Before Higginbotham, Stewart, and Southwick, Circuit Judges. Patrick E. Higginbotham, Circuit Judge: Today we return to the “highly compensated employee” and “learned professional” exemptions to the Fair Labor Standards Act of 1939, a statute which mandates that employees receive time-and-a-half pay for hours worked in excess of the standard forty-hour workweek.[1] To qualify for either exemption, employers must pay their employees on a “salary basis.”[2] The district court found that Hamilton-Ryker IT Solutions (“HR-IT”) did not pay Terry Gentry and Marc Taylor on a salaried basis and owed both employees actual and liquidated damages for prior overtime work. We earlier affirmed the district court’s judgment but withdrew the opinion. On reconsideration, we again affirm the district court’s judgment that the workers here were not exempt. We also vacate and remand for reconsideration of liquidated damages. I. A. Terry Gentry worked as a senior control systems engineer for HR-IT from 2015 to 2019. Marc Taylor began working at HR-IT in August 2017. On September 25, 2019, Gentry filed a putative class action alleging that HR-IT violated the Fair Labor Standards Act (“FLSA”) by failing to pay overtime wages to its non-exempt, hourly-paid employees. Taylor joined the lawsuit on May 28, 2020. During the relevant time period, both men were paid on a two-tiered system. First, a “Guaranteed Weekly Salary equal to 8 hours of pay.”[3] The “weekly salary” only compensated Gentry and Taylor for, at most, one eight-hour workday. Then, for any hour they worked beyond their eighth hour, Plaintiffs were paid at their hourly rates, including any hours worked over 40. The parties led cross motions for summary judgment. HR-IT argued Gentry and Taylor were exempt from the FLSA’s time-and-a-half requirement as either “highly compensated employees” or “learned professionals.” The essential issue was whether Gentry and Taylor were paid on a “salary basis,” a requirement for either exemption. The magistrate judge recommended, and the district court agreed, that, as Plaintiffs were not paid on a salary basis, they were not exempt from the FLSA’s overtime requirements. The magistrate also advised the district court to impose liquidated damages equal to Plaintiffs’ actual damages, as authorized by the FLSA.[4] HR-IT objected to the magistrate judge’s report and recommendations and offered additional evidence regarding its good faith defense to the liquidated damages award. Specifically, HR-IT submitted evidence from a May 10, 2021 deposition in a separate case to show its good faith belief that it complied with the FLSA. The deposition reflected that HR-IT’s President consulted with the company’s attorney, attended staffing conferences, and performed independent research to “stay up to date” on the industry and to develop HR-IT’s pay practices regarding exempt employees. The district court reviewed the magistrate judge’s report de novo and concluded that it could not consider HR-IT’s new evidence. Ultimately, the district court adopted the magistrate judge’s report and recommendation in full on March 25, 2022. B. HR-IT timely appealed on April 8, 2022. Shortly thereafter, the Supreme Court granted certiorari in another FLSA case, Helix Energy Solutions Group, Inc. v. Hewitt.[5] We stayed this case pending Helix‘s resolution. The Supreme Court issued its Helix decision on February 22, 2023 and, with the benefit of Helix, the parties resumed briefing this case.[6] On June 20, 2023, the Secretary of Labor filed a brief as amicus curiae in support of Plaintiffs and asked this court to affirm the district court’s judgment. In its brief, the Secretary explained that in light of Helix, Gentry and Taylor were not exempt from the FLSA’s overtime requirements because they were not paid on a salary basis. We affirmed the district court’s judgment, and HR-IT petitioned for panel rehearing. This court granted HR-IT’s motion, withdrew its opinion, and reopened the case. HR-IT now advances two arguments on appeal.[7] First, HR-IT challenges the district court’s conclusion that Plaintiffs were not exempt employees. Second, HR-IT asserts that the district court abused its discretion by rejecting HR-IT’s new evidence and ordering HR-IT to pay liquidated damages. Upon reconsideration, we AFFIRM the judgment of the district court related to the FLSA exemption but VACATE the judgment on liquidated damages and REMAND for reconsideration of that issue. II. We review summary judgment determinations de novo and apply the same standard as the district court.[8] When considering cross motions for summary judgment, we examine “each party’s motion independently”[9] and “each movant bears the burden of establishing that no genuine issue of material fact exists and that it is entitled to judgment as a matter of law.”[10] The employer has the burden of establishing by a preponderance of the evidence that an exemption applies.[11] “[T]he ultimate decision [of] whether [an] employee is exempt from the FLSA’s overtime compensation provisions is a question of law.”[12] “This [c]ourt reviews liquidated damages awards for clear error.”[13] “Clear error exists when although there may be evidence to support it, the reviewing court on the entire record is left with the denite and rm conviction that a mistake has been committed.”[14] III. We rst address HR-IT’s argument that the district court erred when it found Plaintiffs non-exempt under the FLSA. After reviewing this question de novo, we nd that it did not. Plaintiffs do not qualify for an exemption under the FLSA because they were not paid on a salary basis under either 29 C.F.R. §§ 541.602(a) or 541.604(b). A. The Fair Labor Standards Act of 1938 guarantees covered employees overtime pay at a rate “not less than one and one-half times the regular rate” when they work more than 40 hours a week.[15] Employees working “in a bona fide executive, administrative, or professional” capacity are exempt from this protection.[16] The Secretary of Labor in turn has promulgated regulations exempting “highly compensated employees” (“HCEs”) and “learned professionals.”[17] HR-IT argued that Plaintiffs were exempt from FLSA protection under either the HCE or learned professional exemptions. To meet either the HCE or learned professional exemption, employees must satisfy three tests: (1) the “job duties” test;[18] (2) the “salary level” test;[19] and (3) the “salary basis” test.[20] As the parties agree that Gentry and Taylor meet the job duties and salary level tests, only the salary basis test is at issue. There are two ways to satisfy the salary basis test: through the avenue provided by 29 C.F.R. §§ 541.602(a) and 541.604(a) (“§ 602(a)” and “§ 604(a)”); or through the alternative route established by 29 C.F.R. § 541.604(b) (“§ 604(b)”). The issue today is which regulation applies. HR-IT argues that its compensation structure is governed by § 602(a), while Plaintiffs rely on § 604(b). Section 602 provides: (a) General rule. An employee will be considered to be paid on a “salary basis” within the meaning of this part if the employee regularly receives each pay period on a weekly, or less frequent basis, a predetermined amount constituting all or part of the employee’s compensation, which amount is not subject to reduction because of variations in the quality or quantity of the work performed. (1) Subject to the exceptions provided in paragraph (b) of this section, an exempt employee must receive the full salary for any week in which the employee performs any work without regard to the number of days or hours worked. Exempt employees need not be paid for any workweek in which they perform no work.[21] Section 604(a) supplements § 602(a) and explains: “[a]n employer may provide an exempt employee with additional compensation without losing the exemption or violating the salary basis requirement, if the employment arrangement also includes a guarantee of at least the minimum weekly-required amount paid on a salary basis.”[22] The provision provides three examples of permissible, additional compensation: (1) commissions on sales; (2) percentages of sales or profits; and (3) “additional compensation based on hours worked for work beyond the normal workweek.”[23] Together, sections 602(a) and 604(a) allow employers to pay a true weekly salary, a salary paid on a weekly or less frequent basis, plus additional compensation in the form of commissions, profit-sharing, or hourly wages for hours worked beyond the normal workweek. Section 602(a) provides a stable and predictable source of income while § 604(a) allows performance incentives for work beyond the regular workweek.[24] While sections 602(a) and 604(a) define the permissible compensation schemes for employees paid on weekly or less frequent basis, § 604(b) concerns situations when employees paid on a more frequent basis—such as by the hour, shift, or day—are still considered to be paid on a “salary basis”: An exempt employee’s earnings may be computed on an hourly, a daily or a shift basis, without losing the exemption or violating the salary basis requirement, if the employment arrangement also includes a guarantee of at least the minimum weekly required amount paid on a salary basis regardless of the number of hours, days or shifts worked, and a reasonable relationship exists between the guaranteed amount and the amount actually earned. The reasonable relationship test will be met if the weekly guarantee is roughly equivalent to the employee’s usual earnings at the assigned hourly, daily or shift rate for the employee’s normal scheduled workweek.[25] The regulations explain that a salary is “roughly equivalent” to an employee’s weekly earnings when the ratio of usual earnings to salary is 1.5 to 1.[26] In sum, hourly-rate employees can be paid on a “salary basis” pursuant to § 604(b) only if: (1) they also receive a “minimum weekly required amount paid on a salary basis,” and (2) there is a reasonable relationship between the weekly guaranteed salary and the employee’s actual earnings. In Helix, the Supreme Court claried that sections 602(a) and 604(b) provide alternative, independent methods for satisfying the salary basis test.[27] Helix held that § 602(a) (aided by § 604(a)) applies to employees paid on a weekly basis while § 604(b) applies to employees paid on a more frequent basis, such as by the hour or day.[28] In doing so, Helix established that the “basis” of an employee’s purported salary determines which regulatory test governs a particular compensation scheme. This determination is dispositive here. B. 1. Section 602(a) requires that salaried employees be paid on a “weekly basis.”[29] In Helix, the Supreme Court dened the phrase “basis” as “the unit of time used to calculate pay.”[30] Accordingly, employees are paid on a “weekly basis” only when their “predetermined sum” is calculated, not merely provided, by the week.[31] Put simply, payment on a “weekly basis” requires that an employee be paid a “weekly rate.”[32] And just as employees paid an hourly rate are paid for all work performed that hour, a weekly rate compensates employees for all work performed that week.[33] Gentry’s and Taylor’s “guaranteed weekly salar[ies]” were valued at their individual hourly rate times eight hours.[34] The “unit or method for calculating pay” was by the hour, meaning that Plaintiffs’ “salary” was paid on an hourly basis and not by the week as § 602(a) requires.[35] Nor can HR-IT reasonably argue that eight hours of pay constitutes a “weekly rate.” Far from it, Plaintiffs’ “guaranteed weekly salary” typically accounted for less than 20% of their total paychecks. Because the “guaranteed weekly salary” failed to provide a weekly rate, it was not a true salary but was illusory.[36] Instead, Plaintiffs’ actual earnings could only be ascertained by determining the number of hours worked that week.[37] Just as “[a] daily-rate worker’s weekly pay is always a function of how many days he has labored,” Gentry’s and Taylor’s paychecks were a function of the hours worked.[38] Phrased differently, their pay could “be calculated only by counting those [hours] once the week is over—not, as § 602(a) requires, by ignoring that number and paying a predetermined amount.[39] HR-IT offers several arguments to defend its claim that Plaintiffs were paid on a weekly basis. None are persuasive. First, HR-IT argues that it satised § 602(a) because Gentry and Taylor were paid above the weekly $455 salary screening threshold.[40] This argument conates the salary level test and the salary basis test. But these tests are distinct, and it is irrelevant that the guaranteed sum satised the salary level test if HR-IT nonetheless failed to provide payment on a salary basis.[41] Indeed, this argument echoes the Helix dissent.[42] Second, HR-IT argues Plaintiffs received a salary because they were “paid for every ‘seven consecutive 24-hour periods’ in which [they] performed any work.”[43] But Helix makes clear that the frequency of a paycheck does not determine whether payments are made on a “weekly basis.”[44] Third, it is no answer that the “guaranteed weekly salary” provided only “part” of Plaintiffs’ total compensation.[45] Again, the Helix majority rejected this argument.[46] The language in § 602(a) regarding “all or part” of an employee’s compensation does not absolve employers from paying a weekly rate; it only references additional compensation under § 604(a).[47] Employers must still provide a salary, which HR-IT did not do.[48] We therefore conclude that § 602(a) does not govern this appeal because HR-IT did not compensate Plaintiffs on a “weekly basis.” 2. In a nal attempt to persuade the court that § 602(a) governs, HR-IT argues its payment scheme satises § 602(a) in conjunction with § 604(a). So long as employees receive a minimum, predetermined, and guaranteed sum every week, HR-IT argues any hourly compensation is permissible under § 604(a). We disagree. Section 604(a) builds upon § 602(a) and makes clear that salaried employees may receive “additional” or “extra” compensation only if “the employment arrangement also includes a guarantee of at least the minimum weekly-required amount paid on a salary basis.”[49] Here, § 604(a) is inapplicable because, again, HR-IT did not pay Gentry and Taylor on a salary basis. And HR-IT’s argument requires that § 604(a) permit hourly compensation for hours worked during the normal work week. It does not. Section 604(a) allows, inter alia, “additional compensation based on hours worked for work beyond the normal workweek.”[50] A straight-forward reading of the text makes clear that § 604(a) does not envision hourly pay for work within the normal workweek. As the Department of Labor advanced, it would be “nonsensical for the Department [of Labor] to qualify the example of additional pay for hours worked—limiting it to time ‘beyond the normal workweek’—if pay for all or most of an employee’s hours within the normal workweek could also constitute ‘additional compensation’ under 604(a).”[51] Here, Plaintiffs’ hourly pay was for work performed during the workweek and impermissible under § 604(a). It is true that § 604(a) and (b) both permit employees to be paid by the hour (in some form) so long as the employer guarantees “at least the minimum weekly-required amount paid on a salary basis.”[52] However, there are two essential differences. First, § 604(a) expressly contemplates hourly compensation for work “beyond the normal workweek,” while § 604(b) concerns hourly compensation within “the employee’s normal scheduled workweek.”[53] Second, paragraph (b) requires there be a reasonable relationship between the guaranteed amount and the employee’s usual weekly earnings; paragraph (a) contains no such requirement. HR-IT’s argument—that § 604(a) allows hourly compensation for hours worked within the workweek—would vitiate the first distinction.[54] It would also effectively eliminate the second distinction, allowing employers to circumvent paragraph (b) by permitting the same compensation structure as paragraph (a) but without the reasonable relationship test. HR-IT’s interpretation impermissibly steps past the distinctions between § 604(a) and (b), and offers a runaround to paragraph (b)’s reasonable relationship test.[55] We cannot simply “cart[] § 604(b) off the stage” but must read sections 602(a), 604(a), and 604(b) in harmony.[56] While § 604(a) permits hourly compensation for work “beyond the normal workweek,” § 604(b) applies to hourly compensation for work within the normal workweek.[57] Plaintiffs’ hourly pay was for work performed during the workweek, rendering § 604(a) inapplicable. As such, § 604(a) does not save HR-IT’s payment plan. C. Because HR-IT paid Plaintiffs on an hourly basis, its payment scheme must comply with § 604. Section 604(b) recognizes that hourly-rate employees may be paid on a “salary basis” so long as “[1] the employment arrangement also includes a guarantee of at least the minimum weekly required amount paid on a salary basis regardless of the number of hours, days or shifts worked, and [2] a reasonable relationship exists between the guaranteed amount and the amount actually earned.”[58] The reasonable relationship test is satisfied so long as the “weekly guarantee is roughly equivalent to the employee’s usual earnings at the assigned hourly, daily or shift rate for the employee’s normal scheduled workweek.”[59] Department of Labor opinion letters advise that a 1.5 to 1 ratio of actual earnings to a guaranteed weekly salary satisfies this test.[60] HR-IT guaranteed Gentry and Taylor $984 and $1,200 per week, respectively, and these amounts were grossly disproportionate to Plaintiffs’ typical earnings. As detailed in Plaintiffs’ summary judgment brief: [O]n average, Plaintiff Terry Gentry worked 43.48 hours per week. The ratio between Plaintiff Terry Gentry’s average gross hourly earnings ($5,347.66) and the amount HRI purported to designate as “Guaranteed Weekly Salary” ($984.00) is 5.42-to-1. On average, Opt-in Plaintiff Marc Taylor worked 41.52 hours per week. The ratio between Opt-in Plaintiff Marc Taylor’s average gross hourly earnings ($6,228.57) and the amount HRI purported to designate as “Guaranteed Weekly Salary” ($1,200.00) is 5.19-to-1. Ratios of 5.42-to-1 and 5.19-to-1 are not roughly equivalent. We agree with the magistrate judge that “these numbers are far beyond what is considered reasonable.” Because HR-IT’s compensation structure fails the reasonable relationship test, Plaintiffs were not paid on a salary basis and were not exempt from FLSA protection. D. Our interpretation of sections 602(a), 604(a), and 604(b) is consistent with three pre-Helix decisions from the Second, Third, and Eighth Circuits. To the extent our interpretation is in tension with the Tenth Circuit’s recent decision in Wilson v. Schlumberger Technology Corp.,[61] we respectfully believe the Schlumberger court overlooked a key aspect of Helix. To start, both the Second and Eighth Circuits have upheld compensatory schemes wherein employees were assured an annual salary, whose weekly or biweekly pay was a portion of that salary based on the expected hours worked per week, and who received additional compensation for hours worked beyond the agreed-upon workweek.[62] In other words, they upheld compensation schemes that are markedly distinct from HR-IT’s, which provided a guaranteed weekly rate equivalent to one eight-hour workday and “additional compensation” for work performed during the workweek. Furthermore, these employees were paid a true weekly rate based upon their agreed-upon work schedule with their employer. As such, these practices are consistent with our understanding of sections 602(a) and 604(a), as discussed above. In Brock v. Claridge Hotel & Casino, the Third Circuit considered and rejected a pay scheme analogous to that here. In Brock, all employees with supervisory capacity were guaranteed a weekly salary of $250 and were paid by the hour once they reached the $250 minimum, which was typically within a few hours of work.[63] Finding that the guaranteed salary bore “no relation” to the supervisors’ typical week and the “additional” hourly compensation was dissimilar to the regulatory examples, the Third Circuit concluded the supervisors were not paid on a salary basis.[64] The Department of Regulations has cited this case several times when explaining the salary basis test.[65] We recognize that our conclusion may be in tension with the Tenth Circuit’s recent decision in Schlumberger, however, as the Tenth Circuit acknowledged in that case, Gentry is factually dissimilar[66] In Schlumberger, the Tenth Circuit found that a measurement-while-drilling operator was paid on a salary basis when he was guaranteed a xed, biweekly salary in addition to extra compensation for time spent on a drilling rig.[67] The court held that the employee was paid on a salary basis because he received the “same salary every week” which was “not based upon his hours, days, or shifts of work.[68] With all due respect to our sister circuit, we believe that Schlumberger overlooked the “antecedent” question in Helix: whether the salary, regardless of the frequency with which it was distributed, provided a true weekly rate.[69] In our view, Helix and sections 602(a), 604(a), and 604(b) require courts to take a hard look at whether a purported “salary” truly compensates employees for a week’s worth of work or, instead, provides an artificial distinction between a salary and additional compensation. As such, our holding is consistent with Helix, the regulatory text, and decisions from our sister circuits upholding salaries that—unlike HR-IT’s—paid employees a weekly rate.[70] IV. Next, we address HR-IT’s argument that the district court erred by awarding Plaintiffs liquidated damages and, specifically, by refusing to consider HR-IT’s new evidence regarding its good faith defense. When employers violate the FLSA, courts may award liquidated damages in an amount equal to actual damages.[71] Employers may defend themselves on the basis that they believed, in good faith, that their payment practices complied with the law.[72] However, the district court retains ample discretion to award liquidated damages even if employers demonstrate their good faith.[73] The magistrate judge recommended awarding Plaintiffs liquidated damages because HR-IT failed to demonstrate a good-faith basis for its wage practices. In its objections to the magistrate judge’s recommendation, HR-IT attempted to offer new evidence demonstrating its good-faith belief that it complied with the FLSA. In afirming the magistrate judge’s report, the district court refused to consider this new evidence because it had not been submitted to the magistrate judge and was thus “not properly before the court.” This was error. A district court may receive further evidence when considering objections to a magistrate judge’s recommendation[74] and “need not reject newly-proffered evidence simply because it was not presented to the magistrate judge.”[75] Thus, the district court erred to the extent it believed it could not review the new evidence. On remand, the district court may consider HR-IT’s proffered evidence. But we reafirm the well-established rule in this circuit that the decision to award liquidated damages remains within the discretion of the district court. V. We AFFIRM the district court’s judgment that Plaintiffs were not paid on a salary basis under either § 602(a) or § 604(b) and are not exempt from the FLSA’s protection. However, because the district court erred in concluding that it could not consider HR-IT’s new evidence regarding liquidated damages, we VACATE the judgment on liquidated damages and REMAND for reconsideration on this issue.