LIPEZ, Circuit Judge.

The Fair Labor Standards Act requires that non-exempt employees who work more than forty hours in a week must be paid overtime at a rate of at least one-and-a-half times their "regular rate" of pay. Plaintiffs in this case contend that their employer wrongly labeled part of their regular hourly wage a "per diem" and excluded the per diem when calculating the rate for overtime, thus depriving them of overtime pay. The proof, plaintiffs claim, is in the numbers. When they worked a full forty-hour week, the per diem and hourly wage added up to $60 per hour, the regular wage that they claimed they were promised when recruited. When plaintiffs worked less than forty hours in a week, the per diem payment was reduced. Plaintiffs contend that this scenario unmasked the scheme: the reductions show the per diem was tied to hours worked in a week and thus, in reality, was a shadow wage.

The district court granted summary judgment in favor of the employer after examining the company's formula for calculating the per diem. This disposition was erroneous. As we explain, the company's formula, as guidance from the Department of Labor puts it, was impermissibly "based upon and thus varie[d] with the number of hours worked" per week. Wage & Hour Div., Dep't of Labor, Field Operations Handbook § 32d05a(c) (1983). We therefore reverse the summary judgment for the employer and remand for entry of partial summary judgment in plaintiffs' favor as to liability.

I.

Plaintiffs Eric Newman and Nestor Patague both found engineering jobs in 2010 at a General Dynamics Land Systems plant in Woodbridge, Virginia, through Advanced Technology Innovation Corporation ("Advanced Technology"), a recruiting firm. The jobs required them to be away from their homes: Newman lived in West Virginia, about 65 miles away, and Patague lived in California. Although General Dynamics supervised plaintiffs and set their job tasks, they were paid by Advanced Technology.

Each plaintiff signed a consulting agreement and offer letter with Advanced Technology. Both agreements listed an hourly wage, an overtime rate more than one-and-a-half times that hourly wage, and a "per diem expense reimbursement" in light of their remote work assignments. Newman's agreement set his hourly wage at $35.32 per hour, overtime at $60 per hour, and a weekly per diem of no more than $987. Patague's agreement set his hourly wage at $42.37, overtime at $63.56, and a weekly per diem of no more than $705.

For the per diem, each plaintiff signed a Consultant Per Diem Certification that provided for reimbursement "for any business expenses on a per diem basis" using the relevant Internal Revenue Service Federal Travel Reimbursement rate. This rate was a maximum of $141 at the time of Newman's agreement.1 Newman was eligible for that per diem figure for "each day actually worked" up to seven days, with a per diem paid for Saturdays and Sundays "if work is actually performed on those days or performed on the immediate preceding client work day." Patague's agreement set the same per diem, but capped it at a weekly maximum of $705 for five days if each day was "actually worked."

Because a per diem either can be excluded from, or counted as, a regular wage depending on how it operates, plaintiffs assert that here the per diem operated like an hourly wage. The per diem, if calculated by the hour, was about $24.68 for Newman and $17.63 for Patague. These figures made up the difference between the regular rate in each plaintiff's contract and the supposedly promised hourly figure of $60 ($35.32 + $24.68 for Newman; $42.37 + $17.63 for Patague). Plaintiffs contend the per diem should count as part of the regular wage, and thus they should have been paid at least one-and-a-half times this wage for overtime, meaning at least $90 per hour.

Newman worked for Advanced Technology from May 2010 until July 2011; Patague worked for the company from November 2010 until April 2011. In January 2012, plaintiffs filed suit in the Eastern District of Virginia, alleging that the company violated 29 U.S.C. § 207(a)(1)-(2) by failing to pay the required overtime rate. After the case was transferred to the District of Massachusetts, Advanced Technology moved for summary judgment and plaintiffs moved for partial summary judgment as to liability.

At oral argument and in its opinion, the district court focused on Advanced Technology's formula for the per diem payment when plaintiffs did not work forty hours in one week. There were eight such weeks for Newman, and three for Patague. Those weeks were particularly important because they could shed light on the formula for prorating the per diem and, consequently, on whether the per diem varied simply by hours worked. An affidavit from Anthony Calisi, chairman and treasurer of Advanced Technology, described the formula used.2 Citing this affidavit, the district court held that Calisi's explanation "disapproves Plaintiffs' contention that the per diem was calculated simply by multiplying the number of hours worked in a week" by an hourly "per diem" supplement. Further, the court noted that plaintiffs' proposed hourly value for the per diem "only arrives at the actual payment amount on certain weeks." The district court thus held that Advanced Technology "properly paid Plaintiffs' overtime based upon the hourly rates to which they agreed in the contract, and paid per diem rates provided in the federal travel regulations that reasonably approximated work-related expenses."

On appeal, plaintiffs again press their argument that the company tied the per diem to hours worked. They seek reversal of the summary judgment in Advanced Technology's favor and entry in their favor on liability, with a remand for proceedings to assess damages. They offer two other theories of liability, both of which we do not reach because we agree with plaintiffs on their central argument.

II.

We review the district court's grant of summary judgment de novo. One Nat'l Bank v. Antonellis, 80 F.3d 606, 608 (1st Cir.1996). Summary judgment is appropriate when "the movant shows that there is no genuine dispute as to any material fact and the movant is entitled to judgment as a matter of law." Fed. R.Civ.P. 56(a). "A fact is material if it carries with it the potential to affect the outcome of the suit under the applicable law." Antonellis, 80 F.3d at 608 (internal quotation marks omitted).

A. Legal Framework

1. Statutes And Regulations

The Fair Labor Standards Act ("FLSA"), 29 U.S.C. §§ 201-219, requires that when non-exempt employees work more than forty hours in a work week, they must be paid for overtime hours at a rate of at least one-and-a-half times the "regular rate" of pay. Id. § 207(a)(1).3 The regular rate includes "all remuneration for employment paid to, or on behalf of, the employee." Id. § 207(e). This general rule has exceptions, see id. § 207(e)(1)-(8), which "are to be interpreted narrowly against the employer, and the employer bears the burden of showing that an exception applies." O'Brien v. Town of Agawam, 350 F.3d 279, 294 (1st Cir.2003) (citation omitted).

As is relevant here, the regular rate does not include "reasonable payments for traveling expenses, or other expenses, incurred by an employee in the furtherance of his employer's interests and properly reimbursable by the employer; and other similar payments to an employee which are not made as compensation for his hours of employment." 29 U.S.C. § 207(e)(2) (emphasis added). A regulation interpreting Section 207(e) provides examples of payments that "will not be regarded as part of the employee's regular rate." 29 C.F.R. § 778.217(b). These include amounts "expended by an employee, who is traveling `over the road' on his employer's business, for transportation ... and living expenses away from home," id. § 778.217(b)(3), "`[s]upper money' ... to cover the cost of supper when he is requested by his employer to continue work during the evening hours," id. § 778.217(b)(4), and expenses incurred "because the employee, on a particular occasion, is required to report for work at a place other than his regular workplace," id. § 778.217(b)(5). By contrast, the employer's payments for "expenses normally incurred by the employee for his own benefit," such as "buying lunch, paying rent, and the like," are included in the regular rate. Id. § 778.217(d).

"[T]he regular rate cannot be stipulated by the parties; instead, the rate must be discerned from what actually happens under the governing employment contract." O'Brien, 350 F.3d at 294 (citing Bay Ridge Operating Co. v. Aaron, 334 U.S. 446, 462-63, 68 S.Ct. 1186, 92 L.Ed. 1502 (1948)). Thus, the regular wage rate here is a fact question. See Bay Ridge, 334 U.S. at 461, 68 S.Ct. 1186 ("`The regular rate by its very nature must reflect all payments which the parties have agreed shall be received regularly during the workweek, exclusive of overtime payments. It is not an arbitrary label chosen by the parties; it is an actual fact.'" (quoting Walling v. Youngerman-Reynolds Hardwood Co., 325 U.S. 419, 424, 65 S.Ct. 1242, 89 L.Ed. 1705 (1945))).

2. Department of Labor Handbook

The Department of Labor Wage and Hour Division's Field Operations Handbook ("Handbook") contains further guidance, which we treat as persuasive authority. See Gagnon v. United Technisource, Inc., 607 F.3d 1036, 1041 n. 6 (5th Cir.2010) ("Although the Handbook does not bind our analysis, we can and do consider its persuasive effect." (citing Skidmore v. Swift & Co., 323 U.S. 134, 140, 65 S.Ct. 161, 89 L.Ed. 124 (1944))). Both parties focus their arguments on Section 32d05a(c) of the Handbook. That paragraph states in full:

There is seemingly some tension in the Handbook's guidance. On the one hand, the passage notes that it is a permissible result for an employer to reduce a day's per diem, such as by paying half of a day's worth of per diem where an employee worked for half of the day. Yet it also states that the per diem is part of the regular rate of pay if it is based upon, and varies with, hours worked in a week or day. In an eight-hour workday, paying an employee half of a day's per diem yields the same result as paying for four hours' worth of per diem.

This coincidence suggests that the Handbook's concern is not the result of paying half of a day's per diem, which is by itself innocuous. Instead, the Handbook's teaching is that the method of calculating the per diem in that circumstance must use a day as its measuring unit, and not an hour. Breaking a day into two segments to reflect the presumably common practice of an early departure at week's end is not the same as paying only a portion of the maximum weekly per diem based precisely on the time worked during the week. If the per diem method makes reductions from that maximum on an hourly basis — such that it would reduce the total per diem by a mere hour's worth — it runs afoul of the Handbook's guidance.

B. Applicability to the Summary Judgment Record

The key to this case is the comparison between how Advanced Technology says it reduces per diem payments and the actual formula it used. The comparison makes clear that not only was summary judgment wrongly entered in the company's favor, but in fact plaintiffs must prevail on partial summary judgment as to liability.

Advanced Technology contends that it reduced the per diem only when the shortfall below forty hours worked was entirely attributable to an early end of the work week. Anthony Bonanno, the company's president, asserted in an affidavit that in "those weeks when [plaintiffs] reported that they did not work a full week, and worked less than a full day on the last work day ... then ... Advanced Technology paid the [p]laintiffs a [prorated] amount of that day's per diem expense reimbursement." The company further insists that these reductions were not based on hours worked.

Despite this claim that it complied with the Handbook, the description of the formula from company treasurer Anthony Calisi makes clear that the only factor that mattered in calculating the weekly per diem was the number of hours worked. Recognizing that "a full week traditionally means working a full forty (40) hours," Calisi explained that for Newman the company:

As Calisi's explanation indicates, the "fractional number of days worked" is the measure of how many days' worth of per diem the plaintiff should receive. This measure is determined by the only variable in the formula, the total number of hours worked in the week. All other numbers are fixed: forty hours in a work week, five available days of per diem for Patague or seven for Newman, and $141 for the value of the per diem. In this formula of straightforward division and multiplication, a reduction to the per diem is necessarily hours-based.

Indeed, in the most glaring example, the company reduced Newman's per diem for one week to reflect that he would receive only 38.5-hours' worth of per diem. Further, because the company's formula uses hours, not days, as its frame of reference, an employee who worked for seven hours in a day, in a five-day work week, could accrue less than the $141 daily per diem through the formula, while an employee who worked for 12 hours in a day could accrue more than the $141 daily per diem. Yet in both circumstances the employees must receive no less, and no more, than the day's $141 per diem if the reimbursement formula is based on days and not hours. For these reasons, even in those instances where Advanced Technology reduced the per diem only for an early end to the week, the reductions remain precisely tied to the total hours worked in the week.4

In rejecting plaintiffs' claim that the per diem was hourly, the district court noted that plaintiffs' proposed "hourly per diem" figures did not yield results that quite matched the weekly pay statements in the record. That is true, but only because the company's formula rounded at an intermediate step of the calculations, thereby slightly altering the final number. Plaintiffs furthered the confusion by offering rounded figures at times for the proposed hourly per diem rates — $24.68 for Newman and $17.63 — rather than the precise figures of $24.675 and $17.625 respectively. If neither plaintiffs' hourly figures nor Advanced Technology's "fractional number of days worked" were rounded, both formulas yield the same per diem results for all the weeks where plaintiffs were paid less than the full per diem.5 In short, each side's rounding made the calculations harder to recreate. But once these rounding steps are identified, it becomes clear that Advanced Technology's formula neatly falls within the Handbook's concern: it is "based upon and thus varies with the number of hours worked per day or week," Handbook § 32d05a(c).

III.

The animating concern of the FLSA statutes, regulations, and DOL Handbook is to examine the substance of a purported per diem payment and to ensure that it is actually used to offset expenses an employee incurs due to time spent away on the employer's business. The goal is to pierce the labels that parties affix to the payments and instead look to the realities of the method of payment. Here, even if Advanced Technology reduced the per diem only for an early end to the work week, it still based those reductions on the exact number of hours worked in the week. The reduction of one-and-a-half hours of per diem for one week for Newman, described above, illustrates this approach. Although the Handbook provision allows a discount in the per diem for partial days, it does not permit an employer to set this discount as a reduction of a fixed amount for each missing hour in the weekly total. We see no material dispute of fact once the formula is examined, and thus the correct outcome is partial summary judgment in plaintiffs' favor as to liability.6

Specifically, we reverse the district court's decision to grant summary judgment for Advanced Technology and remand for the court to enter partial summary judgment in plaintiffs' favor as to liability, and then to conduct further proceedings as to damages.

So ordered.