Fourth of July the use of firecrackers "used to be just a regular thing," J.A. at 108 (Trial Tr. at 31). Further, there was evidence that CWS employees who witnessed the specific incidents described were not surprised by such incidents, but instead considered the incidents humorous or "no big deal." J.A. at 106 (Trial Tr. at 29). On the basis of evidence indicating that firecracker use at CWS was relatively common and that there was no effort to conceal their use, we believe that the district court could reasonably infer that senior managers should have known that fireworks were being used. J.A. at 55 (Mem. & Order at 5).
Finally, there is the problem posed by the fact that Madden was fired not by his supervisor, Templin, but by senior managersTempleton and Leachwho were unaware of incidents in which white workers set off fireworks without facing discipline. CWS argues that the district court erred "by attributing or imputing Wilkerson or Templin's knowledge of alleged prior incidences of non-protected employees using fire-crackers without being disciplined to Templeton and Leach." CWS Br. at 23. We have held that when a plaintiff challenges his termination as motivated by a supervisor's discriminatory animus, he must offer evidence of a "causal nexus" between the ultimate decisionmaker's decision to terminate the plaintiff and the supervisor's discriminatory animus. See Wilson v. Stroh Cos., 952 F.2d 942, 946 (6th Cir. 1992); see also Christian v. Wal-Mart Stores, Inc., 252 F.3d 862, 877 (6th Cir.2001) (applying causal-nexus requirement in the context of a 42 U.S.C. § 1981 discrimination claim by shopper against retailer). The district court found that the requisite causal nexus was established based on "discrimination in what information was presented to [senior managers]." J.A. at 56 (Mem. & Order at 6). That is, the district court concluded that "racial discrimination" affected Templin's decision to "inform senior management about [Madden's] firecracker incident, while not informing senior management about white employees who had used firecrackers during work." J.A. at 57 (Mem. & Order at 7). Because the decision of Templeton and Leach was tainted by the discriminatory animus of Templin and the discriminatory information he supplied, the district court concluded that discriminatory animus could be imputed to Templeton and Leach.
We believe that Madden presented sufficient evidence from which a reasonable factfinder could find a causal nexus between the ultimate decisionmaker's decision to terminate Madden and his supervisor's discriminatory animus. See Christian, 252 F.3d at 877-78; Wilson, 952 F.2d at 945-46. In Wilson, we found such a causal nexus lacking in a Title VII suit by a black factory employee, Wilson, alleging wrongful termination *678 from his job at Stroh's. Assuming on appeal that Wilson's supervisor had discriminatory animus, the Wilson court refused to impute that animus to the ultimate decisionmakers, even though it was that supervisor who alerted senior managers to the conduct for which the employee was fired. Because the decision of the general manager to terminate Wilson was based on an independent investigation of the events by the industrial relations manager, and Wilson had presented no evidence that the supervisor's discriminatory animus had influenced the decision, the court concluded that Wilson had failed to establish a prima facie case. However, the Wilson court noted that "[if] Wilson were to offer evidence that [the supervisor] had not reported such misconduct from white employees, then he would establish a prima facie case." 952 F.2d at 946.
In the instant case, there was an investigation of the events for which Madden was fired, which was conducted by Boyd and Templeton.[4] This investigation led to Templeton's recommendation that Madden be fired, which Leach accepted. J.A. at 154-57 (Trial Tr. at 84-87). Unlike Wilson, however, there was evidence in this case that the supervisor had not reported similar misconduct by white employees. Two witnesses testified that Templin was present when a white employee threw firecrackers (or "poppers") at the smoke pit, and one witness testified that Templin himself also threw poppers on that occasion. Thus, there was evidence that Templin discriminated in the information that he provided about employee misconduct to senior managers by reporting the misconduct of a black employee, but not the virtually identical misconduct of white employees. By relying on this discriminatory information flow, the ultimate decisionmakers "acted as the conduit of [the supervisor's] prejudicehis cat's paw." Christian, 252 F.3d at 877 (quoting Shager v. Upjohn Co., 913 F.2d 398, 405 (7th Cir.1990)).
In sum, we conclude that given all of the evidence in this case, the district court did not clearly err in finding that CWS's proffered reason for Madden's termination was not the actual reason motivating the discharge. Further, "giv[ing] due regard to the trial court's opportunity to judge the witnesses' credibility," Fed.R.Civ.P. 52(a)(6), we conclude that the district court did not clearly err in believing Madden's explanation of intentional discrimination.

C. Damages

1. Back Pay
We review a district court's award of back pay for abuse of discretion. Suggs v. ServiceMaster Educ. Food Mgmt., 72 F.3d 1228, 1233 (6th Cir.1996). The district court awarded Madden back pay of $36,935.50 for the twenty-one months he was out of work from the date of his termination through the date of the judgment. J.A. at 57 (Mem. & Order at 7). CWS argues that the district court erred in awarding back pay for this entire period because it mitigated its liability when it offered Madden an "unconditional restatement offer." CWS Br. at 23. However, because CWS's offer was not unconditional, but rather conditioned on Madden compromising his claims, the district court correctly awarded back pay for the entire period.
The Supreme Court has held that "an employer charged with unlawful discrimination *679 often can toll the accrual of backpay liability by unconditionally offering the claimant the job he sought, and thereby providing him with an opportunity to minimize damages." Ford Motor Co. v. EEOC, 458 U.S. 219, 232, 102 S.Ct. 3057, 73 L.Ed.2d 721 (1982). However, the Court went on to note that this rule "does not require [a claimant] to settle his claim against the employer, in whole or in part." Id. at 232 n. 18, 102 S.Ct. 3057. Accordingly, a claimant "is not required to accept a job offered by the employer on the condition that his claims against the employer be compromised." Id.
The reinstatement offer in this case stated as follows:
As a settlement to your previous grievances and EEO charges, the city agrees to reinstate you as a city employee in a department other than the one for which you were previously employed. If this agreement is acceptable by you, you in turn agree to drop all complaints against the City, including your appeal to the... city council. This agreement will be [] effective immediately by your signature.
J.A. at 118 (Trial Tr. at 41). It is clear that CWS's offer to Madden was an offer to compromise Madden's claims, rather than an "unconditional" offer that would have been effective to mitigate CWS's liability. Accordingly, we conclude that the district court correctly awarded back pay from the date of termination through the date of judgment.

2. Front Pay
We review a district court's award of front pay for abuse of discretion. Suggs, 72 F.3d at 1234. "Courts generally award front pay when reinstatement is inappropriate or infeasible." Id. The district court awarded Madden $52,765 in front pay, based on two-and-one-half years of Madden's annual salary. J.A. at 58 (Mem. & Order at 8). CWS argues that the award was excessive because (1) the district court did not expressly consider the factors this court has articulated for calculating front pay, and (2) the district court did not reduce the award to present value.
First, in awarding front pay, the district court should consider the following factors: "(1) the employee's future in the position from which she was terminated; (2) her work and life expectancy; (3) her obligation to mitigate her damages; (4) the availability of comparable employment opportunities and the time reasonably required to find substitute employment; (5) the discount tables to determine the present value of future damages; and (6) `other factors that are pertinent in prospective damage awards.'" Suggs, 72 F.3d at 1234 (quoting Fite v. First Tenn. Prod. Credit Ass'n, 861 F.2d 884, 893 (6th Cir.1988)). Further, "[w]hen a district court determines that front pay is appropriate because reinstatement is inappropriate or infeasible, the court must make its award of front pay reasonably specific as to duration and amount, and the amount of a front pay award must be reduced to present value." Id. at 1235.
After concluding that reinstatement was not an appropriate remedy, the district court awarded a specific amount of front pay, $52,765, based on a specific time period, two-and-one-half years. Moreover, in making this award, the district court considered the second, third, and fourth factors, explaining that its determination was based on Madden's work history and personal characteristics, the prevailing job market in the area, and evidence of Madden's attempts to obtain other employment. J.A. at 58 (Mem. & Order at 8).
CWS is correct that the district court failed to apply the fifth factor to discount *680 the award to present value. However, we conclude that this error is offset by the court's failure to account for cost-of-living and other raises that Madden would likely have received if he had remained at CWS. Accordingly, even though the district court erred in failing to discount for present value, we affirm the district court's award. See, e.g., Killian v. Yorozu Auto. Tenn., Inc., 454 F.3d 549, 558 (6th Cir.2006) (affirming district court's front-pay calculation despite failure to discount to present value based, in part, on offsetting failure to account for likely raises employee would have received).
Finally, CWS argued in the district court that Madden failed to mitigate damagesone of the factors a district court must consider in awarding front pay. We review a district court's ruling on the sufficiency of an employee's mitigation efforts for clear error. Killian, 454 F.3d at 556. In Title VII cases, the defendant bears the burden of establishing that the plaintiff lacked diligence in mitigating damages by showing that there were substantially equivalent positions available and that the plaintiff did not diligently pursue those positions. Id. at 557. The plaintiff is "only required to make reasonable efforts to mitigate damages, and is not held to the highest standards of diligence." Id. (internal quotation marks omitted). Further, the reasonableness of the plaintiff's efforts are "evaluated in light of the individual characteristics of the [plaintiff] and the job market." Id. (internal quotation marks omitted).
The record shows that CWS presented no evidence that either substantially equivalent jobs were available or that Madden did not diligently pursue such positions. Instead, the only evidence presented on the issue came from Madden. Madden introduced evidence that he had sought other employment after being terminated by CWS. He submitted applications for positions at the Chattanooga Housing Authority and the Tennessee Valley Authority and searched for work through a career center as part of the food-stamp program. J.A. at 142 (Trial Tr. at 65). Despite these efforts, Madden failed to obtain substantially equivalent employment and only obtained, temporarily, part-time employment as a cook earning $5.85 per hour (compared to more than $10 per hour at CWS) for only ten hours per week. J.A. at 141 (Trial Tr. at 64). Madden also testified that after his termination from CWS he had enrolled in school. J.A. at 142 (Trial Tr. at 65). Given CWS's failure to offer any evidence to meet its burden and the rather limited evidence on this issue in the record, we cannot say that the district clearly erred in finding that Madden made a sufficient effort to mitigate his damages.

III. CONCLUSION
For the foregoing reasons, we AFFIRM the district court's judgment for Madden.
NOTES
[*]  The Honorable Myron H. Bright, Circuit Judge of the United States Court of Appeals for the Eighth Circuit, sitting by designation.
[1]  According to Templin, when he asked Madden why he had set off the fireworks, Madden said, "I was just playing." Joint Appendix ("J.A.") at 171 (Trial Tr. at 101). Although Madden admits setting off the firecrackers, he testified at trial that he used the fireworks to ward off a dog that approached when he got out of the truck. J.A. at 124 (Trial Tr. at 47). According to Madden, crew workers commonly used firecrackers to scare off dogs and other animals. Id. Madden testified that when Templin asked him why he had set off the firecrackers, he responded, "Didn't you see that dog come up?" Id. Templin testified that Madden did not mention a dog and that he did not see any dogs. J.A. at 171 (Trial Tr. at 101). It is unclear whose version of events was credited by the district court. See J.A. at 52 (Mem. & Order at 2).
[2]  In his testimony, Wilkerson denied witnessing such an incident. J.A. at 150 (Trial Tr. at 80).
[3]  Because the analysis of Madden's wrongful-termination claim is the same under both Title VII and the THRA, the analysis that follows also applies to Madden's THRA claims.
[4]  The scope and nature of this investigation are unclear, but appear to have been limited to receiving Templin's account of the incident and then interviewing Madden. See J.A. at 174-79 (Trial Tr. at 104-09).
