LARSEN, Circuit Judge.

ARGUED: Daniel J. Clark, VORYS, SATER, SEYMOUR AND PEASE LLP, Columbus, Ohio, for Appellants/Cross-Appellees. Gary L. Greenberg, JACKSON LEWIS P.C., Cincinnati, Ohio, for Appellee/Cross-Appellant. Michael J. Prame, GROOM LAW GROUP, CHARTERED, Washington, D.C., Yaakov M. Roth, JONES DAY, Washington D.C., for Amici Curiae. ON BRIEF: Daniel J. Clark, Allen S. Kinzer, Daniel E. Shuey, VORYS, SATER, SEYMOUR AND PEASE LLP, Columbus, Ohio, for Appellants/Cross-Appellees. Gary L. Greenberg, Mark B. Gerano, JACKSON LEWIS P.C., Cincinnati, Ohio, for Appellee/Cross-Appellant. Michael J. Prame, GROOM LAW GROUP, CHARTERED, Washington, D.C., Yaakov M. Roth, JONES DAY, Washington D.C., Adam G. Unikowsky, JENNER & BLOCK LLP, Washington, D.C., Andrew M. Johnstone, US FOODS, INC., Rosemont, Illinois, Thomas W.H. Barlow, KOSTOPOULOS RODRIGUEZ, PLLC, Birmingham, Michigan, Gregory J. Ossi, FAEGRE DRINKER BIDDLE & REATH LLP, Washington, D.C., Kathleen Keller, BREDHOFF & KAISER, P.L.L.C., Washington, D.C., Ronald L. Mason, Aaron T. Tulencik, MASON LAW FIRM CO., LPA, Dublin, Ohio, Brendan Collins, GKG LAW, P.C., Washington, D.C., Paul A. Green, MOONEY, GREEN, SAINDON, MURPHY & WELCH P.C., Washington, D.C., for Amici Curiae.

Before: COOK, GRIFFIN, and LARSEN, Circuit Judges.

LARSEN, J., delivered the opinion of the court in which COOK, J., joined, and GRIFFIN, J., joined in all but Part IV. GRIFFIN, J. (pp. 434-35), delivered a separate opinion concurring in part and dissenting in part.

LARSEN, Circuit Judge.

Sofco Erectors, Inc. terminated its collective bargaining agreement with a local union. The Ohio Operating Engineers Pension Fund then assessed almost a million dollars in withdrawal liability against Sofco under the Employee Retirement Income Security Act (ERISA). Sofco challenged the assessment on several grounds in ERISA-mandated arbitration. The arbitrator upheld the assessment, but the district court affirmed in part and reversed in part. The Fund appealed, and Sofco cross-appealed. For the reasons that follow, we AFFIRM in part, REVERSE in part, VACATE in part, and REMAND for further proceedings.

I. Background

A. Legal Background

Through ERISA, Congress created a comprehensive statutory scheme to regulate private pension plans. Nachman Corp. v. PBGC , 446 U.S. 359, 361–62, 100 S.Ct. 1723, 64 L.Ed.2d 354 (1980) (citing 29 U.S.C. § 1001(a) ). Informed by nearly a decade of research, id . at 361, 100 S.Ct. 1723, ERISA established reporting and disclosure requirements, 29 U.S.C. § 1021 ; minimum funding standards, id. § 1082; fiduciary duties, id. § 1104; and plan termination insurance, id. §§ 1322, 1322a. It also established the Pension Benefit Guaranty Corporation (PBGC), an administrative agency under the Department of Labor that manages the plan termination insurance program. See id. § 1302; PBGC v. LTV Corp. , 496 U.S. 633, 637, 110 S.Ct. 2668, 110 L.Ed.2d 579 (1990).

ERISA differentiates between single-employer and multiemployer pension plans. See 29 U.S.C. § 1002(41). Multiemployer plans are "maintained pursuant to one or more collective bargaining agreements," "to which more than one employer is required to contribute." Id. § 1002(37)(A)(i), (ii). These plans provide benefits for union members who work for employers in the same industry. See PBGC, Introduction to Multiemployer Plans , https://www.pbgc.gov/prac/multiemployer/introduction-to-multiemployer-plans (Sept. 13, 2021). Employees do not sacrifice pension benefits by working for multiple employers because service for any contributing employer is credited by the plan. Concrete Pipe & Prods. of Cal., Inc. v. Constr. Laborers Pension Tr. for S. Cal. , 508 U.S. 602, 605–06, 113 S.Ct. 2264, 124 L.Ed.2d 539 (1993). A board of trustees administers these plans. Participating unions select half of the board's members; contributing employers select the other half. Connolly v. PBGC , 475 U.S. 211, 232, 106 S.Ct. 1018, 89 L.Ed.2d 166 (1986) (O'Connor, J., concurring).

ERISA requires that multiemployer pension funds prepare annual financial reports and actuarial valuations. E.g. , 26 U.S.C. § 6059 ; 29 U.S.C. § 1023. The funds must also meet minimum-funding standards. 26 U.S.C. §§ 412, 431 ; 29 U.S.C. §§ 1082, 1084. If they do not, contributing employers are subject to a tax. 26 U.S.C. § 4971. In addition, funds become subject to certain rehabilitation requirements if their funding levels are too low. See id. § 432.

In the late 1970s, Congress directed the PBGC to report on the challenges of insuring multiemployer pension plans and to propose legislative solutions. PBGC v. R.A. Gray & Co. , 467 U.S. 717, 721, 104 S.Ct. 2709, 81 L.Ed.2d 601 (1984) ; S. Rep. No. 95-570, at 7 (1977). The PBGC found that ERISA did not adequately protect multiemployer plans from individual employer withdrawals. R.A. Gray , 467 U.S. at 722, 104 S.Ct. 2709 ; PBGC, Multiemployer Study Required by P.L. 95–214, at 95 (1978). As the Supreme Court noted:

A key problem of ongoing multiemployer plans, especially in declining industries, is the problem of employer withdrawal. Employer withdrawals reduce a plan's contribution base. This pushes the contribution rate for remaining employers to higher and higher levels in order to fund past service liabilities, including liabilities generated by employers no longer participating in the plan, so-called inherited liabilities. The rising costs may encourage—or force—further withdrawals, thereby increasing the inherited liabilities to be funded by an ever decreasing contribution base. This vicious downward spiral may continue until it is no longer reasonable or possible for the pension plan to continue.

Connolly , 475 U.S. at 216, 106 S.Ct. 1018 (quoting Pension Plan Termination Insurance Issues: Hearings before the Subcomm. on Oversight of the H. Comm. on Ways and Means , 95th Cong., at 22 (1978) (statement of Matthew M. Lind)). Thus, the PBGC recommended imposing withdrawal liability on employers leaving multiemployer plans, requiring them to pay for their "fair share of the plan's unfunded liabilities." R.A. Gray , 467 U.S. at 723 & n.3, 104 S.Ct. 2709 (quoting Lind at 23). This would both discourage withdrawals and protect plans from their negative financial effects. Connolly , 475 U.S. at 217, 106 S.Ct. 1018. Congress incorporated these recommendations into the Multiemployer Pension Plan Amendments Act (MPPAA), Pub. L. 96-364, 94 Stat 1208, 29 U.S.C. §§ 1381 – 1461, which became law on September 26, 1980. Concrete Pipe , 508 U.S. at 609, 113 S.Ct. 2264.

The MPPAA imposes liability for complete and partial withdrawals from multiemployer pension plans. See 29 U.S.C. §§ 1383, 1385. But Congress designed special rules for the construction industry because its work often fluctuates and is done on a project-by-project basis. See id. §§ 1383(b), 1388(d) ; see also Definition of "Building and Construction Industry," 47 Fed. Reg. 42588-02, 1982 WL 132214 (proposed Sept. 28, 1982). When a construction employer stops contributing to a plan (for example, because its project is over), the plan's contribution base does not necessarily decline in response; the workers employed by the withdrawing construction firm are often hired for other projects by other contributing employers. H.C. Elliott, Inc. v. Carpenters Pension Tr. Fund for N. Cal. , 859 F.2d 808, 811 (9th Cir. 1988). The plan is not threatened as long as contributions continue to be made for work done in that area. Id. at 812. Thus, the construction industry rules focus on whether the employer, though no longer contributing to the plan, continues to perform work for which contributions were previously required. Id. Only then is withdrawal liability imposed. See id. ; 29 U.S.C. § 1383(b)(2).

Lastly, through ERISA and the MPPAA, Congress has established a comprehensive scheme for assessing and challenging an assessment to withdrawal liability. Concrete Pipe , 508 U.S. at 609, 113 S.Ct. 2264. When an employer withdraws from a multiemployer plan, the plan sponsor is responsible for assessing withdrawal liability and sending the employer a demand for payment. 29 U.S.C. §§ 1382, 1399. The plan sponsor is the organization that establishes and maintains the plan. Id. § 1002(16)(B). Here, the sponsor is the Ohio Operating Engineers Pension Fund (the Fund). Withdrawal liability is calculated by professional actuaries who must use "actuarial assumptions and methods which, in the aggregate, are reasonable (taking into account the experience of the plan and reasonable expectations) and which, in combination, offer the actuary's best estimate of anticipated experience under the plan." Id. § 1393(a)(1). If the employer disagrees with the assessment, it can request that the plan review it. Id. § 1399(b)(2)(A).

ERISA prohibits employers from challenging a plan's assessment directly in federal court; the plan and the employer must arbitrate their disputes first and then appeal the arbitrator's decision. Id. § 1401(a)(1), (b)(2). The arbitrator must presume that the plan sponsor's factual determinations are correct unless the employer disproves a determination by a preponderance of the evidence. Id. § 1401(a)(3)(A); Sherwin-Williams Co. v. N.Y. State Teamsters Conf. Pension & Ret. Fund , 158 F.3d 387, 392 (6th Cir. 1998) (citing Concrete Pipe , 508 U.S. at 629, 113 S.Ct. 2264 ). To challenge an actuary's calculation of withdrawal liability, the employer must show "that the actuarial assumptions and methods used in the determination were, in the aggregate, unreasonable (taking into account the experience of the plan and reasonable expectations), or the plan's actuary made a significant error in applying the actuarial assumptions or methods." 29 U.S.C. § 1401(a)(3)(B). On review in federal court, "there shall be a presumption, rebuttable only by a clear preponderance of the evidence, that the findings of fact made by the arbitrator were correct." Id. § 1401(c).

B. Factual and Procedural History

Sofco Erectors, Inc. is a building company that erects steel and precast for commercial buildings and hospitals. It works in parts of Ohio, Kentucky, and Indiana. It began operations on April 1, 2004, when the company owners purchased the assets of its predecessor, also called Sofco Erectors, Inc. (Old Sofco). The owners of Sofco worked at Old Sofco but did not own any part of it. Sofco did not assume any of Old Sofco's obligations or liabilities.

Sofco has signed collective bargaining agreements (CBAs) with several unions. It has agreements with three different local chapters of the International Association of Bridge, Structural, Ornamental, and Reinforcing Iron Workers (Ironworkers). It also had an agreement with the International Union of Operating Engineers, Local 18 (Local 18). Sofco hired Local 18 primarily to operate cranes, both those owned by Sofco and those rented from other companies.

Sofco terminated its CBA with Local 18, effective April 28, 2017, largely because of disagreements over Sofco's assigning of forklift work to the Ironworkers. The Fund then assessed withdrawal liability against Sofco for $824,300: complete-withdrawal liability of $368,315 for the plan year ending July 31, 2017; partial-withdrawal liability of $344,627 for the plan year ending July 31, 2011; and partial-withdrawal liability of $111,358 for the plan year ending July 31, 2012. It also found that a partial withdrawal had occurred for the plan year ending July 31, 2013, but that the liability for that year was $0. Following the Fund's demand for payment, Sofco requested review of the determination. After the Fund failed to respond to Sofco's request, Sofco initiated arbitration. See 29 U.S.C. § 1401(a)(1). Sofco began making quarterly payments, as required, on October 18, 2017, and paid its balance on October 17, 2019. See id. § 1399(c).

In arbitration, Sofco and the Fund filed cross motions for summary judgment. The arbitrator granted summary judgment in the Fund's favor on all issues. He determined that the forklift work and shop work Sofco disputed were in Local 18's jurisdiction and that Sofco was required to contribute to the fund for that work; that the Fund had properly assessed complete-withdrawal liability; that the Fund properly assessed partial-withdrawal liability because Sofco's contributions dropped to an "insubstantial" level; that the Fund had properly included the contribution history of Sofco's predecessor in its withdrawal-liability calculations; and that the interest rate the Fund had used to calculate withdrawal liability was reasonable.

Sofco filed a complaint seeking to vacate or modify the arbitration award in federal court. The Fund moved to enforce the award, and Sofco moved for summary judgment. The district court granted summary judgment in favor of Sofco on two issues. First, it held that Sofco was not required to make contributions for shop work. Sofco Erectors, Inc. v. Trs. of the Ohio Operating Eng'rs Pension Fund , No. 2:19-cv-2238, 2020 WL 2541970, at *7–8 (S.D. Ohio May 19, 2020). Second, it held that, although the interest rate used by the Fund to calculate withdrawal liability need not always be the same as that used for minimum funding purposes, the interest rate used here was unreasonable because it was not the actuary's "best estimate of the anticipated experience under the plan." Id. at *8–10 ; see 29 U.S.C. § 1393(a)(1).

But the district court upheld the arbitrator's determination and granted the Fund's motion to enforce on three issues: that forklift work was properly included in the Fund's withdrawal determination, Sofco , 2020 WL 2541970, at *7 ; that it was proper for the Fund to include Old Sofco's contribution history in its calculations, id. at *10 ; and that the Fund had properly determined that Sofco's contributions fell to an "insubstantial" level, thus triggering partial-withdrawal liability, id. at *10–11. Both parties moved for attorney's fees. Because "this was a close case" and "both parties [ ] prevailed on issues," the court denied both motions. Id. at *11–12.

The Fund appealed the district court's order, and Sofco cross-appealed.

II. Standard of Review

We review a district court's grant of summary judgment de novo. Cent. States, Se. & Sw. Areas Pension Fund v. Int'l Comfort Prods., LLC , 585 F.3d 281, 284 (6th Cir. 2009). Summary judgment is appropriate where "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). We presume that findings of fact made by the arbitrator are correct unless the challenging party can disprove them by a preponderance of the evidence. 29 U.S.C. § 1401(c). We review questions of law de novo. Sherwin-Williams , 158 F.3d at 393 ; see also Concrete Pipe , 508 U.S. at 630, 113 S.Ct. 2264.

III. The Interest Rate

The primary dispute in this case is the propriety of the interest rate assumption the Fund used to calculate withdrawal liability. Multiemployer plans are considered "defined benefit plans." See Concrete Pipe , 508 U.S. at 607, 113 S.Ct. 2264. Such plans guarantee a certain monthly benefit, determined by a formula established by the plan, payable to beneficiaries for the rest of their lives. Pension Rev. Bd., Understanding the Basics of Actuarial Methods 2 (April 2013), https://www.prb.texas.gov/txpen/wp-content/uploads/2019/11/finalbasicsofactmethod.pdf. Employer contributions to the plan are dictated by the terms of the CBAs to which it is a party. PBGC, Introduction to Multiemployer Plans. For example, an employer might be required to contribute a specific dollar amount per hour of hired labor. Id.

Pension funds hire actuaries to prepare annual reports and calculate funding levels and withdrawal liability. E.g. , 26 U.S.C. §§ 431, 6059 ; 29 U.S.C. §§ 1023, 1084, 1393. Generally, employer contributions plus the income generated from them need to be sufficient to pay future benefits and cover administrative expenses. See Pension Rev. Bd., Basics of Actuarial Methods at 2. Determining a fund's future liabilities, or how much it will have to pay out in benefits, requires actuaries to make assumptions about how many employees will vest their benefits, how much they will receive in benefits, and how long they will live. See id. at 2, 4–5, 10–12. Once an actuary determines how much the fund will need to spend on benefits payments and administrative costs, it must determine the present value of future liabilities—how much the fund needs in assets today in order to pay those liabilities in the future. See id. at 2, 4–6. This requires the actuary to make certain assumptions about the income the assets will generate. See id. at 4–5; see also Nat'l Ret. Fund v. Metz Culinary Mgmt., Inc. , 946 F.3d 146, 148 (2d Cir. 2020). If the actuary assumes that the fund's investments will have a higher long-term growth rate, then the fund will not need as many assets today to pay liabilities in the future. Pension Rev. Bd., Basics of Actuarial Methods , at 4–5. However, if the actuary assumes a lower long-term growth rate, the fund will need more assets now to pay those liabilities in the future (and thus may have to take in more money through contributions). Id. The actuary must then compare the present value of future liabilities (how much money do we need?) to the current assets in the fund (how much money do we have?). See Metz , 946 F.3d at 147–48 (citing R.A. Gray , 467 U.S. at 725, 104 S.Ct. 2709 ). This can be done by looking at the market value of those assets. Pension Rev. Bd., Basics of Actuarial Methods , at 6; R.A. Gray , 467 U.S. at 725, 104 S.Ct. 2709. If the fund has less money than it needs, then there is an unfunded liability. See Pension Rev. Bd., Basics of Actuarial Methods , at 7; R.A. Gray , 467 U.S. at 725, 104 S.Ct. 2709. The interest-rate assumption is a critical factor in determining the present value of future liabilities. The higher the interest rate, the less money the fund needs today to pay liabilities in the future. The lower the interest rate, the more money the fund needs today.

The interest-rate assumption is also critical to minimum-funding calculations. Minimum-funding standards require pension funds to have a certain amount of assets to pay their future liabilities. See 26 U.S.C. §§ 412, 431 ; 29 U.S.C. §§ 1082, 1084. As mentioned above, when funds fall below certain funding levels, employers contributing to the fund may be taxed or face other regulatory burdens. See 26 U.S.C. § 4971. For minimum-funding purposes, a higher interest-rate assumption is more favorable for the fund because it makes it easier to meet minimum-funding standards.

The interest-rate assumption is critical in withdrawal-liability calculations too. A lower interest rate garners a higher unfunded liability. Because employers withdrawing from funds must pay a proportionate amount of the unfunded liability, see R.A. Gray , 467 U.S. at 725, 104 S.Ct. 2709, a lower interest-rate assumption results in higher withdrawal liability. For withdrawal-liability purposes, a lower interest-rate assumption is more favorable for the fund.

A. The Fund's Calculations

Here, the Fund's actuary used a 7.25% growth rate on assets for minimum funding purposes. But for withdrawal-liability purposes, the actuary used the "Segal Blend," which takes the interest rate used for minimum-funding purposes and "blend[s]" it with the PBGC's published interest rates on annuities. The PBGC publishes interest rates on annuities because, in certain circumstances, pension funds are required to purchase annuities to cover promised benefits. 29 U.S.C. § 1341a(c)(2). Here, the PBGC rates were in the range of 2–3%.

The arbitrator upheld the actuary's use of the Segal Blend, finding that it was "in the aggregate, reasonable." He also noted that using this blend reflected "accepted actuarial practice" and was in accordance with PBGC Opinion Letter 86-24, which concluded that ERISA does not require that the same actuarial assumptions be used in withdrawal-liability and minimum-funding calculations. The district court overturned the arbitrator's decision. Sofco , 2020 WL 2541970, at *10. It held that while using two different interest rates was not per se unlawful, the actuary's use of the Segal Blend here violated ERISA because it did not comport with the statute's command that the interest rate assumption be the "actuary's best estimate of [the] anticipated experience under the plan." 29 U.S.C. § 1393(a)(1) ; see Sofco , 2020 WL 2541970, at *9–10.

What is acceptable under ERISA and controlling Supreme Court caselaw is a question of law that we review de novo. Wilson v. Safelite Grp., Inc. , 930 F.3d 429, 433 (6th Cir. 2019).

B. ERISA and The Segal Blend

Sofco raises two principal challenges to the Fund's assessment of withdrawal liability. First, it argues that both ERISA and the Supreme Court's decision in Concrete Pipe forbid the actuary from using one interest rate for minimum funding purposes and another to calculate withdrawal liability. It points to the fact that the statutory directions for calculating minimum funding are almost identical to the language directing calculation of withdrawal liability; the actuary must use "actuarial assumptions and methods, each of which is reasonable (taking into account the experience of the plan and reasonable expectations) and which, in combination, offer the actuary's best estimate of anticipated experience under the plan ." 26 U.S.C. § 431(c)(3) ; 29 U.S.C. § 1084(c)(3) (emphasis added). In both contexts, Congress required that the actuary's estimate be based on the "anticipated experience under the plan." It also argues that the Supreme Court in Concrete Pipe upheld ERISA's statutory presumptions in favor of the actuary in large part because this textual requirement limits the actuary's discretion by requiring that the same assumptions be used in both contexts. Second, Sofco argues that, even if the interest rates could be different, the interest rate used to calculate withdrawal liability here did not comport with the statute because it was not based on the actuary's "best estimate of anticipated experience under the plan." See 29 U.S.C. § 1393(a)(1). Because we agree with Sofco on the second point, we need not decide the first.

ERISA says that an actuary calculating withdrawal liability must use "actuarial assumptions and methods which, in the aggregate, are reasonable (taking into account the experience of the plan and reasonable expectations) and which, in combination, offer the actuary's best estimate of anticipated experience under the plan ." Id. (emphasis added). The statute allows the PBGC to promulgate regulations requiring alternative assumptions or methods for calculating withdrawal liability, but the agency has not done so. Id. § 1393(a)(2) ; see also 29 C.F.R., Subtitle B, Chapter XL, Subchapter I. The default rule of § 1393(a)(1) therefore applies: the actuary's estimate must be based on the "anticipated experience under the plan." The actuary's use of the Segal Blend fails for this very reason.

The Segal Blend is a weighted blend of the interest rate used for minimum-funding purposes and annuity rates published by the PBGC. The PBGC rates are used to determine the present value of future liabilities for plans that are terminated by a "mass withdrawal," which occurs when all employers completely withdraw from a multiemployer plan. Id. §§ 1383(b)(3), 1341a(a)(2), 1441(b); 29 C.F.R. § 4281.13(a) (2021) ; see also PBGC, ERISA 4044 Annuities , https://www.pbgc.gov/prac/interest/ida (Sept. 15, 2021). When a plan undergoes a mass withdrawal, the plan must purchase annuities to cover the promised benefits unless the plan assets can be distributed "in full satisfaction" of all covered benefits. 29 U.S.C. § 1341a(c)(2).

Using the Segal Blend here violates the statute because the resulting interest rate is not "the actuary's best estimate of anticipated experience under the plan." Id. § 1393(a)(1). Rather, it dilutes the actuary's best estimate with rates on investments that the plan is not required to and might never buy, based on a set formula that is not tailored to "the unique characteristics of the plan." Bd. of Trs., Mich. United Food & Com. Workers Unions v. Eberhard Foods, Inc. , 831 F.2d 1258, 1263 (6th Cir. 1987). An actuary using the Segal Blend is factoring in an interest rate used for plans that essentially go out of business, even though these plans are neither going out of business nor required to purchase annuities to cover the departing employer's share of vested benefits.

That's what happened in this case. The actuary testified that the 7.25% interest rate he used for minimum-funding purposes was based on "past experiences and future expectations taking into account the plan's asset allocation and expected returns." But when testifying that the Segal Blend was his "best estimate calculation basis," the actuary explained that "the way you settle up a multiemployer pension plan is by using those—is by doing an annuity purchase on behalf of all the participants, and the interest rates published by PBGC approximate annuity purchase rates." In other words, the actuary justified the rate used for withdrawal liability by considering a hypothetical mass withdrawal, rather than the "anticipated experience under the plan," 29 U.S.C. § 1393(a) ; by looking to assets that the fund has not indicated it will ever purchase, rather than the fund's actual portfolio, see Eberhard Food , 831 F.2d at 1263 ; and by factoring in rates mandated by the PBGC in other contexts, but not here, instead of looking at the "experience of the plan and reasonable expectations," 29 U.S.C. § 1393(a). While the actuary's true "best estimate" deserves deference, it must be his "best estimate of anticipated experience under the plan."

The Fund defends the use of the Segal Blend on three grounds. It begins by directing us to Rhoades, McKee & Boer v. United States , 43 F.3d 1071 (6th Cir. 1995). There, we described the "best estimate" language as being "procedural," not "substantive." Id. at 1075. And in so doing, the Fund argues, we stripped the statute's requirement that actuaries base their estimates on the "anticipated experience under the plan" of any limiting force.

The Fund misunderstands Rhoades . There, we held that language identical to that used in § 1393(a)(1) "establishes a two-part test for actuarial assumptions: (1) they must be reasonable; and (2) they must be the actuary's best estimate." Id. at 1073. The government in that case had challenged the actuary's assumptions as "too conservative." Id. at 1074. Relying on out-of-circuit caselaw, we described the "best estimate" requirement as procedural and said that it "does not place a second substantive hurdle in the path of actuarial assumptions." Id. at 1075. Thus, the "best estimate" requirement is not aimed at coming up with the most "accura[te] ... predictive calculation." Vinson & Elkins v. Comm'r of Internal Revenue , 7 F.3d 1235, 1239 (5th Cir. 1993). The actuary's estimate does not need to withstand the scrutiny of "outside experts" who suggest a different figure is "best." See Rhoades , 43 F.3d at 1074 ; Vinson & Elkins , 7 F.3d at 1238. Rather, it serves "principally" to "[e]nsure that the chosen assumptions actually represent the actuary's own judgment rather than the dictates of plan administrators or sponsors." Rhoades , 43 F.3d at 1075 (quoting Wachtell, Lipton, Rosen & Katz v. C.I.R. , 26 F.3d 291, 296 (2d Cir. 1994) ). If they do, the court will not "second-guess" those assumptions on the ground that some other assumptions might have been better. See id. at 1074 (quoting Vinson & Elkins , 7 F.3d at 1238 ). This enables "actuaries to incorporate a degree of conservatism in their estimates," " ‘provided the chosen assumption is the actuary's best estimate of anticipated plan experience.’ " Id. at 1075 (quoting Wachtell , 26 F.3d at 296 ) (emphasis added).

The proviso is important. Nothing in our cases suggests that actuaries may disregard the statute's requirement that they base their estimates on the "anticipated experience under the plan." 29 U.S.C. § 1393(a)(1). "[T]he statutory scheme contemplates that the actuary will be determining an interest rate based on the unique characteristics of the plan—not dictating the future investment portfolio of the plan." Eberhard Food , 831 F.2d at 1263. While "an element of conservatism [may be] appropriate in the selection of actuarial assumptions ... factoring in a discount for conservatism after an actuary has arrived at his or her best estimate of anticipated experience would be contrary to the statutory mandate." Wachtell , 26 F.3d at 296.

The Fund offers two more arguments in defense of the Segal Blend. Both depend on characterizing an employer withdrawal as a "final settlement" with the fund. See Segal Co., What is the Segal Blend? , https://www.segalco.com/consulting-insights/segal-blend. Neither is persuasive.

First, the Fund contends that blending the actuary's growth-rate assumption with the interest rate on risk-free annuities is fair because this transfers investment risk from the pension fund to the withdrawing employer. Perhaps this is a laudable policy proposal. But, even if it is, we see no indication in the statute that Congress has adopted it. ERISA does incorporate a risk-shifting regime for mass withdrawals, which the statute does treat as a "settlement." See 29 U.S.C. § 1341a(c)(2). And certain parts of the statute do direct actuaries to make calculations "without taking into account the experience of the plan." See id. § 1084(c)(6)(E). But there is nothing in the statutory text to indicate that ERISA adopted a similar regime for individual withdrawals from multiemployer plans. Nor can we find any suggestion that Congress intended to give an actuary the discretion to dilute her best estimate of anticipated experience under the plan in order to shift risk onto the departing employer. The PBGC has not adopted this approach either. The Fund next argues that treating a withdrawal as a one-time settlement is an "accepted actuarial practice," as reflected in Actuarial Standard of Practice No. 27 § 3.9. That seems to be true. But ERISA does not yield to the Actuarial Standards of Practice; the standards must succumb to the statutory requirements. Here, the standards offer an alternative: "[t]he actuary may use a discount rate that reflects the anticipated investment return from the pension fund," or "[a]n actuary measuring a plan's present value of benefits on a defeasance or settlement basis may use a discount rate implicit in annuity prices or other defeasance or settlement options." Actuarial Standards Bd., Actuarial Standard of Practice No. 27, § 3.9(a), (b). As between these two professionally accepted standards, ERISA requires the former: an actuary must choose a rate that reflects "anticipated experience under the plan." 29 U.S.C. § 1393(a)(1).

It is no answer to say, as the Fund does, that ERISA places the burden on the employer to show "that the actuarial assumptions and methods used in the [withdrawal liability] determination were, in the aggregate, unreasonable." Id. § 1401(a)(3)(B). It is true that Concrete Pipe described this language as casting on employers the "burden to show that the combination of methods and assumptions employed in the calculation would not have been acceptable to a reasonable actuary." 508 U.S. at 635, 113 S.Ct. 2264. After all, the Court reasoned, "the methodology" used by actuaries "is a subject of technical judgment within a recognized professional discipline"; and so, "it would make sense to judge the reasonableness of [the] method" by reference to professional standards. Id. But these observations do not answer the objection raised here. There is a difference between the "technical judgment" a reasonable actuary might use to decide how to estimate something and the policy choice about what to estimate. A fund's determination is not insulated from review when an actuary uses otherwise reasonable assumptions to estimate the wrong thing. ERISA, not the Actuarial Standards of Practice, tells the actuary what to project.

We hold that using the Segal Blend here violates ERISA's mandate that the interest rate for withdrawal liability calculations be based on the "anticipated experience under the plan." 29 U.S.C. § 1393(a)(1). The district court did not err.

IV. Partial-Withdrawal Liability

Sofco challenges the Fund's assessment of partial-withdrawal liability. A construction-industry employer is liable for a partial withdrawal when its contributions decline to an "insubstantial portion of its work in the craft and area jurisdiction of the collective bargaining agreement of the type for which contributions are required." 29 U.S.C. § 1388(d)(1). The Fund determined that Sofco had partially withdrawn from the fund in 2011, 2012, and 2013 because Sofco's contributions had fallen by more than 70% in those years. Sofco challenged this assessment, arguing that a construction employer's contributions become "insubstantial" only when the employer has come close to ceasing contributions altogether. Drawing on a definition of "insubstantial" found in an IRS publication, Sofco suggested that the proper benchmark would be a 98% decline (or a 2% contribution level) compared to prior years. The arbitrator upheld the actuary's assessment, finding that "[n]one of the figures on which the Fund based its determination ... exceed what [he found] to be the ‘insubstantial’ threshold appropriate to the circumstances of this case." The district court then upheld the arbitrator's determination, largely because "the lack of clear guidelines on this issue" meant that Sofco could not prove "that the Fund's determination was unreasonable or clearly erroneous." For the reasons that follow, we vacate the district court's decision on this point and remand for further proceedings.

A. Partial-Withdrawal Liability, Generally

The MPPAA sets out a complicated formula for how to determine whether a partial withdrawal has occurred. See 29 U.S.C. § 1385. Generally, an employer is liable for a partial withdrawal in a plan year if "there is a 70[%] contribution decline." Id. § 1385(a)(1). But the decline is not measured by looking only at the single year in which it is assessed; an actuary considers that year and the two preceding years, looking for a sustained 70% contribution decline for three years straight. Id. § 1385(b)(1)(B)(i). This is called the "3-year testing period." Id. Contributions in these years must, of course, be assessed against some sort of baseline. The baseline is the average of the two years with the highest contributions in the five-year period preceding the three-year testing period. Id. § 1385(b)(1)(B)(ii). This is called the "high base year." Id. Finally, the contributions for that year are measured in "contribution base units"—the units for which an employer must contribute. Id. § 1301(a)(11). Here, the unit is hours because Sofco was required to contribute to the fund a certain amount per hour worked under the CBA. If in each year of the three-year testing period the contributions in that year "do not exceed 30[%]" of the contributions for the high base year, a partial withdrawal is assessed in the third year. Id. § 1385(b)(1)(A).

Here is a simple example. Let's say we are trying to determine whether an employer is liable for a partial withdrawal in 2012. We would look at the employer's annual contributions in 2012, 2011, and 2010. This is the numerator of our ratio. To determine the high base year, or the denominator in our ratio, we look at annual contributions in 2009, 2008, 2007, 2006, and 2005. We take the two years in which contributions were the highest and average them. Then, for each of the years 2012, 2011, and 2010, we divide the contributions in those years by the high base year. If for three straight years—in 2012, 2011, and 2010—that ratio does not exceed 30%, there has been a partial withdrawal. If in any of those years the ratio does exceed 30%, no partial withdrawal liability is assessed, even if the ratio in the other two years is below 30%. So in the example below, the denominator (or contributions in the high base year) would be 100, because that is the average of 90 and 110. We would then divide 30, 28, and 30—the contributions in 2010, 2011, and 2012—by 100. This gives us ratios of 30%, 28%, and 30%. Because none of those figures exceed 30%, a partial withdrawal would be assessed.B. "Insubstantial Portion"

Slightly different rules govern the construction industry. Per an exception in the MPPAA, a construction-industry employer "is liable for a partial withdrawal only if the employer's obligation to contribute under the plan is continued for no more than an insubstantial portion of its work in the craft and area jurisdiction of the collective bargaining agreement of the type for which contributions are required." 29 U.S.C. § 1388(d)(1). The parties, the arbitrator and the district court all read this provision to mean that although a regular employer would be assessed partial-withdrawal liability if its contributions in the three-year testing period "d[id] not exceed 30[%]," id. § 1385(b)(1)(A), a construction employer should be assessed partial-withdrawal liability if its contributions amounted to "an insubstantial portion," id. § 1388(d)(1), of what it contributed in the high base year.

No court has defined "an insubstantial portion" as used in this provision. And the PBGC has expressly declined to opine on the meaning of this statutory term, concluding instead that "such fact-specific determinations are the responsibility of the plan sponsor." PBGC Opinion Letter 95-2, 1995 WL 912004, at *2 (Aug. 18, 1995). The Fund echoes the PBGC, arguing that "what constitutes an insubstantial portion [should be] left to the discretion of the Fund." But neither the PBGC nor the Fund offers any hint as to what "fact-specific" considerations might generally go into deducing whether a "portion" is "insubstantial"; and the Fund offered no fact- or context-specific reason why it deemed Sofco's contributions to be "insubstantial" in this case. As best we can tell, the Fund simply determined that the amounts Sofco had contributed (ranging from 4%–18% of its prior contributions) were less than the 30% that, by statute, would have made a non-construction employer liable. See 29 U.S.C. § 1385(b)(1)(A). Based on this calculation, it sent Sofco a bill.

The arbitrator upheld the Fund's assessment of withdrawal liability. He thought that the "area of ‘insubstantial’ must lie between [ § 1385(b)(1)(A) ]’s 30% figure [for non-construction employers] and [a] 5% figure that Congress declined to adopt." But the arbitrator declined to specify that percentage, or even a narrower range; instead, he simply concluded that "[n]one of the figures on which the Fund based its determination ... exceed what [he found] to be the ‘insubstantial’ threshold appropriate to the circumstances of this case." Just what those circumstances might have been, we are left to wonder.

The district court was similarly stumped. It appeared to agree with Sofco that " ‘insubstantial portion’ must mean something." Sofco , 2020 WL 2541970, at *11. But given "the lack of clear guidelines on" what constitutes an "insubstantial portion," the district court fell back on § 1401(a)(3)(A) ’s "presumption in favor of the Fund's determination." Id. Because Sofco had failed to "establish that the Fund's determination was unreasonable or clearly erroneous," the district court upheld the Fund's determination. Id.

The district court's reliance on the § 1401(a)(3)(A) presumption was error. The Supreme Court in Concrete Pipe gave every indication that this presumption applies only to questions of fact. See 508 U.S. at 621, 630, 113 S.Ct. 2264. We have suggested as much too, Sherwin-Williams , 158 F.3d at 392, as has at least one of our sister circuits, see Joseph Schlitz Brewing Co. v. Milwaukee Brewery Workers’ Pension Plan, 3 F.3d 994, 1000 (7th Cir. 1993) (" Concrete Pipe ... understood this language to mean that in the proceeding before the arbitrator the employer must ‘disprove a [plan sponsor's] challenged factual determination by a preponderance’ of the evidence." (second alteration in original)). And we are not sure how it could be otherwise; one cannot disprove a legal determination "by a preponderance of the evidence." 29 U.S.C. § 1401(a)(3)(A). Here, the factual determinations include the percentages Sofco contributed in the relevant years compared to the baseline. Those percentages (4% to 18%) are not in dispute. "[I]nsubstantial portion," by contrast, is a statutory term; discerning its meaning presents a question of law. Safelite Grp. , 930 F.3d at 433. And whether particular percentages fall within the definition of an "insubstantial portion" is also a legal question, or a mixed question of law and fact. See Concrete Pipe , 508 U.S. at 630, 113 S.Ct. 2264 (explaining that the § 1401(a)(3)(A) presumption does not apply to a plan's determination of the date of "complete withdrawal"; the presumption applies to the historical facts, but "the question whether these facts amount to a ‘complete withdrawal’ " within the meaning of ERISA "is one of law").

Because the district court erred by relying on the § 1401(a)(3)(A) presumption to uphold the Fund's determination, we vacate the district court's decision on this issue and remand for the court to consider the legal question in the first instance. We proceed this way, in part, because the PBGC has indicated that what counts as an "insubstantial" contribution might be "fact-specific," PBGC Opinion Letter 95-2, 1995 WL 912004, at *2, and the arbitrator also suggested that the " ‘insubstantial’ threshold" might vary with "circumstances." Perhaps that is so. But if there is some reason why context could matter, no one has explained it to us; nor has anyone indicated what factors a decisionmaker should look for or how to weigh them. By contrast, Sofco seems to suggest that an "insubstantial portion" must be a fixed percentage. We take no position on this question here. But to the extent that facts may inform the legal standard to be applied, this question is best explored in another forum.

We note another wrinkle, however. In addition to relying on the § 1401(a)(3)(A) presumption, the Fund also invokes a purported delegation of regulatory or interpretive authority. The Fund claims that "both Congress and the PBGC" have delegated to the individual pension funds the "statutory discretion" to decide whether a construction employer's contributions have satisfied the (otherwise undefined) " ‘insubstantial portion’ standard." The Fund locates this authority in a PBGC Opinion Letter. When asked for an opinion defining "insubstantial portion," the PBGC noted that many sections of ERISA "contain specific numerical thresholds and tests governing withdrawal liability determinations." PBGC Opinion Letter 95-2, 1995 WL 912004, at *2. By contrast, the agency noted that Congress had not "specif[ied] a comparable numerical test" governing "whether any given percentage of work constitutes an ‘insubstantial portion’ " for construction-industry withdrawal liability. Id. But rather than reading this lack of specificity as a delegation to the agency to deploy its regulatory expertise and "fill [the] gap left ... by Congress," see Chevron, U.S.A., Inc. v. Nat. Res. Def. Council , 467 U.S. 837, 843, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), the PBGC read Congress's silence as a delegation "to the plan sponsor[s]" themselves to make these "fact-specific determinations." PBGC Opinion Letter 95-2, 1995 WL 912004, at *2. These determinations would, presumably, be made by individual plan sponsors, on a case-by-case basis, and the agency provided no standards to guide the funds’ decisionmaking. We question whether the PBGC, or even Congress, could delegate such discretion.

"[A]gency ‘subdelegations [of statutory powers] to outside parties are assumed to be improper absent an affirmative showing of congressional authorization.’ " Nat'l Truck Equip. Ass'n v. Nat'l Highway Traffic Safety Admin ., 711 F.3d 662, 675 (6th Cir. 2013) (second alteration in original) (quoting U.S. Telecom Ass'n v. FCC , 359 F.3d 554, 565 (D.C. Cir. 2004) ); see also Fund for Animals v. Kempthorne , 538 F.3d 124, 132 (2d Cir. 2008) ; La. Forestry Ass'n, Inc. v. Sec'y U.S. Dep't of Labor , 745 F.3d 653, 671 (3d Cir. 2014). Here, the PBGC read congressional silence as authority to delegate the definition of "insubstantial portion" to a private (and interested) party, and provided no guideposts, that we can discern, to channel the funds’ discretion. There is, at a minimum, reason to question whether the PBGC was right to say that the meaning of "insubstantial portion" can be for each plan sponsor to decide for itself. See PBGC Opinion Letter 95-2, 1995 WL 912004, at *2.

Ordinarily, we might have asked the parties for supplemental briefing on this question. "[A] court may consider an issue ‘antecedent to ... and ultimately dispositive of’ the dispute before it, even an issue the parties fail to identify and brief." U.S. Nat'l Bank of Or. v. Indep. Ins. Agents of Am., Inc ., 508 U.S. 439, 447, 113 S.Ct. 2173, 124 L.Ed.2d 402 (1993) (second alteration in original) (quoting Arcadia v. Ohio Power Co. , 498 U.S. 73, 77, 111 S.Ct. 415, 112 L.Ed.2d 374 (1990) ). And here, the parties do arguably attempt to address the issue. Though not quite framing it as a delegation question, Sofco argues that "[t]he statute cannot give the Fund this level of discretion and be constitutional," and that the Fund cannot be given "responsibility for legal determinations, such as the interpretation of a federal statute." The Fund, meanwhile, insists that "what constitutes an insubstantial portion is left to the discretion of the Fund," relying on "statutory discretion" granted to it by Congress and the PBGC. Because we vacate the district court opinion on this issue in any event, the parties may brief this question in the district court on remand.

Accordingly, we vacate the district court's decision upholding the Fund's assessment of partial-withdrawal liability and remand for further proceedings on this question.

V. Liability for Forklift and Shop Work

We now consider the parties’ challenges to whether forklift work and shop work should be included in the withdrawal-liability calculation. It was Sofco's practice to assign forklift work to the Ironworkers. But Sofco would also occasionally assign forklift work to Local 18 members: sometimes because there were not enough Ironworkers, sometimes to keep the Local 18 members on its payroll between crane operation projects, and sometimes to settle minor grievances. Local 18 insisted that forklift work was within its jurisdiction. Sofco, meanwhile, insisted that forklift work belonged to the Ironworkers.

Sofco also employs individuals to do shop work. Sofco has assigned shop work to members of other unions, non-union individuals, and sometimes to Local 18 members. In particular, Sofco assigned shop work to Jon Allen, who belonged to Local 18. After Jon retired, Sofco assigned shop work to his son, Jason Allen. Jason used to be a Local 18 member but has since withdrawn and joined the Laborers union. Sofco made contributions to the Local 18 plan for the shop work that Jon and Jason did but says it did so voluntarily. Local 18 never claimed that shop work was within its jurisdiction before this dispute.

The Fund assessed complete-withdrawal liability against Sofco for both forklift work and shop work, and the arbitrator upheld that determination. The district court affirmed with regard to the forklift work but overturned the assessment for shop work. Sofco , 2020 WL 2541970, at *7–8.

A construction employer is liable for a complete withdrawal from a pension plan if it "ceases to have an obligation to contribute under the plan" but "continues to perform work in the jurisdiction of the collective bargaining agreement of the type for which contributions were previously required." 29 U.S.C. § 1383(b)(2). When Sofco terminated its CBA with Local 18 as of April 30, 2017, it ceased to have an obligation to contribute under the plan. And Sofco continues to perform both forklift work and shop work. So whether the Fund properly included forklift work and shop work in its withdrawal-liability calculation depends on whether (1) this work was in the jurisdiction of the CBA, and (2) contributions to the fund were required for this work. Id. § 1383(b)(2)(B)(i).

"Jurisdiction" over work is determined by the "jurisdictional provisions of the relevant collective bargaining agreement," Stevens Eng'rs & Constructors, Inc. v. Loc. 17 Iron Workers Pension Fund , 877 F.3d 663, 670 (6th Cir. 2017), and an "obligation to contribute" arises under a CBA, 29 U.S.C. § 1392(a). "We interpret collective-bargaining agreements, including those establishing ERISA plans, according to ordinary principles of contract law, at least when those principles are not inconsistent with federal labor policy." M & G Polymers USA, LLC v. Tackett , 574 U.S. 427, 435, 135 S.Ct. 926, 190 L.Ed.2d 809 (2015). "Where the words of a contract in writing are clear and unambiguous, its meaning is to be ascertained in accordance with its plainly expressed intent." Id. (quoting 11 R. Lord, Williston on Contracts § 30:6, (4th ed. 2012) ). Contract interpretation is a question of law that we review de novo. First Am. Nat'l Bank v. Fid. & Deposit Co. of Md. , 5 F.3d 982, 984 (6th Cir. 1993). We presume that the arbitrator's findings of fact are correct unless rebutted by a preponderance of the evidence. See 29 U.S.C. § 1401(c).

Forklift Work. The arbitrator included forklift work in the withdrawal-liability calculation, and the district court upheld that decision. Sofco , 2020 WL 2541970, at *6–7. On appeal, Sofco argues that the district court erred because it never had an obligation to contribute to the plan for forklift work. Alternatively, it argues that even if contributions were required at some point, Local 18 forfeited its right to that work by not properly challenging the Ironworkers’ jurisdiction.

Sofco's CBA with Local 18 clearly establishes jurisdiction over forklift work. The "Jurisdiction of Work" section of the most recent agreement lays out the work for which Sofco "shall employ" Local 18 members. It states: "It is further understood that all equipment for which classifications and wages have been established in this Agreement ... shall be manned, when operated on the job site, by a member of the International Union of Operating Engineers." The agreement goes on to establish classifications and wages for forklifts no fewer than fourteen times. Thus, under the CBA, forklift work was in Local 18's jurisdiction.

The CBA also required contributions to the pension plan for forklift work. The agreement specifies that "[f]ringe benefit contributions shall be paid ... for all hours paid to each employee by the Employer under this Agreement." It then lists Pension Fund immediately below. A later portion of the agreement, setting out job classifications and wages, lists specific contribution amounts corresponding to each classification, including forklift work. As a result, Sofco was required to contribute to the Fund for forklift work performed by Local 18 members.

Sofco argues that forklift work belongs to the Ironworkers and that Local 18 forfeited any claim to that work by not challenging the Ironworkers’ jurisdiction. It relies on our decision in Stevens Engineers & Constructors, Inc. v. Local 17 Iron Workers Pension Fund , 877 F.3d 663 (6th Cir. 2017), for the proposition that "where two unions both claim certain work and a union fails to submit its jurisdictional challenge to secure a determination as to which union the work belongs to, the union abandons its claim to the work." Stevens is inapposite.

The CBA in Stevens included a qualifier stating that the agreement's jurisdiction was subject to national agreements "covering work jurisdiction and [the] allocation and division of work." Id. at 667 (alteration in original). The union was party to a national agreement providing "that, where multiple unions can claim the same work, employers must conduct a pre-job conference to assign work on a project." Id. at 668. By the terms of the agreement, a union failing to challenge the resulting assignment of work through the agreement's dispute resolution process, forfeited jurisdiction over that work. Id. at 667–68. The union in Stevens did not challenge the assignment of work to another union and, thus, forfeited its jurisdiction over it. Id. at 668. Consequently, Stevens was not performing work in the jurisdiction of the CBA and did not owe withdrawal liability. Id. at 669–70.

Here, the Local 18 CBA contains a provision covering jurisdiction of work assigned during pre-job conferences similar to that in Stevens . But critically, no such conference occurred here, nor has Sofco suggested that any other outside agreement applies. Stevens does not govern.

Alternatively, Sofco argues that it had a practice of assigning forklift work to the Ironworkers and that Local 18 implicitly ceded its claim to forklift work by failing to challenge the work Sofco assigned to the Ironworkers. That argument is unavailing. We have held that because multiemployer plans "may rely on the literal terms of written agreements between the employer and the union, any oral understandings or practices between the contracting parties are immaterial." Operating Eng'rs Loc. 324 Health Care Plan v. G&W Constr. Co. , 783 F.3d 1045, 1051 (6th Cir. 2015) (internal quotations and citations omitted). A fund has the right to collect, and an employer has an obligation to contribute, payments due as established by the written provisions of the agreement. See id. at 1053. Extrinsic evidence, such as the union's conduct, does not void the clear terms of the contract. See id. ; Stevens , 877 F.3d at 672.

Here, the CBA clearly establishes Local 18's jurisdiction over forklift work and Sofco's obligations to contribute to the fund for that work. The district court did not err by concluding that the Fund properly included forklift work in the withdrawal liability calculation.

Shop Work. The arbitrator found that Jon and Jason Allen "perform[ed] maintenance and repair work," that this work was "shop work," and that Sofco had an obligation to contribute to the Fund for this work. He added that, in his view and despite Sofco's arguments to the contrary, Sofco could not have voluntarily contributed to the Fund without running afoul of the Labor Management Relations Act (LMRA). The district court overturned the arbitrator's decision. Sofco , 2020 WL 2541970, at *8. It noted that the arbitrator had failed to cite any specific portion of the CBA that covered "shop work," and concluded on that basis that shop work was not within the jurisdiction of the agreement. Id. This was error.

First, Sofco failed to carry its burden of rebutting the arbitrator's findings of fact. We are to presume that the arbitrator's findings of fact are correct unless the challenging party disproves those findings by a preponderance of the evidence. 29 U.S.C. § 1401(c). The arbitrator found that what the parties refer to as "shop work" is maintenance and repair work. Not only has Sofco failed to produce any evidence disproving this finding, but Sofco's own witnesses defined "shop work" as including maintenance and repair work. The arbitrator also determined that Jon and Jason Allen performed maintenance and repair work. Sofco does not challenge this finding either.

Second, the arbitrator correctly determined that the CBA covers maintenance and repair work. As the Fund pointed out, the agreement's "Jurisdiction of Work" section states that "the Employer shall employ Operating Engineers for ... maintenance and repair [work]." The agreement then requires payments to the pension fund "for all hours paid to employees who perform any covered work." Thus, maintenance and repair work is in the jurisdiction of the CBA and the agreement requires contributions to the fund for this work. Id. § 1383(b)(2)(B)(i). And because these contributions were required, the parties’ dispute over whether Sofco could have made such contributions voluntarily is beside the point. The district court erred in vacating the arbitrator's determination that Sofco is liable for shop work.

VI. Successor Liability

Next, Sofco challenges the Fund's inclusion of its predecessor's contribution history in its withdrawal liability calculation. Sofco argues that this was error because when Sofco purchased Old Sofco's assets in an arm's-length transaction in 2004, it became a new, independent entity and did not assume any of Old Sofco's liabilities.

The arbitrator determined that including Old Sofco's contribution history was appropriate because " ‘new’ Sofco is clearly ‘old’ Sofco's successor employer with respect to its collective bargaining and employee benefit obligations." He noted that both companies operated under the same name (Sofco Erectors, Inc.); contributed to the fund using the same employer code number; used the same equipment, assets, management, and personnel; and had overlapping ownership. The district court upheld the arbitrator's decision.

Successor liability is an equitable doctrine, the application of which we review for an abuse of discretion. Tsareff v. ManWeb Servs. , 794 F.3d 841, 848 (7th Cir. 2015) ; see PBGC v. Findlay Indus., Inc. , 902 F.3d 597, 611 (6th Cir. 2018). "A district court abuses its discretion when it relies on clearly erroneous findings of fact, improperly applies the law, or uses an incorrect legal standard." Robertson v. Simpson , 624 F.3d 781, 784 (6th Cir. 2010).

Sofco gets the legal rule right. "[T]he universally-accepted general rule [is] that a corporation that purchases the assets of another corporation does not, simply by virtue of the asset purchase transaction, become liable for the obligations of the seller." City Mgmt. Corp. v. U.S. Chem. Co. , 43 F.3d 244, 251 (6th Cir. 1994) ; see also Chi. Truck Drivers, Helpers & Warehouse Workers Union (Indep.) Pension Fund v. Tasemkin, Inc. , 59 F.3d 48, 49 (7th Cir. 1995) ; CenTra, Inc. v. Cent. States, Se. & Sw. Areas Pension Fund , 578 F.3d 592, 601 (7th Cir. 2009) ("[A]n asset sale generally results in a complete withdrawal if the seller's controlled group no longer has covered operations or an obligation to contribute. By the same token, the buyer generally does not inherit the contribution history.") (quoting Jayne E. Zanglein & Susan J. Stabile, ERISA Litigation 1474, 1476 (3d ed. 2008)). But our court has recognized successor liability, as an equitable doctrine, as an exception to the rule. See Findlay , 902 F.3d at 609 ; see also Tasemkin , 59 F.3d at 49. Successor liability is appropriate where "(1) the successor had notice of the claim before the acquisition; and (2) there was substantial continuity in the operation of the business before and after the sale." Tsareff , 794 F.3d at 845 (quoting Tasemkin , 59 F.3d at 49 ).

The district court did not abuse its discretion in applying this doctrine. First, it noted that Sofco had knowledge of the claim before the sale because "all of its officers had worked for the company for decades, during which Sofco contributed to the Fund and was a party to the Local 18 CBA." Sofco , 2020 WL 2541970, at *10. Second, it concluded that there was "substantial continuity in the operation of the business before and after the sale," Tsareff , 794 F.3d at 845 (quotation omitted), because "Sofco used the same employer code, used the same equipment, assets, and personnel, and had nearly identical management and overlapping ownership," Sofco , 2020 WL 2541970, at *10.

Sofco has not shown that the district court "relie[d] on clearly erroneous findings of fact, improperly applie[d] the law, or use[d] an incorrect legal standard." Robertson , 624 F.3d at 784. Sofco's only argument on appeal is that because the sale of Old Sofco was not structured under 29 U.S.C. § 1384, Sofco cannot be responsible for Old Sofco's contribution history. But Sofco misunderstands the purpose of § 1384, which sets out a list of conditions that will relieve a seller of withdrawal liability following a "bona fide, arm's-length sale of assets to an unrelated party." Id. § 1384(a)(1). These conditions include the seller and purchaser having "substantially the same" obligations to the plan, id. § 1384(a)(1)(A) ; the purchaser providing a surety bond, id. § 1384(a)(1)(B) ; and the seller agreeing to be secondarily liable if the purchaser withdraws from the plan within five years after the sale, id. § 1384(a)(1)(C). This provision simply states what is necessary for a seller to be relieved of withdrawal liability after a sale. See id. § 1384(a). It does not say that this is the only circumstance in which a buyer will be subject to successor liability. We affirm the district court on this issue.

VII. Attorney's Fees

Finally, both parties request attorney's fees. ERISA permits a court to award "all or a portion of the costs and expenses incurred ..., including reasonable attorney's fees, to the prevailing party." 29 U.S.C. § 1451(e). The district court declined to award attorney's fees to either party because "[t]his case presented very close arguments on complicated legal matters ... and both parties have prevailed on issues." Sofco , 2020 WL 2541970, at *11–12. "We review a district court's denial of a request for attorney fees to a prevailing claimant under ERISA for an abuse of discretion." Moon v. Unum Provident Corp. , 461 F.3d 639, 642 (6th Cir. 2006) (per curiam). A district court abuses its discretion when we are left with "a definite and firm conviction that the trial court committed a clear error of judgment." Id. (internal quotations omitted).

In our circuit, a district court considers the following factors in determining whether to award discretionary attorney's fees to a prevailing party under ERISA: "(1) The degree of the opposing party's culpability or bad faith; (2) The ability of the opposing party to satisfy an award of attorney's fees; (3) Whether an award of fees against the opposing party would deter others from acting in similar circumstances; (4) Whether the party requesting fees sought to benefit all participants and beneficiaries of a multiemployer plan or to resolve a significant legal question; and (5) The relative merits of the parties’ position." Cent. States, Se. & Sw. Areas Pension Fund v. 888 Corp. , 813 F.2d 760, 767 (6th Cir. 1987).

As the district court noted, this case involved complicated legal questions without clear answers. Each party prevailed on some issues. There is no evidence of bad faith from either party. Sofco was fully justified in exercising its right to challenge the Fund's withdrawal-liability determination, as was the Fund in defending it. And neither parties’ positions were frivolous. We cannot say that the district court abused its discretion in denying fees under § 1451(e).

The Fund now invokes other statutory provisions, arguing that we are required to award it attorney's fees under 29 U.S.C. § 1451(b) and 29 U.S.C. § 1132(g)(2)(D). But the Fund failed to present this mandatory-fee argument to the district court, instead claiming that the court should award discretionary attorney's fees under § 1451(e). The Fund made no effort to cite the authority it believed mandated attorney's fees; did not develop its mandatory fee argument in its briefs to the district court, despite filing a counterclaim for attorney's fees; and, whether or not it believed it had presented a mandatory fee argument to the district court, it did not file a post-judgment motion once the district court ruled without mentioning mandatory fees. The Fund has thus forfeited any right to have us address it on appeal. Vance v. Wade , 546 F.3d 774, 781 (6th Cir. 2008).

Even if we were to excuse the forfeiture, the Fund's argument lacks merit. Attorney's fees under 29 U.S.C. § 1132(g)(2)(D) are mandatory "[i]n any action ... on behalf of a plan to enforce section 1145 [delinquent contributions]." But the Fund does not suggest that Sofco failed to timely contribute to the fund, and this case is not an enforcement action under 29 U.S.C. § 1145. So this provision does not apply. Nor does the Fund contest that Sofco timely made quarterly withdrawal liability payments before paying its balance in full. Thus, 29 U.S.C. § 1451(b), which grants mandatory attorney's fees for actions that "compel an employer to pay withdrawal liability," does not apply either. Even the cases the Fund cites recognize that mandatory fees do not apply here. See, e.g. , United Retail & Wholesale Emps. Teamsters Union Loc. No. 115 Pension Plan v. Yahn & Mc Donnell, Inc. , 787 F.2d 128, 134–35 (3d Cir. 1986) ("[I]n any action ... other than an action to recover a delinquent payment, an award of attorney's fees and costs is discretionary.").

* * *

For the foregoing reasons, we AFFIRM in part, REVERSE in part, VACATE in part, and REMAND to the district court for further proceedings consistent with this opinion.

CONCURRING IN PART AND DISSENTING IN PART

GRIFFIN, Circuit Judge, concurring in part and dissenting in part.

I join Judge Larsen's opinion in this ERISA dispute, except for Section IV. Although I agree with the majority that the district court erred when it relied on 29 U.S.C. § 1401(a)(3)(A) ’s presumption in favor of the Fund's determination regarding partial-withdrawal liability, I would hold that the Fund wrongly assessed partial-withdrawal liability in the first instance. I therefore would reverse the district court's ruling to the contrary and remand with instructions to vacate the arbitrator's confirmation of that assessment. Accordingly, I respectfully concur in part and dissent in part.

As the majority opinion explains, ERISA provides for partial-withdrawal liability when a construction-industry employer's contributions decline to an "insubstantial portion of its work in the craft and area jurisdiction of the collective bargaining agreement of the type for which contributions are required." § 1388(d)(1). As did the district court, see Sofco Erectors, Inc. v. Trs. of the Ohio Operating Eng'rs Pension Fund , 2020 WL 2541970, at *10–11 (S.D. Ohio May 19, 2020), the majority acknowledges what constitutes an "insubstantial portion" is not defined. But, instead of remanding to the district court without providing any guidance, I would employ our standard and familiar tools of statutory construction to resolve this issue.

Because Congress did not define "insubstantial," we should fill in the gap to make § 1388(d)(1) "work." Continental Can Co. v. Chicago Truck Drivers, Helpers & Warehouse Workers Union (Indep.) Pension Fund , 916 F.2d 1154, 1155 (7th Cir. 1990). That requires examining its ordinary meaning. See In re Application to Obtain Discovery for Use in Foreign Proc. , 939 F.3d 710, 717 (6th Cir. 2019). Dictionaries in use at the time the Multiemployer Pension Plan Amendments Act was enacted (1980) provide a good starting place. Id. They demonstrate the term refers to a nominal amount: "Insubstantial" is something that is not of "considerable value" or "quantity." See Funk & Wagnalls Standard College Dictionary (1978); The American Heritage Dictionary of the English Language (1976); Merriam-Websters New Collegiate Dictionary (1975) (all defining insubstantial as not substantial, and defining substantial as something of "considerable value," "considerable ... value," and "considerable [ ] quantity," respectfully). And more contemporaneous dictionaries, to which we can also turn, see In re Application , 939 F.3d at 717, agree. See, e.g. , The American Heritage Dictionary of the English Language (2020) (defining insubstantial as "very small or negligible, as in importance, size or amount"); Webster's Unabridged Dictionary (2001) (defining insubstantial as "not substantial in amount or size; inconsiderable," and "inconsiderable" as "small, as in value, amount, or size"). So too does the caselaw; the Supreme Court has read "insubstantial" as interchangeable with "de minimis" many times over. See, e.g. , Goss v. Lopez , 419 U.S. 565, 576, 95 S.Ct. 729, 42 L.Ed.2d 725 (1975) ; Fortner Enters. v. U.S. Steel Corp. , 394 U.S. 495, 501, 89 S.Ct. 1252, 22 L.Ed.2d 495 (1969) ; Local 761, Int'l Union of Elec., Radio & Mach. Workers, AFL-CIO v. N. L. R. B. , 366 U.S. 667, 682, 81 S.Ct. 1285, 6 L.Ed.2d 592 (1961) ; Anderson v. Mt. Clemens Pottery Co. , 328 U.S. 680, 693, 66 S.Ct. 1187, 90 L.Ed. 1515 (1946).

Indeed, there have been several occasions in which courts have placed a single-digit value on "insubstantial." See, for example, Tampa Electric Co. v. Nashville Coal Co. , 365 U.S. 320, 333, 81 S.Ct. 623, 5 L.Ed.2d 580 (1961), where the Supreme Court commented in an antitrust dispute that control of one percent of the market is "quite insubstantial." We too have suggested that insubstantial means "something less than 5%." Seasongood v. C.I.R. , 227 F.2d 907, 912 (6th Cir. 1955) (examining 26 U.S.C. § 501(c)(3) ’s restriction on tax-exempt organizations from using a "substantial part of activities ... to influence legislation"); see also Himmel v. C.I.R. , 338 F.2d 815, 820 (2d Cir. 1964) ("[A] difference of 5% ... is [not] so insubstantial as to make the redemption[ of corporate stock] ‘essentially equivalent to a dividend’ " under 26 U.S.C. § 302(b)(1) ). And we have even done so en banc, noting in a copyright-infringement matter that the use of "as much as 30 percent of one copyrighted work, and in no case ... less than 5 percent of the copyrighted work as a whole" constituted percentages that were "not insubstantial" for purposes of 17 U.S.C. § 107 ’s fair-use doctrine. Princeton Univ. Press v. Mich. Document Servs., Inc. , 99 F.3d 1381, 1389 (6th Cir. 1996) (en banc).

Given this, an "insubstantial portion" in my view can only mean a low-single-figure percentage. Sofco's contributions plainly did not fall under that threshold. During the applicable three-year testing periods, Sofco's contribution ratio spanned from four to eighteen percent. More specifically, the testing periods produced the following ratios for each of the three years at issue:

• 2011: 13% (2009); 4% (2010); and 9% (2011);

• 2012: 4% (2010); 9% (2011); and 18% (2012); and

• 2013: 9% (2011); 18% (2012); and 28% (2013).

Save the four-percent calculation (for 2010), I cannot agree that as a matter of law, these ratios remotely approach the "insubstantial portion" threshold. 29 U.S.C. § 1388(d)(1). And because they do not, the Fund did not cumulatively satisfy the three-year lookback period for the calculation of partial withdrawals. § 1385(b).

For these reasons, the Fund's assessment of partial-withdrawal liability was erroneous. I would therefore reverse the district court's holding to the contrary and remand with instructions to vacate the arbitrator's confirmation of that assessment. In all other respects, I join the majority opinion.