Trinity Industries Inc v. Greenlease Holding Co

JORDAN, Circuit Judge. OPINION OF THE COURT This is a dispute about the proper allocation of costs to remediate a contaminated manufacturing site in Greenville, Pennsylvania. From 1910 until 1986, Greenlease Holding Co. ("Greenlease"), 1 a subsidiary of the Ampco-Pittsburgh Corporation ("Ampco"), owned the site and operated railcar manufacturing facilities there. Trinity Industries, Inc. and its wholly-owned subsidiary, Trinity Industries Railcar Co. (together referred to as "Trinity"), acquired the site from Greenlease in 1986 and continued to manufacture railcars there until 2000. An investigation by the Commonwealth of Pennsylvania into Trinity's waste disposal activities resulted in a criminal prosecution and eventual plea-bargained consent decree which required, in relevant part, that Trinity remediate the contaminated land. That effort cost Trinity nearly $9 million. This appeal arises out of the District Court's determination that, under the Comprehensive Environmental Response, Compensation, and Liability Act, 42 U.S.C. § 9601 et seq. , ("CERCLA"), and Pennsylvania's Hazardous Sites Cleanup Act, 35 Pa. Stat. § 6020.101 et seq ., ("HSCA"), Trinity is entitled to contribution from Greenlease for remediation costs. After eight years of litigation, and having sorted through a century of historical records, the District Court allocated 62% of the total cleanup costs to Greenlease and the remainder to Trinity. The parties filed cross-appeals challenging a number of the District Court's rulings, including its ultimate allocation of cleanup costs. For the reasons that follow, we will affirm the District Court's pre-trial rulings on dispositive motions; we will vacate its cost allocation determination; and we will remand for further proceedings consistent with this opinion. I. FACTUAL BACKGROUND 2 The site in question, known by the parties as the "North Plant," is a tract of land that was used as a manufacturing site by a succession of companies. Greenlease and Trinity also, at different times, operated facilities on a nearby tract of land called the "South Plant," though that property does not figure prominently in this appeal. Over time, the footprint of the North Plant grew from eleven to thirty-four acres. That industrial development, as well as the many years of manufacturing activity that occurred there, resulted in multiple releases of hazardous materials -primarily lead-into the ground. A. The North Plant - 1898 to 1986 From at least 1898 until sometime before Greenlease's acquisition of the North Plant in 1910, Shelby Steel Tube Company owned and operated a steel tube factory on eleven acres of land that is now part of the North Plant. Over the course of its ownership, Shelby Steel deposited historic fill as it was constructing its manufacturing facilities. According to the District Court, "[h]istoric fill is 'a soil mixed with various non-native materials, including construction demolition debris, concrete, asphalt, or it could be industrial materials such as slag or ash.' " (App. at 186.) Unfortunately, historic fill often contains lead and other contaminants. Greenlease began its manufacturing activities at the North Plant soon after acquiring the property. Between 1911 and 1922, it significantly expanded the North Plant to support its growing business of building and repairing railcars. During that expansion, Greenlease used historic fill in the foundations supporting the new structures and rail lines. Operations at the North Plant included two shops to paint the railcars, and Greenlease used a variety of toxic chemicals and lead paint during the painting process, without doing anything meaningful to collect or contain the runoff. B. Relationship Between Greenlease and Ampco In 1983, Ampco acquired Greenlease, 3 but their relationship predated that acquisition. They had had three overlapping board members since 1979 and continued to do so until 1986. Other than those three shared board members and one shared officer, no other persons were employees of both Ampco and Greenlease. Greenlease employees alone "were responsible for all day-to-day operations at the North Plant, including any waste disposal, waste handling, painting, abrasive blasting, welding, and fabrication operations." (App. at 81-82.) Those employees coordinated disposal with outside contractors and communicated with the Pennsylvania Department of Environmental Protection ("PADEP") on environmental matters. Indeed, Ampco "did not employ any engineers or persons with technical experience in manufacturing that could make decisions for [Greenlease] with respect to environmental compliance or waste management." (App. at 82.) Instead, "Ampco employed only a professional staff, such as accountants, actuaries, and lawyers[.]" (App. at 82.) Ampco did provide Greenlease with advice regarding the laws and regulations related to Greenlease's waste generation, and Ampco monitored that waste generation. The cooperation between parent and subsidiary was complete enough that Greenlease adopted a resolution declaring that any action taken by Ampco that it "may think necessary and desirable to take on behalf of [Greenlease] shall be deemed to be the action of [Greenlease's Board]." (App. at 72 (citation omitted).) Ampco also asserted the right to approve Greenlease's expenditures that exceeded a certain amount, though Greenlease was solely responsible for placing and paying any purchase orders. In addition, Ampco provided certain services to Greenlease to minimize costs, including overseeing a single retirement plan and providing centralized financial planning and master insurance policies. C. Trinity's Acquisition of the North Plant In 1986, Ampco authorized the Greenlease board of directors to sell the North Plant to Trinity. The Purchase and Sale Agreement between Trinity and Greenlease (the "Agreement") included a clause declaring that Greenlease "makes no representation or warranty regarding compliance with the Environmental Protection Act, any other environmental laws or regulations or any hazardous waste laws or regulations (collectively, 'Environmental Laws')." (App. at 199.) Mutual indemnification provisions specific to environmental liabilities provided, in pertinent part: [Greenlease] agrees to indemnify and hold harmless [Trinity] against Damages arising out of or related to violations of Environmental Laws, which were caused by [Greenlease] or its predecessors in title to the assets at the [North Plant] on or prior to the date of Closing. [Trinity] agrees to indemnify and hold harmless [Greenlease] against Damages arising out of or related to violations of Environmental Laws, which are caused by [Trinity] or its successors in title to the assets at the [North Plant] after the date of the Closing. It is the intention of the parties that liability under this Section for any condition that is caused by the acts of [Greenlease] or its predecessors in title to the assets prior to the date of the Closing and by the acts of [Trinity] or its successors in title to the assets after the date of Closing shall be allocated between the parties in a just manner taking into account degree of fault, period of violation and other relevant factors. (App. at 61 (some alterations in original).) Those indemnities were stated to be effective for only three years after the closing of the property sale. The Agreement further provided that Trinity "has not assumed, and expressly denies assumption hereby of, any other liability, obligation or commitment of [Greenlease] other than as set forth above or otherwise expressly set forth herein." (App. at 60-61 (alteration in original).) Finally, a "[n]on-waiver of [r]emedies" clause in the Agreement provided that "[t]he rights and remedies herein provided are cumulative and are not exclusive of any rights or remedies which the parties hereto may otherwise have at law or in equity." (App. at 62.) Following the 1986 sale of the North Plant to Trinity, Greenlease continued to exist only as a "shell holding company without any [employees,] business activities, for profit activities, or other commercial undertakings[.]" (App. at 89.) Its assets decreased at the end of each year following the sale of the North Plant, from about $51 million in 1987 to $658,594 in 1990. In the third and fourth years following the sale of the North Plant to Trinity, Greenlease issued dividends to Ampco, leaving Greenlease with only a $250,000 reserve for liabilities. At that time, Greenlease had no known liabilities beyond the reserve. The executive vice president and chief administrative officer for Ampco, who was also an officer and director of Greenlease, stated that it was common for dividends to be made from a subsidiary to Ampco after an indemnification period ended. An environmental reserve was placed on Greenlease's books when Trinity sued Greenlease and Ampco. 4 D. The North Plant - 1987 to 2004 After purchasing the North Plant, Trinity continued the manufacture of railcars there. In one of the paint shops, it installed concrete floors and used tar paper to capture paint drippage. Beginning in late 1987, it implemented a policy preventing the use of metal-containing paints at the North Plant. In 1994, Trinity removed the second paint shop, excavated the old dirt floors, and dumped the soil onto a field at the South Plant. Trinity then erected a new paint shop at the North Plant. Six years later, in 2000, Trinity ceased the North Plant operations. It sold the property in 2004 to a third-party (the "Buyer"). In connection with that sale, Trinity did not conduct an environmental assessment to determine whether the soil was contaminated, and it prohibited the Buyer from performing such testing without its consent. The Buyer demolished almost all of the existing buildings at the North Plant to sell the scrap steel for profit. Trinity maintains that, at some point, the Buyer dumped onto the North Plant property hazardous chemicals and waste that had been produced by the demolition of the North Plant buildings, exacerbating the pre-existing environmental harm. E. The Commonwealth's Investigation and the Consent Decree In 2004, the Commonwealth of Pennsylvania and PADEP began an investigation into allegations that Trinity had improperly disposed of hazardous waste at the North Plant. The Commonwealth filed a criminal complaint against Trinity in 2006, raising three felony counts and eight misdemeanor counts related to the illegal handling and disposal of hazardous waste. Trinity entered into a plea agreement with the Commonwealth that required the repayment of investigative costs, payment of a fine, contribution to a nonprofit organization, and, pursuant to a consent decree authorized by PADEP (the "Consent Decree"), the remediation of environmental contamination. The Consent Decree stated that further investigation of the North Plant was "necessary to fully identify the nature and extent of the release of hazardous substances at and/or potentially migrating from the North Plant ... and to determine the Response Actions necessary to remediate the hazardous substances at and/or potentially migrating from [the North] Plant." (App. at 513.) The cleanup was governed by Pennsylvania's Land Recycling and Environmental Remediation Standards Act, 35 Pa. Stat. § 6026.101 et seq. , commonly known as "Act 2," and the associated investigation was not limited to the time during which Trinity owned and operated the North Plant. Trinity was on a short leash. It was ordered to get approval from PADEP before it took any "significant step" pertaining to the property, and it was required to submit to PADEP "an investigation work plan, a supplemental investigation work plan, a notice of intent to remediate, a remedial investigation report, a proposed cleanup work plan, a supplemental cleanup work plan, and a final report." (App. at 213-14.) Those additional mandates increased the difficulty and expense of the remediation project. The remediation efforts were also affected by the fact that "[t]he North Plant was a 'high profile, high visibility location' " and is bordered by residential communities on three sides. (App. at 218 (citation omitted).) PADEP approved Trinity's remedial investigation work plan in 2007. Trinity later sent Greenlease a pre-suit notice describing the contamination and its legal position that Greenlease had contributed to the pollution. F. Trinity's Cleanup of the North Plant To perform the necessary cleanup, Trinity had to buy back the North Plant. It then selected Golder Associates, Inc. ("Golder") to perform, direct, and supervise the cleanup operations. PADEP approved that selection. Trinity did not employ a competitive bidding process to select Golder because it had been impressed by Golder's cleanup operations at several other sites and because the Consent Decree's deadlines created an urgency to get a remediation consultant in place as soon as possible. Trinity and Golder agreed to an "open billing" process that provided Golder would be paid only for the work it ultimately needed to perform. (App. at 218-19.) Billing was on a "cost plus 10 percent" basis, which gave Golder a ten percent markup on the expenses it incurred. (App. at 219.) Golder's cleanup efforts required it to first identify areas of the property that were of concern. It analyzed available historical information concerning construction and manufacturing activities that had taken place at the North Plant. It then conducted soil sampling to further identify areas requiring remediation. Golder ultimately divided the North Plant into twenty impact areas that required remediation. Thirteen of the twenty impact areas were primarily contaminated by lead. The remaining impact areas were primarily contaminated by volatile and semi-volatile organic compounds and a variety of other hazardous substances. Major remediation activities included excavating contaminated soil, refilling excavated areas with clean material, chemically treating contaminated soil, transporting excavated soil to appropriate landfills, and placing asphalt caps over parts of the North Plant. In total, Golder disposed of approximately 39,000 tons of soil off-site and capped about 15,000 tons of soil with asphalt. Those efforts cost nearly $9,000,000 and made the property usable again. Parts of the North Plant with asphalt caps are suitable for use as a parking lot. Other areas are suitable for industrial or commercial use. There is ongoing work at the North Plant to ensure that the safety mechanisms created as part of the environmental remediation continue to function. 5 II. PROCEDURAL HISTORY Invoking federal and state laws, Trinity filed a complaint against Greenlease and Ampco in 2008 to defray the North Plant remediation costs. More specifically, Trinity sought cost recovery under CERCLA pursuant to 42 U.S.C. § 9607 , cost recovery under the Resource Conservation and Recovery Act ("RCRA") pursuant to 42 U.S.C. § 6972 (a)(1)(B), and contribution under CERCLA pursuant to 42 U.S.C. §§ 9613 (f)(1) and 9613(f)(3)(B). It also brought cost recovery and contribution claims under the HSCA, as well as state common law claims for contribution and negligence per se . A. Pre-Trial Motions and Rulings Trinity's claims against Ampco were premised on Ampco's alleged direct or derivative liability for Greenlease's conduct at the North Plant. Upon cross motions for summary judgment on that issue, the District Court concluded that Ampco was not directly or derivatively liable for pollution at the North Plant. Greenlease also moved for judgment on the pleadings, arguing that Trinity's claims were barred by the indemnification provisions of their Agreement. It claimed that once the mutual indemnities expired, neither party was entitled to seek compensation from the other. The District Court rejected that argument, ruling that the existence and expiration of the indemnification provisions did not prevent Trinity from seeking other remedies available at law or in equity. Greenlease and Trinity later filed cross motions for summary judgment on Trinity's CERCLA, RCRA, HSCA, and common law claims. The District Court granted partial summary judgment for Trinity, holding as a matter of law that Greenlease was a potentially responsible person under CERCLA and the HSCA. It also granted Greenlease's cross-motion in part, granting it summary judgment on all of Trinity's claims other than those for contribution under 42 U.S.C. § 9613 (f)(3)(B) and 35 Pa. Stat. § 6020.705(c)(2). The litigation proceeded to a bench trial to determine the equitable allocation of cleanup costs between the parties. Prior to trial, Trinity tried to recoup costs associated with its cleanup of the South Plant, but the District Court concluded that Trinity was not entitled to those costs because Greenlease had never owned or operated that property or disposed of any hazardous waste at the South Plant. B. The Parties' Cost Allocation Proposals Trinity's and Greenlease's experts each provided the District Court with a proposal for the equitable allocation of cleanup costs between the parties. Trinity's expert, Joseph B. Gormley, Jr., relied on available historical information to identify three sources of contamination at the North Plant: volatile chemicals used in manufacturing operations; general dispersions caused by painting; and historic fill used for construction. He then employed that same historical information to assign each party a percentage of responsibility for the contamination found within each impact area. Next, Gormley analyzed the major remediation activities and associated costs required to clean up each impact area. To arrive at a total cost allocation for the major remediation activities, he multiplied the percentage of responsibility for each specific impact area by the major remediation activity costs in that specific area and added those results together. That produced an overall percentage allocation. Gormley applied that same overall percentage to general project costs not tied to any specific impact area. Ultimately, he allocated 99% of the costs to Greenlease and 1% to Trinity. Not surprisingly, Greenlease's expert, Steven Gerritsen, proposed a very different cost allocation. He concluded that most of the lead present at the North Plant was caused by the use of historic fill rather than Greenlease's operations at the facility. He calculated that Greenlease was responsible for depositing fill on only 2.8 acres of the thirty-four acre North Plant. He opined that the rest of the fill predated Greenlease's purchase of the property and was thus not Greenlease's responsibility. Gerritsen also suggested that much of Golder's work was unreasonable and unnecessary and thus that Trinity had spent more money than it should have to perform the cleanup. Gerritsen ultimately concluded that Greenlease should be allocated only 12-13% of the cleanup costs. C. The District Court's Cost Allocation Opinion In an admirably thorough opinion, the District Court endeavored to make sense of the extensive record, including the competing expert contentions. It first concluded that Greenlease was not responsible for any of the contamination attributable to Shelby Steel or any other non-party because Trinity had failed to show that those parties were "unknown, insolvent, or otherwise immune from suit." 6 (App. at 351.) The Court, however, rejected Greenlease's contention that Golder incurred unreasonable or excessive costs when performing its cleanup at the North Plant. To assign each party a percentage of responsibility for the contamination within each impact area, the District Court relied heavily on historic maps and schematics of the North Plant. For many impact areas, the Court agreed with Greenlease that the lead contamination could be attributed solely to Shelby Steel's use of historic fill, and therefore should not be a source of liability for Greenlease. For other impact areas, the Court found that Greenlease was responsible for the deposit of historic fill, or was solely responsible for the use of volatile chemicals, and that Greenlease should thus bear full responsibility for the pollution. For the remaining impact areas, the District Court split responsibility between the parties based on the number of years that each had owned the property or on various other considerations such as known use of a specific chemical contaminant. After determining the percentages of responsibility within each impact area, the District Court considered the major remediation activities that took place in each impact area to determine an overall allocation of cost. Though it purported to follow Gormley's methodology, the Court departed from it in an important respect: Gormley's methodology accounted for the fact that different remediation activities cost different amounts of money, whereas the District Court's methodology did not. To arrive at its cost allocation, the Court multiplied the percentage of responsibility it attributed to Greenlease by the square footage or cubic yardage involved in each remediation activity. The District Court then added the results and divided by the total square footage and cubic yardage for all remediation activities at the North Plant to arrive at the overall cost allocation percentage. By those calculations, it concluded that Greenlease was responsible for 83% of the total costs, while Trinity was responsible for 17%. The District Court then considered a variety of equitable factors to ensure the fairness of the overall cost allocation. It ultimately reduced Greenlease's percentage of responsibility, based on three equitable factors. First, it found that at least a portion of Trinity's remediation costs were attributable to the actions of the third-party Buyer and, in particular, the Buyer's decision to demolish buildings at the North Plant. The Court said that Trinity failed to "specify the amount of response costs it incurred to remediate the waste left at the North Plant by [the Buyer]." (App. at 380.) Therefore, "there [was] an equitable need to reduce Greenlease's percentage of responsibility for response costs to reflect an amount attributable to [the Buyer]." (App. at 380.) Accordingly, the Court reduced Greenlease's responsibility by 6%. Second, it concluded that the existence of the indemnification provisions demonstrated the parties' intent to shift liability, so it further reduced Greenlease's share of responsibility by 5%. Third, it recognized that the property value of the North Plant had increased as a result of remediation since the land was now suitable for some commercial or industrial uses. The Court concluded that an additional 10% reduction in Greenlease's responsibility was appropriate to account for that increased market value that would inhere to Trinity. After accounting for those equitable deductions, the District Court determined that Greenlease was responsible for 62% of "all response costs incurred by ... Trinity ... for the cleanup at the North Plant[.]" (App. at 388-89.) III. DISCUSSION 7 A. Statutory Background Congress enacted CERCLA in 1980 "to promote the timely cleanup of hazardous waste sites and to ensure that the costs of such cleanup efforts were borne by those responsible for the contamination." Burlington N. & Santa Fe Ry. v. United States , 556 U.S. 599 , 602, 129 S.Ct. 1870 , 173 L.Ed.2d 812 (2009) (internal quotation marks and citation omitted). Under CERCLA, a party who has paid for environmental remediation may seek to hold other potentially responsible parties ("PRPs") liable through the cost recovery mechanisms of § 107(a) or the contribution mechanisms of § 113(f) of that statute. 8 Agere Sys., Inc. v. Advanced Envtl. Tech. Corp. , 602 F.3d 204 , 216-18 (3d Cir. 2010). The remedies under those two provisions are distinct. Id. at 217 (citing United States v. Atl. Research Corp. , 551 U.S. 128 , 138, 127 S.Ct. 2331 , 168 L.Ed.2d 28 (2007) ). While § 107(a) authorizes complete cost recovery under a joint and several liability theory, § 113(f) permits a party to seek contribution from other PRPs following a CERCLA suit brought by a governmental authority against that first party, or after that party has resolved its "liability to the United States or an individual State through an administratively or judicially approved settlement." Id. Pennsylvania, meanwhile, enacted the HSCA in 1988 to provide additional statutory tools to deal with the improper disposal of hazardous waste within the Commonwealth. 35 Pa. Stat. § 6020.102; Gen. Elec. Envtl. Servs., Inc. v. Envirotech Corp. , 763 F.Supp. 113 , 115 (M.D. Pa. 1991). Although Trinity initially sought both cost recovery and contribution from Greenlease, the only claims remaining on appeal are claims for contribution pursuant to CERCLA subsection § 113(f)(3)(B), and the analogous section of the HSCA, 35 Pa. Stat. § 6020.705(c)(2). See also Trinity Indus., Inc. v. Chi. Bridge & Iron Co. , 735 F.3d 131 , 136 (3d Cir. 2013) (holding that a party who enters into a consent decree under state law is entitled to seek contribution under § 113(f)(3)(B) ). Because a party's "liability under the HSCA mirrors liability under CERCLA" and "the cost recovery and contribution provisions in HSCA are virtually identical to those in CERCLA," Agere Sys., Inc. , 602 F.3d at 236 , our resolution of Trinity's claim for contribution under CERCLA is determinative of its companion HSCA claim. B. Greenlease's Appeal Greenlease raises three primary issues on appeal. First, it appeals the District Court's determination that the indemnification provisions of the Agreement between it and Trinity do not preclude Trinity from seeking contribution. We will affirm because the language of the Agreement better supports the District Court's conclusion. Second, Greenlease appeals the ruling that the costs Trinity and Golder incurred in cleaning up the North Plant were all necessary and reasonable under CERCLA. We will affirm because those costs have the requisite nexus to remedying environmental harm at the North Plant and because the record does not support Greenlease's contention that Trinity incurred excessive costs. Third, Greenlease challenges the overall cost allocation ordered by the District Court. We agree with Greenlease that the Court's cost allocation analysis was flawed, and we will therefore vacate the judgment and remand for further proceedings. 1. The Agreement's Indemnification Provisions Do Not Preclude Trinity from Seeking Contribution from Greenlease. Greenlease argues that, at the conclusion of the three-year mutual indemnification period stated in its Agreement with Trinity, the parties were released from any subsequent statutory or common law responsibility to one another. Greenlease thus asserts that it was error to deny its motion for judgment on the pleadings. Our review of a motion for judgment on the pleadings is plenary. Caprio v. Healthcare Revenue Recovery Grp., LLC , 709 F.3d 142 , 146 (3d Cir. 2013). Such a motion should not be granted unless the moving party has established that there is no material issue of fact to resolve, and that it is entitled to judgment as a matter of law. Rosenau v. Unifund Corp. , 539 F.3d 218 , 221 (3d Cir. 2008). We also exercise plenary review over questions of contract interpretation. Great Am. Ins. Co. v. Norwin Sch. Dist. , 544 F.3d 229 , 243 (3d Cir. 2008). CERCLA allows parties to utilize indemnification agreements "to shift the ultimate financial loss" for environmental cleanup costs. Hatco Corp. v. W.R. Grace & Co. Conn. , 59 F.3d 400 , 404 (3d Cir. 1995). The statute says plainly that it does not "bar any agreement to insure, hold harmless, or indemnify a party to such agreement for any liability under this section." 42 U.S.C. § 9607 (e)(1). Whether the expiration of the indemnification provisions at issue here effectively shifted all financial burden for CERCLA cleanup costs to Trinity thus turns on the proper interpretation of the Agreement. "[A]greements among private parties ... addressing the allocation of responsibility for CERCLA claims are to be interpreted by incorporating state ... law." Hatco , 59 F.3d at 405 . Here, that means Pennsylvania law. When a contract is clear and unambiguous, Pennsylvania binds the parties to the intent contained within the writing itself. Wert v. Manorcare of Carlisle PA, LLC , 633 Pa. 260 , 124 A.3d 1248 , 1259 (2015). "The whole instrument must be taken together in arriving at contractual intent." Great Am. Ins. , 544 F.3d at 243 (quoting Murphy v. Duquesne Univ. of the Holy Ghost , 565 Pa. 571 , 777 A.2d 418 , 429 (2001) ). Courts are not to interpret one provision of the contract in a way that annuls a different provision of it, Capek v. Devito , 564 Pa. 267 , 767 A.2d 1047 , 1050 (2001), and "when specific or exact provisions seem to conflict with broader or more general terms, the specific provisions are more likely to reflect the intent of the parties[,]" Musko v. Musko , 548 Pa. 378 , 697 A.2d 255 , 256 (1997). Those interpretive rules lead us to conclude that the Agreement at issue reserved Trinity's right to seek contribution from Greenlease for environmental cleanup costs. The Agreement's indemnification provisions stated, in relevant part, that each party indemnified the other for any "[d]amages arising out of or related to violations of Environmental Laws" and that liability for any such violations would be "allocated between the [parties] in a just manner taking into account degree of fault, period of violation and other relevant factors." (App. at 599-600.) It is true that the mutual indemnification expired after three years. The Agreement did not, however, contain language expressing the parties' intent that Trinity would assume all of Greenlease's obligations and liabilities after that three-year period. Rather, the Agreement contained explicit "non-assumption of liabilities" and "non-waiver of remedies" clauses. The "non-assumption of liabilities" clause provided that Trinity "has not assumed, and expressly denies assumption hereby of, any other liability, obligation or commitment of [Greenlease] other than as set forth above or otherwise expressly set forth herein." (App. at 567.) It is reading far too much into the words "any other liability" to think they meant that the prominent risk of environmental liability was the one thing the parties meant for Trinity to be stuck with. Moreover, the "non-waiver of remedies" clause plainly provided that "[t]he rights and remedies herein provided are cumulative and are not exclusive of any rights or remedies which the parties hereto may otherwise have at law or in equity." (App. at 612-13.) The express language of the contract, therefore, provides both that Trinity did not assume any of Greenlease's liabilities or obligations following the three-year mutual indemnification period, and that Trinity did not waive its statutory rights under CERCLA and the HSCA to seek contribution from Greenlease. In short, while the contractual right to indemnification ended, all other rights remained. Greenlease's three primary arguments to the contrary do not persuade us. First, Greenlease argues that the indemnification provision should control our interpretation of the entire Agreement because it is more specific than the "non-waiver of remedies" clause. That reasoning, however, puts too high a premium on specificity. Yes, the contractual indemnity is specific. But the non-assumption of liabilities and non-waiver of remedies provisions are plain enough for us to discern the intent of the parties, and that intent was to preserve non-contractual rights. Besides, there is a sense in which the indemnification language is not more specific than the other relevant provisions: it does not address the parties' liabilities after the first three years following the sale. The "non-assumption of liabilities" and "non-waiver of remedies" clauses do. They are not time limited and therefore can be understood as specifically addressing the time period after the expiration of the contractual indemnities. We will not construe the indemnification provision to cover time periods that, by the plain language of the contract, it does not cover. See Jacobs Constructors, Inc. v. NPS Energy Servs., Inc. , 264 F.3d 365 , 373 (3d Cir. 2001) ("[B]ecause the nature and purpose of any indemnity agreement involves the shifting and voluntary assumption of legal obligations, they are to be narrowly construed."). Second, Greenlease argues that allowing Trinity to seek contribution against it pursuant to the "non-waiver of remedies" clause "renders the environmental indemnity provision meaningless[.]" (Green. Opening Br. at 36.) But that argument again ignores the critical fact that the parties, by agreeing to the three-year mutual indemnification provision, granted to each other certain contractual rights separate and distinct from any statutory, legal, or equitable rights or remedies. The "non-waiver of remedies" clause is perfectly clear in that regard, reserving to both parties "any rights or remedies which the parties ... may otherwise have at law or in equity." (App. at 613.) As the District Court concluded, the contractual remedies created by the indemnification provision were, by the terms of the Agreement, "cumulative" and not "exclusive" of the remedies available at law or in equity. (App. at 66, 613.) Greenlease could have bargained for a provision in the Agreement whereby Trinity would have assumed all of Greenlease's obligations and liabilities following the expiration of the three-year indemnification provision. But it did not. Third, Greenlease relies on Keywell Corporation v. Weinstein , 33 F.3d 159 (2d Cir. 1994), a decision by the United States Court of Appeals for the Second Circuit, to argue that all CERCLA and HSCA liability automatically transferred to Trinity after the expiration of the three-year mutual indemnification provision. There are, though, important differences between the contract at issue in Keywell and the Agreement here that are sufficient to make that case inapposite. The corporate plaintiff in Keywell sought to recover CERCLA cleanup costs from two individual defendants, who had been officers of the corporation that sold the relevant piece of land to the plaintiff. Id. at 160 . The purchase agreement for the land included a two-year indemnification provision guaranteeing to hold the plaintiff harmless for any damages arising out of "any breach of warranty or representation" by the selling entity "or its management stockholders" and for "any liabilities or obligations of [s]eller" not explicitly listed in the purchase agreement. Id. at 162 . The plaintiff then entered into a separate thirty-year indemnification agreement with the corporate seller that guaranteed to hold the plaintiff harmless for any damages that "arose or existed" prior to the purchase agreement. Id. Importantly, that thirty-year indemnification agreement stated that only the corporate entity would be held to the longer indemnification period, not its individual officers. Id. Furthermore, prior to seeking to recover CERCLA cleanup costs from the individual defendants, the plaintiff had entered into yet another contract, this last one "unconditionally releas[ing]" the corporate entity's former "Management Group," which included the individual defendants, from any claims the plaintiff might have had under the purchase agreement. Id. On that set of facts, the Second Circuit held that the plaintiff could not recover CERCLA cleanup costs from the individual defendants because the relevant contractual documents unequivocally expressed the parties' intent to shift any and all liability away from the individual officers of the corporate entity after the initial two-year indemnification period. Id. at 166 . In contrast, the Agreement between Trinity and Greenlease does not demonstrate an unequivocal intent to shift liability away from Greenlease after the three-year contractual indemnification period expired. On the contrary, rather than releasing Greenlease from liability, the Agreement states that Trinity did not assume any of Greenlease's liabilities or obligations, unless otherwise expressly provided by the Agreement. Greenlease's reliance on Keywell is therefore misplaced, and we will affirm the denial of its motion for judgment on the pleadings. 2. The Costs Trinity Incurred Were Necessary and Reasonable. Greenlease next argues that the District Court impermissibly allocated to it costs that Trinity unnecessarily incurred by failing to impose cost controls on the remediation work at the North Plant. We review the District Court's factual findings for clear error, but review de novo its interpretation of CERCLA. Agere Sys., Inc. , 602 F.3d at 216 . A plaintiff can obtain contribution from a PRP under § 113(f)(3)(B) of CERCLA only if it first demonstrates a prima facie case of liability under § 107(a). See N.J. Tpk. Auth. v. PPG Indus., Inc. , 197 F.3d 96 , 104 (3d Cir. 1999). Here, that requires Trinity to demonstrate the following: first, that the North Plant is a facility; second, that Greenlease is a PRP; third, that "the release or threatened release of a hazardous substance has occurred"; and fourth, that Trinity incurred "necessary response costs consistent with the [National Contingency Plan.]" 9 Chevron Mining Inc. v. United States , 863 F.3d 1261 , 1269 (10th Cir. 2017) (internal quotation marks and citation omitted). Greenlease does not dispute the District Court's conclusions on the first three points. It only argues that the District Court erred by determining, as a legal matter, that Trinity's response costs were per se necessary because they were undertaken in compliance with the Consent Decree. That argument, however, even if it had merit, is irrelevant, since the record is clear that Trinity's response costs were in fact necessary under CERCLA. We thus need not address whether response costs undertaken in compliance with a consent decree should be considered necessary per se . A cost is considered "necessary" and hence subject to shared liability if there is "some nexus between [it] and an actual effort to respond to environmental contamination." 10 Young v. United States , 394 F.3d 858 , 863 (10th Cir. 2005) ; cf. Black Horse Lane Assoc., L.P. v. Dow Chem. Corp. , 228 F.3d 275 , 297 (3d Cir. 2000) (determining that a plaintiff did not meet its burden to demonstrate the necessity of a response action because it "did not relate to any remedial or response action at the" relevant site). It must be, in other words, a response cost, and CERCLA broadly defines a "response" to a hazardous release to include a wide variety of investigative, removal, and remedial actions. See 42 U.S.C. § 9601 (23) - (25) (providing a non-exhaustive list of "response" actions); W.R. Grace & Co.-Conn. v. Zotos Int'l, Inc. , 559 F.3d 85 , 92 (2d Cir. 2009) (noting that "response costs are liberally construed under CERCLA"). The District Court's detailed factual findings make clear that there was a nexus between the costs Trinity incurred and its effort to investigate and remediate the contamination at the North Plant. The cleanup activities at the North Plant were guided by the Consent Decree's requirement that those efforts be undertaken pursuant to the dictates of Pennsylvania's Act 2. That statute requires that remediation activities meet one of three standards: a background standard comparing contaminated areas to unaffected areas; a uniform statewide health standard set by a state agency, which differs depending on whether the site is meant for residential or commercial use; or a site-specific standard "based on a site-specific risk assessment so that any substantial present or probable future risk to human health and the environment is eliminated or reduced" so that the site could be utilized in accordance with its "present or currently planned future use[.]" (App. at 212 (citing 35 Pa. Stat. § 6026.301(a) ).) Trinity used the statewide health standard to determine which areas required "some type of response action" and then used the site-specific standard to guide the actual "soil cleanup." 11 (App. at 223.) It did not use the background standard. During the investigation phase of Trinity's cleanup activities, its consultant Golder used soil sampling to determine the areas of concern requiring remediation. That necessitated the establishment of a "standard action level," which is the numerical threshold for determining when soil is contaminated to an extent requiring treatment. For example, to determine whether areas contaminated by lead -the primary contaminant of concern-required treatment, Golder originally selected a standard action level of 1000 milligrams of lead per kilogram of soil. That was not a random choice. It selected that standard because it had observed that, at a threshold level of 1500 mg/kg, some soil samples passed toxicity testing, while others failed. At the more exacting 1000 mg/kg level, Golder was confident that it would catch all of the soil requiring remediation. But Golder was also cost conscious on that point. The selection of an accurate standard was important because failure to adequately remove all of the contaminated soil would require Golder to put in place more costly hazardous waste caps that could leave the land unusable. It initially chose the 1000 mg/kg standard for the reasons just noted, but when, during the cleanup process, it discovered that a significant amount of soil exceeded the 1000 mg/kg standard yet could still safely remain in place because it was going to "be capped anyway as part of the approved remedy" (App. at 234), it conducted a "site characterization study" to determine whether there was a more appropriate standard action level (App. at 234-35). Golder settled on a 2500 parts per million standard that was approved by PADEP. The record accordingly establishes an appropriate cost sensitivity and a nexus between Golder's (and hence Trinity's) investigative efforts and the purpose of remedying environmental harms. The same is true with regard to the activities Golder undertook to remediate the contaminated areas. It used three primary response actions: first, simply consolidating contaminated soil and placing an asphalt cap atop that soil; second, excavating and chemically treating contaminated soil to render it nonhazardous and then placing an asphalt cap over the remediated area; and third, transporting contaminated soil to an appropriate landfill. 12 Golder's soil excavation efforts allowed it to use simple asphalt caps to cover the excavated areas, as opposed to what are called Subtitle C caps. Subtitle C of RCRA regulates the precise manner in which a hazardous waste cap is put in place and maintained. Installing and maintaining a cap in compliance with Subtitle C is more difficult, complex, and expensive than installing and maintaining a simple asphalt cap. The District Court found that use of a Subtitle C cap would have made the North Plant site look like a "landfill," would not have been "consistent with the residential character of Greenville," (App. at 241), and would have rendered much of the North Plant unusable for any purpose. Those factual findings reinforce that Golder's activities had the required nexus to the stated purpose of remedying environmental harms. The response costs Trinity incurred were therefore necessary under CERCLA. Although Greenlease is correct that "[t]he cleanup at the North Plant was more difficult, inclusive, and expensive because it was done pursuant to the consent order and with oversight by ... PADEP," (App. at 225), we do not agree that those extra costs were consequently unnecessary. The Consent Decree required compliance with state environmental standards. To ensure that those statutory requirements were met, Trinity and Golder had to get PADEP's approval for each step of the cleanup. The costs incurred to comply with the Consent Decree were thus aimed directly at satisfying state environmental standards and are appropriately classified as "necessary to the containment and cleanup of hazardous releases." Redland Soccer Club, Inc. v. Dep't of Army of U.S. , 55 F.3d 827 , 850 (3d Cir. 1995) (citation omitted). A clearer way to understand Greenlease's contentions is to see them as challenging the reasonableness of Trinity's expenditures, not their necessity. Greenlease does not point to any specific activity that was not "necessary." Rather, it complains that Trinity incurred excessive costs because the Consent Decree lacked meaningful cost control mechanisms, because Trinity hired Golder without competitive bidding, and because Trinity agreed to a "cost-plus" billing arrangement with Golder. Those arguments fare poorly precisely because they do not address necessity, as that concept is applied in the context of CERCLA. Greenlease's arguments fall flat in light of the District Court's factual findings that we have already recounted in some detail. Greenlease does not point to any record evidence demonstrating how any of those facts resulted in unreasonably excessive spending. In contrast, as the Court found, Trinity and Golder worked together "to try to control costs or pay only reasonable costs," (App. at 218), and worked with PADEP "to reduce the amount of work [Trinity] had to do to comply with the" Consent Decree (App. at 225). The District Court credited expert testimony that the billing methods used by Trinity "contributed to the cost efficiency of the response work at the North Plant" and "prevented Golder from up-charging [Trinity.]" (App. at 219-20.) Greenlease has given us no sound reason to disagree with that assessment. 13 We will therefore affirm the District Court's determination that Trinity's response costs were necessary and reasonable. 3. The District Court Erred in Allocating Costs Between Trinity and Greenlease. Greenlease argues that the District Court used a purely speculative methodology, different from the methodology proposed by Trinity's expert witness Gormley to allocate costs between the parties. 14 In particular, the criticism is that the District Court relied on "volumes and surface areas ... as a proxy for the costs Trinity incurred at each impact area[.]" (Green. Opening Br. at 22.) Greenlease contends that that methodology was arbitrary because it failed to account for the reality that different units of measure are not interchangeable and because volumetric data cannot reliably serve as a proxy for costs when some remediation activities cost more than others. According to Greenlease, the District Court was forced to resort to a methodology based on volumetric data alone because Trinity failed to present sufficient evidence documenting how much it cost to undertake each of the major remediation activities within each impact area. Greenlease's position is thus that the District Court's cost allocation methodology cannot stand, given the Court's failure to include actual costs in its analysis. We agree that the Court materially deviated from the methodology presented by Gormley and so arrived at a speculative cost allocation methodology that must be corrected. CERCLA provides PRPs with a right to contribution for remediation expenses. Atl. Research Corp. , 551 U.S. at 138 , 127 S.Ct. 2331 . A district court "may allocate response costs among liable parties using such equitable factors as the court determines are appropriate." 42 U.S.C. § 9613 (f)(1). "[T]he law does not command mathematical preciseness from the evidence in finding damages. Instead, all that is required is that sufficient facts ... be introduced so that a court can arrive at an intelligent estimate without speculation or conjecture." Scully v. US WATS, Inc. , 238 F.3d 497 , 515 (3d Cir. 2001) (alterations in original) (internal quotation marks and citations omitted). We review an allocation of CERCLA damages for abuse of discretion. Agere Sys., Inc. , 602 F.3d at 216 . A district court abuses its discretion when its decision depends "upon a clearly erroneous finding of fact, an errant conclusion of law or an improper application of law to fact." Id. (citation omitted). The parties and their experts in this case placed the District Court in an unenviable position. Each of the parties staked out extreme positions on cost allocation, with Trinity's expert Gormley opining that Greenlease should be held responsible for 99% of all cleanup costs and Greenlease's expert opining that, despite Greenlease's 76 years of building and manufacturing activity at the North Plant, Trinity should be held responsible for nearly 90% of all cleanup costs. The record became even more difficult to sort out when, on direct examination, Gormley gave testimony that was unclear at best and departed from the methodology contained in his expert report. Although we commend the District Court's painstaking effort to analyze nearly a century of building and manufacturing activity by multiple parties to allocate costs equitably between Greenlease and Trinity, the attempt to untangle the evidentiary knot presented by the parties fell short. Before addressing the District Court's cost allocation methodology, we begin with the methodology that Gormley proposed in his expert report and explained somewhat at trial. Gormley's report presented a six-step approach to allocating costs. First, using "historical information and investigation findings," Gormley assigned a percentage of responsibility to each party for contamination in each area of concern, (D.I. 285-2 at 10), and he applied those percentages to the impact areas within each area of concern. He documented that step in Tables 4-1 and 6-2. Second, he calculated the quantity of material in each impact area that was subject to specific major remediation activities. That step was documented in Table 6-2. Third, he multiplied the estimated quantities of material used for (or remediated by) major remediation activities by each party's percentage of responsibility for contaminating each impact area. Fourth, he summed results from step three to develop Trinity's and Greenlease's respective responsibility percentages "for each major remediation activity[.]" ( Id. ) Fifth, he multiplied the percentage of responsibility for each major remediation activity by the cost of each such activity to determine how to allocate the costs for each. Finally, Gormley totaled how much in costs each party was responsible for across all major remediation activities "to calculate a total percent cost allocation for the major remediation activities." (D.I. 285-2 at 10.) Steps five and six were documented in Table 7-1. The report opined that the final percentage calculated at step six could be used to allocate the "general construction costs" (i.e., costs that were incurred on a project-wide basis that were not tied to a specific impact area) between both parties. Gormley's expert report presented his methodology as a single analysis with multiple steps. 15 Gormley's testimony at trial, however, muddied his otherwise straightforward methodology. At trial, he described his methodology as a "three-stage process." (D.I. 340 at 108.) Stage 1, termed the "AOC-by-AOC percentage allocation," involved creating a percentage allocation specific to each area of concern; stage 2, termed the "IA-by-IA percentage allocation," involved creating a percentage allocation for each impact area; and stage 3, termed "major remediation allocation," involved creating a specific allocation for each major remediation activity. (D.I. 340 at 108-11.) Trinity's counsel, in a perhaps confusingly worded set of questions, asked if each stage was meant "to be mutually exclusive" of the other stages, (D.I. 340 at 111), by which he appears to have been asking if each "stage" was a separate and distinct methodology that could be used to allocate costs, as opposed to steps in a single methodology. In a truly confusing answer, Gormley stated that the three stages "weren't supposed to be mutually exclusive," and he went on to testify that "[t]he first [stage] could be taken on its own," but that the second and third stages built on the first stage. (D.I. 340 at 111.) He ultimately agreed with Trinity's counsel, however, that each of his three stages "could be used by someone who was trying to develop their own logical or fair means to allocate responsibility for the contamination at the North Plant[.]" (D.I. 340 at 111.) Gormley's testimony departed from his expert report in a crucial way - his report made clear that each step in the methodology built on those that came before it, and that they were not independent means to come up with a cost allocation. His testimony, however, was less than clear as to whether the "stages" of his methodology were each independent analytical means to allocate costs or steps that built on one another. Led by the unclear testimony, the District Court chose Gormley's "stage 3" - divorced from the analytical foundations for that stage in the earlier steps of Gormley's analysis - to guide its cost allocation analysis. 16 That at least appears to have been the Court's approach because it titled its allocation analysis, "Overall Allocation of Responsibility based upon Major Remediation Activity"; it stated that it "determined an overall allocation based upon the extent of each major remediation activity in each [impact area]"; it explicitly listed the major remediation activities it "considered ... in its calculation"; and it cited Table 7-1 - the table corresponding to Gormley's stage 3 - when reaching its allocation determination. (App. at 375-77.) The District Court, however, materially deviated from Gormley's suggested major remediation activity allocation methodology by focusing only on the quantity of material involved in all major remediation activities, without distinguishing between activities and without regard to cost. That was despite Gormley's testimony confirming "that a central feature of the analysis ... reflected in [Table] 7-1 is [the] notion of the ... costs[.]" (D.I. 341 at 33.) The District Court's allocation methodology proceeded in four steps. First, it made its own factual determinations regarding the percentage of responsibility each party bore for contamination in each specific impact area. 17 Second, it totaled, for each impact area, the quantity of material used or remediated by major remediation activities. The Court's analysis did not differentiate between remediation activities. For example, it treated placing asphalt caps and placing topsoil as functionally the same for its cost allocation analysis despite the fact that those two activities' costs vary significantly. Third, it multiplied, on an impact area-specific basis, each party's percentage of responsibility for contamination with the total quantity of material used or remediated. Fourth, it used the resulting numbers to determine the percentage of material, in total, for which each party was responsible. That calculation led the Court to attribute to Greenlease 83% of responsibility for the contamination of the North Plant and to Trinity 17%. The Court, citing Gormley's testimony and expert report, used those percentages to allocate "all response costs ..., including responsibility investigation, removal and remedial past costs incurred through February 2015, for general construction costs, ... and future construction costs for ongoing operations and maintenance work." (App. at 377 (emphasis omitted).) Those percentages, however, were too speculative for two reasons. First, the Court's methodology failed to differentiate between different remediation activities and their varied costs, and, second, the methodology, as applied, treated data measured in square feet as equivalent to data measured in cubic yards. Although the District Court's reliance on volumetric data as the key factor in allocating response costs is not without support in our case law, its use here was flawed. 18 In Agere Systems, Inc. v. Advanced Environmental Technology Corporation , we endorsed a volumetric-centered approach to allocating CERCLA costs because, in that case, "volume allocation likely reflect[ed] the dollar amounts" at issue. 602 F.3d at 236 . We clarify here that such a volumetric-centered approach is only appropriate where the evidence supports a finding that one standardized volumetric unit correlates with a standardized per unit measure of cost. That may often be the case when a CERCLA cleanup involves only one impact area, or when a cleanup involves one primary major remediation activity. But when, as here, an environmental cleanup involves many impact areas and remediation activities with varying costs, a volumetric-centered approach that fails to account for cost differences will very likely lead to an allocation that is inequitable because it is divorced from the record evidence and analytically unsound. When, as a hypothetical example, 100 units of material that costs $1 per unit to remediate are treated the same as 100 units of material that costs $10 per unit to remediate, the analysis will be hard to justify. That kind of error occurred here and was compounded when the District Court treated conceptually distinct units of measurement as equal. It added together data measured in square feet - a unit of surface area - with data measured in cubic yards - a unit of volume. Performing such a calculation was, as Greenlease contends, like comparing "apples to oranges." 19 (Green. Opening Br. at 53.) Without pure speculation as to the depths at issue for the square footage measurements, or record evidence establishing those depths, it would not have been possible for the District Court to equate cubic yards to square feet. The Court's findings of fact and conclusions of law do not reflect any such analysis. Those problematic deviations from Gormley's methodology compel us to conclude that there was an abuse of discretion and that we must vacate the District Court's judgment as to the allocation of costs between Greenlease and Trinity. If the District Court was persuaded by Gormley's analytical approach, then, on remand, it should adhere to the cost allocation methodology he set forth in his expert report - a methodology that both experts relied upon in coming to their respective cost allocation estimates. That methodology will require the Court to conduct a separate cost allocation analysis for each major remediation activity. Much of the information needed for that is readily available in the record, but additional fact-finding by the District Court may be needed. 20 To apply Gormley's methodology properly, the District Court must use volumetric and cost data specific to the remediation activities. For every major remediation activity, then, the Court should calculate how much of that activity each party was responsible for. It can then apply that percentage breakdown to the total cost of that specific activity at the North Plant. Once it assigns each party a cost allocation for every major remediation activity, the Court will be able to add the parties' respective shares of costs together. From those totals, the Court can calculate the overall percentages to use in determining an equitable allocation of costs between Greenlease and Trinity. The District Court remains free to exercise its discretion to adjust those percentages, subject to the guidance provided herein. It is also free to reopen the record, should it determine that it is necessary to do so to carry out the kind of analysis we have described. 21 C. Trinity's Cross-Appeal Trinity raises three primary issues in its cross-appeal. First, it appeals the District Court's factual determination of responsibility for the lead contamination at the North Plant. We will affirm because we cannot say that the Court abused its discretion, given the evidentiary record before it. Second, Trinity challenges the District Court's decision to grant Greenlease equitable deductions to account for the Agreement's indemnification provisions and for the purported increase in value of the North Plant following the cleanup. We agree that the District Court erred in the manner in which it applied those equitable deductions. We emphasize, however, that the District Court is free on remand to apply equitable deductions in accordance with the principles discussed in this opinion. Third, Trinity appeals the District Court's determination that Ampco is not liable for the conduct of Greenlease. We will affirm on that point because Trinity cannot demonstrate that Ampco is either directly or derivatively liable for Greenlease's conduct at the North Plant. 1. The District Court's Allocation of Responsibility for Lead Contamination was Not an Abuse of Discretion. Trinity challenges the District Court's determination that Greenlease's painting operations did not contribute to lead contamination requiring remediation. It contends that it is undisputed that Greenlease's painting operations at the North Plant resulted in lead runoff seeping into the ground. We review an allocation of CERCLA damages for abuse of discretion. Agere Sys., Inc. , 602 F.3d at 216 . Given the evidence and expert testimony in the record supporting the District Court's determination, we do not agree that there was an abuse of discretion. The District Court did not, as Trinity suggests, "disregard the co-contributing effects of Greenlease's lead paint releases." (Trinity Opening Br. at 64.) Rather, as the Court explained, it found that the historic fill utilized at the North Plant by various parties over the years was "the source of the lead contamination that required remediation [.]" (App. at 402.) In other words, the District Court found that any contamination by lead paint alone would not have resulted in contamination requiring remediation. The Court then incorporated "the overall percentage of responsibility for the lead contamination that required remediation " in its equitable cost allocation analysis. (App. at 402.) The District Court's finding that historic fill and not lead paint was the source of the contamination requiring remediation was adequately supported by Greenlease's expert Gerritsen. He supported his conclusion by studying soil samples and observing no correlation between painting operations and lead contamination. In particular, Greenlease's expert observed that lead exceeding PADEP standards was consistently present in historic fill rather than native soil. That Trinity's expert reached a different conclusion - without conducting an analysis of soil samples - is of no import. The District Court was entitled to believe Greenlease's expert analysis, as it had adequate support to be admissible. See United States v. Allegheny Ludlum Corp. , 366 F.3d 164 , 184 (3d Cir. 2004) ("[W]hen presented with two sound but conflicting expert opinions, a district court has discretion to credit one over the other."). Accordingly, we will affirm the conclusion that Greenlease's paint operations did not result in lead contamination requiring remediation. 2. The District Court Abused Its Discretion When Granting Equitable Deductions Premised on the Indemnification Provisions and the Purported Increased Value of the North Plant. CERCLA grants trial courts broad discretion to "allocate response costs among liable parties using such equitable factors as the court determines are appropriate." 42 U.S.C. § 9613 (f)(1). "Congress intended to grant the district courts significant flexibility in determining equitable allocations of response costs, without requiring the courts to prioritize, much less consider, any specific factor." Beazer E., Inc. v. Mead Corp. , 412 F.3d 429 , 446 (3d Cir. 2005). However, "[w]e do not simply 'rubber-stamp' a district court's equitable allocation[.]" Lockheed Martin Corp. v. United States , 833 F.3d 225 , 234 (D.C. Cir. 2016) (citation omitted). Rather, we review the equitable allocation of environmental cleanup costs for abuse of discretion. Agere Sys., Inc. , 602 F.3d at 216 ; Beazer , 412 F.3d at 445 n.18. Trinity argues that the District Court's 5% equitable deduction in favor of Greenlease due to the contractual indemnification provisions, and its 10% equitable deduction in favor of Greenlease due to the purported increased value of the North Plant, were improper. We agree, and so too does Greenlease, which acknowledges that the District Court's "percentage reductions were completely arbitrary and speculative." (Green. Opening Br. at 24.) The District Court abused its discretion when it applied the 5% equitable deduction because it erroneously interpreted our precedent. It also abused its discretion when it applied the 10% equitable deduction because it failed to explain how it arrived at that figure, and we can discern no basis for the figure in the record. i. The 5% Indemnification Provisions Deduction The District Court relied on our opinion in Beazer East, Inc. v. Mead Corporation when it took into consideration the Agreement's indemnification provisions to reduce Greenlease's percentage of responsibility by 5%. It concluded that "it would be error" to not incorporate the parties' intent, as manifested by the three-year limit on the indemnification provisions, into its equitable allocation. (App. at 383.) It reached that conclusion because, in Beazer , we held that it was error for a district court to fail to incorporate the relevant parties' mutual intent when entering a contract as part of its equitable allocation. 412 F.3d at 448 . In that case, the district court had failed to give "significant consideration" to the parties' intent when equitably allocating CERCLA costs, id. , despite finding that both parties had intended that the defendant-seller "would not bear any environmental liability following the ... sale," id. at 445 . The district court had reasoned that, because the contract at issue did not "demonstrate[ ] a clear and unambiguous intent to transfer all CERCLA liability," as required by the relevant state law, the parties' intent to shift liability should be a subordinate factor to the "polluter pays" principle embedded in CERCLA. Id. at 447-48 . We said that the district court erred because the legal interpretation of the contract did not prevent the court from giving, as a matter of equity, significant consideration to "the intent of the parties, which [was] manifested by their actions and in the written agreement[.]" Id. at 447 . Critical to our holding in Beazer was the fact that the district court had determined that both parties expressed a mutual intent to shift CERCLA liabilities following the relevant sale. It was only a nuanced application of state contract law that prevented the parties' mutual intent from being enforced as a matter of law. Therefore, in that case, equity demanded that the district court give significant consideration to the parties' shared intent. Here, in contrast, the District Court's findings make clear that there was no mutual intent, as expressed by the written agreement or by the actions of both parties, to shift CERCLA liability following the sale of the North Plant. It was, at most, only Greenlease's subjective intent to shed all CERCLA liability following the expiration of the three-year indemnification period. A party's subjective intent to avoid liability, which contradicts the agreement at issue, should not be given significant consideration when equitably allocating environmental cleanup costs. Because it appears that the District Court here mistook Beazer to permit Greenlease's subjective intent to be given substantial weight, its 5% equitable deduction in favor of Greenlease was an abuse of discretion. Nothing we have said here should be interpreted as altering the principle set out in Beazer that, as a matter of equity, trial courts can take into consideration "the intent of the parties ... [as] manifested by their actions and in the written agreement[.]" Id. at 447 . But when the intent resulting in the equitable deduction is not shared by both parties and appears contrary to provisions of the contract, a district court must explain why, as a matter of equity, it is nevertheless appropriate to award an equitable deduction. Because we view the District Court as having misapplied Beazer , we remand for it to take a fresh look at whether it is appropriate, on the record before the Court, to award Greenlease an equitable deduction premised on the contractual indemnification provisions. ii. The 10% Property Value Increase Deduction The District Court concluded that a 10% equitable deduction in favor of Greenlease was appropriate because the North Plant's value had increased since the remediation work transformed the site from being unsuitable for any productive purpose to being usable as a site for some commercial or industrial purposes. Although we agree with the District Court's identification of the increased value of a remediated site as an appropriate equitable factor to consider when allocating cleanup costs, we cannot agree with its application of that principle here because the record did not contain any evidence concerning the fair market value of the North Plant, either before or after the remediation. If a landowner successfully seeks contribution from others for environmental cleanup costs, that owner should likely be required to share the benefits of any increase in value brought about by the cleanup. Courts have thus taken the increased market value of a remediated property into consideration when allocating response costs. See, e.g. , Litgo N.J. Inc. v. Comm'r N.J. Dep't of Envtl. Prot. , 725 F.3d 369 , 387 (3d Cir. 2013) (discussing the increased value of remediated land); Minyard Enters., Inc. v. Se. Chem. & Solvent Co. , 184 F.3d 373 , 387 (4th Cir. 1999) (directing a lower court to take into consideration "the fact that the [p]roperty may appreciate following its remediation"); Farmland Indus., Inc. v. Col. & E. R.R. Co. , 944 F.Supp. 1492 , 1500-01 (D. Colo. 1996) (concluding that "it would be inequitable" not to take into account the fact that the former owner "garner[s] no tangible benefit from the cleanup of land it no longer owns"). Limiting a party's ability to benefit from an economic windfall comports with "CERCLA's general policy against double recovery[.]" Litgo , 725 F.3d at 391 . The problem with the District Court's 10% deduction, then, was not in the decision to consider the increased market value of the North Plant as an equitable factor but rather in the application of that factor without any record evidence concerning the North Plant's value. It is only appropriate to take increased value into consideration when there is evidence concerning an actual increase, such as proof of the fair market value of the property before and after the cleanup. See N.Y. State Elec. & Gas Corp. v. FirstEnergy Corp. , 766 F.3d 212 , 239 (2d Cir. 2014) (refusing to take into consideration "the economic benefit of the cleanup" because the party seeking the equitable deduction "fail[ed] to offer evidence about any increase in the value of the land"). Because the District Court may reopen the record for purposes already discussed, see supra subsection III.B.3, it may also receive additional evidence concerning the fair market value of the North Plant site, both before and after the remediation activities, to allow it to come to a reasoned percentage reduction premised on the increased fair market value, if any, of the North Plant site. 3. The District Court Did Not Err in Deciding that Ampco Is Neither Directly Nor Derivatively Liable for the Contamination at the North Plant. Trinity argues that the District Court erred in determining that Ampco was not liable for Greenlease's share of environmental cleanup costs. As Trinity sees it, the evidence it presented demonstrated genuine issues of material fact that were sufficient to entitle it to a trial on the question of Ampco's liability. It advances two closely related theories to support its position that Ampco is legally responsible for Greenlease's conduct at the North Plant. First, Trinity contends that Ampco is directly liable because it qualifies under CERCLA as an "operator" of the North Plant. Second, it asserts that, under a veil-piercing theory, Ampco is derivatively liable for Greenlease's operation of the North Plant. Direct and derivative liability are two analytically distinct bases for holding a parent company liable for environmental cleanup costs resulting from a subsidiary's conduct. United States v. Bestfoods , 524 U.S. 51 , 67-68, 118 S.Ct. 1876 , 141 L.Ed.2d 43 (1998). We review the District Court's grant of summary judgment de novo. Shelton v. Bledsoe , 775 F.3d 554 , 559 (3d Cir. 2015). Summary judgment is appropriate only if, after drawing all reasonable inferences in favor of the non-moving party, there exists "no genuine dispute as to any material fact." Shuker v. Smith & Nephew, PLC , 885 F.3d 760 , 770 (3d Cir. 2018) (quoting Fed. R. Civ. P. 56(a) ). After our own independent assessment of the record evidence, we agree with the District Court that Ampco is not liable for Greenlease's conduct at the North Plant, and we will therefore affirm the grant of summary judgment in favor of Ampco. i. Ampco Is Not Directly Liable for Greenlease's Share of Responsibility for Contamination at the North Plant. CERCLA holds an "operator" of a facility "directly liable for the costs of cleaning up the pollution." Bestfoods , 524 U.S. at 65 , 118 S.Ct. 1876 . Direct liability attaches to a parent company whose subsidiary owns a facility only if the "act of operating a corporate subsidiary's facility is done on behalf of a parent corporation[.]" Id. The term "operate" is read according to its "ordinary or natural meaning" to refer to "someone who directs the workings of, manages, or conducts the affairs of a facility." Id. at 66 , 118 S.Ct. 1876 (citation omitted). To be directly liable, "an operator must manage, direct, or conduct operations specifically related to pollution, that is, operations having to do with the leakage or disposal of hazardous waste, or decisions about compliance with environmental regulations." Id. at 66-67 , 118 S.Ct. 1876 . Whether Ampco is directly liable, therefore, must be based on its "participation in the activities of the" North Plant. Id. at 68 , 118 S.Ct. 1876 . Trinity cannot hold Ampco liable for the environmental cleanup costs merely by showing that "dual officers and directors made policy decisions and supervised activities at the facility." Id. at 69-70 , 118 S.Ct. 1876 . Direct liability will only exist if there is evidence that Ampco managed the day-to-day activities of the North Plant in a manner that exceeds "the interference that stems from the normal relationship between parent and subsidiary." Id. at 71 , 118 S.Ct. 1876 . As the Supreme Court instructed in United States v. Bestfoods , the relevant inquiry for direct liability focuses on the relationship between the parent entity and the polluting facility, not the parent's relationship to its subsidiary. Id. at 68 , 118 S.Ct. 1876 . The District Court rightly determined that the record here would not permit a reasonable fact-finder to conclude that Ampco's involvement in the day-to-day operations of the North Plant exceeded "the normal relationship between parent and subsidiary," id. at 71 , 118 S.Ct. 1876 , in a manner that would support holding Ampco directly liable for Greenlease's conduct. The undisputed facts establish, rather, that "[Greenlease] employees were responsible for all day-to-day operations at the North Plant, including any waste disposal, waste handling, painting, abrasive blasting, welding, and fabrication operations." (App. 81-82.) Greenlease employees, not Ampco employees, coordinated disposal with outside contractors and communicated with PADEP on environmental matters. In fact, Ampco "did not employ any engineers or persons with technical experience in manufacturing that could make decisions for [Greenlease] with respect to environmental compliance or waste management." (App. at 82 . ) Instead, "Ampco employed only a professional staff, such as accountants, actuaries, and lawyers[.]" (App. at 82.) Helping with administrative work is consistent with a typical parent-subsidiary relationship, and certainly does not establish Ampco's direct involvement with the North Plant, which Bestfoods demands to hold a parent directly liable for environmental cleanup costs. Trinity maintains that Ampco crossed the line into operating the North Plant. According to Trinity, Ampco did so through individuals who advised Greenlease with regard to environmental laws and regulations, monitored Greenlease's activities, provided Greenlease with legal advice regarding compliance with environmental laws, and were involved with Greenlease's plans to increase the North Plant's production capacity and to modernize its operations. Trinity does not, however, explain how any of those activities, even if one accepts Trinity's take on the evidence, turns Ampco's supervision of Greenlease into anything other than a typical parent-subsidiary relationship. Bestfoods makes clear that "[a]ctivities that involve the facility but which are consistent with the parent's investor status, such as monitoring of the subsidiary's performance, supervision of the subsidiary's finance and capital budget decisions, and articulation of general policies and procedures, should not give rise to direct liability." 22 524 U.S. at 72 , 118 S.Ct. 1876 (citation omitted). That the policies Ampco advised on may have included environmental issues does not, on this record, change the calculus. Accordingly, we agree with the District Court's conclusion that Ampco's actions with respect to the North Plant did not fall outside the bounds of typical "parental oversight of a subsidiary's facility," id. , and hence are not a basis for direct liability. ii. Ampco Is Not Derivatively Liable for Greenlease's Share of Responsibility. A parent corporation can be held derivatively liable under CERCLA for its subsidiary's actions "only when[ ] the corporate veil may be pierced[.]" Id. at 63 , 118 S.Ct. 1876 . And "the corporate veil may be pierced" only in extraordinary circumstances, such as when "the corporate form would otherwise be misused to accomplish certain wrongful purposes[.]" Id. at 62 , 118 S.Ct. 1876 ; see also Wedner v. Unemp't Comp. Bd. of Review , 449 Pa. 460 , 296 A.2d 792 , 794 (1972) ("The corporate entity or personality will be disregarded [o]nly when the entity is used to defeat public convenience, justify wrong, protect fraud or defend crime." (citation omitted) ). In such circumstances, the law permits a subsidiary to be deemed an "alter ego" of its parent so that the parent can be held liable for the actions of its subsidiary. Pearson v. Component Tech. Corp. , 247 F.3d 471 , 484 (3d Cir. 2001). Piercing the corporate veil is a limited exception to the "general principle of corporate law deeply ingrained in our economic and legal systems that a parent corporation ... is not liable for the acts of its subsidiaries." Bestfoods , 524 U.S. at 61 , 118 S.Ct. 1876 (internal quotation marks and citations omitted); see also Lumax Indus., Inc. v. Aultman , 543 Pa. 38 , 669 A.2d 893 , 895 (1995) ("[T]here is a strong presumption in Pennsylvania against piercing the corporate veil."). Trinity seeks to use both federal law and state law to pierce the corporate veil. The federal law principles we have articulated for when a subsidiary is merely an alter ego of its parent are substantially similar to the principles set forth in Pennsylvania case law. Our analysis of both, therefore, can largely proceed in tandem, though we do specifically note Trinity's state law-specific arguments. Under either theory, Trinity has failed to adduce sufficient evidence to create a triable issue of fact. We have identified several factors helpful in determining whether, as a matter of federal common law, a subsidiary is merely an alter ego of its parent. Those factors include "gross undercapitalization, failure to observe corporate formalities, nonpayment of dividends, insolvency of [subsidiary] corporation, siphoning of funds from the [subsidiary] corporation by the dominant stockholder, nonfunctioning of officers and directors, absence of corporate records, and whether the corporation is merely a façade for the operations of the dominant stockholder." Pearson , 247 F.3d at 484-85 . 23 No single factor is dispositive, and we consider whether veil piercing is appropriate in light of the totality of the circumstances. Cf. Trs. of Nat'l Elevator Indus. Pension, Health Benefit & Educ. Funds v. Lutyk , 332 F.3d 188 , 194 (3d Cir. 2003) (explaining that the alter ego test factors do not comprise "a rigid test"); Am. Bell Inc. v. Fed'n of Tel. Workers of Pa. , 736 F.2d 879 , 887 (3d Cir. 1984) (requiring "specific, unusual circumstances" before piercing the corporate veil (citation omitted) ). 24 Proving that a corporation is merely an alter ego is a burden that "is notoriously difficult for plaintiffs to meet." Pearson , 247 F.3d at 485 . "[I]n order to succeed on an alter ego theory of liability, plaintiffs must essentially demonstrate that in all aspects of the business, the two corporations actually functioned as a single entity and should be treated as such." Id. 25 Under our precedent, the basis for piercing the corporate veil must be "shown by clear and convincing evidence." Lutyk , 332 F.3d at 192 (quoting Kaplan v. First Options of Chi., Inc. , 19 F.3d 1503 , 1522 (3d Cir. 1994) ). 26 Trinity appears to agree that most of the traditional factors we look to when determining whether to pierce the corporate veil are either inapplicable to this case or favor Ampco. Its primary arguments for piercing the corporate veil are that "Greenlease became undercapitalized when Ampco siphoned off Greenlease's assets," that "Ampco and Greenlease's interactions exceeded norms that characterize parent/subsidiary relationships," (Trinity Opening Br. at 74), that the equities tilt in its favor under Pennsylvania's alter-ego test, and that public policy favors holding Ampco responsible. a. Greenlease Was Not Undercapitalized and Ampco Did Not Siphon Funds From Greenlease. Trinity argues that Greenlease's issuing to Ampco some $50 million dollars in dividends in the years following the sale of the North Plant, leaving only $250,000 in reserve for liabilities, favors piercing the corporate veil. But "the inquiry into corporate capitalization is most relevant for the inference it provides into whether the corporation was established to defraud its creditors or [an]other improper purpose such as avoiding the risks known to be attendant to a type of business." Lutyk , 332 F.3d at 197 . There is no basis in the record to suggest that Greenlease was undercapitalized while operating the North Plant. Instead, Trinity suggests only that Greenlease lacked funds after Greenlease's operations of the North Plant had effectively stopped. That is of "little relevancy to determining whether piercing the corporate veil [is] justified here." Id. There is also no evidence that Greenlease issued dividends to Ampco with awareness of its liability to Trinity or to escape subsequent liability. See Zubik v. Zubik , 384 F.2d 267 , 273 (3d Cir. 1967) ("Unless done deliberately, with specific intent to escape liability for a specific tort or class of torts, the cause of justice does not require disregarding the corporate entity."). As the District Court noted, "it would be unreasonable for Ampco to leave Greenlease's earnings from the sale of the North Plant in an account when at the time the dividends were issued Greenlease was a nonoperating company with no known liabilities." (App. 91 (emphasis removed).) b. Greenlease and Ampco's Relationship Was a Typical Parent-Subsidiary Relationship. Trinity emphasizes that there was significant overlap between the boards of Ampco and Greenlease and argues that Ampco dominated Greenlease to an unusual extent. But "duplication of some or all of the directors or executive officers" is not fatal to maintaining legally distinct corporate forms. Bestfoods , 524 U.S. at 62 , 118 S.Ct. 1876 (citation omitted); see also Am. Bell , 736 F.2d at 887 (noting that "there must be specific, unusual circumstances" to justify veil piercing, and mere control and participation in management is inadequate). Greenlease ran the North Plant and hired all of the employees on the ground. Although Ampco was required to approve large decisions, Greenlease generally functioned with autonomy on decisions concerning manufacturing, environmental compliance, and disposal of waste. We have already said and now repeat that the District Court rightly determined that the record simply does not support Trinity's position that Greenlease's relationship with Ampco was materially different than a normal parent-subsidiary relationship. c. Trinity Cannot Pierce the Corporate Veil Under Pennsylvania Law. Trinity argues that the District Court erred by disregarding the "equitable underpinnings" of Pennsylvania's alter-ego framework. (Trinity Reply Br. at 6.) It maintains that Pennsylvania disregards the legal fiction of separate corporate entities "whenever justice or public policy demand[s]" it. (Trinity Reply Br. at 7 (quoting Ashley v. Ashley , 482 Pa. 228 , 393 A.2d 637 , 641 (1978).) According to Trinity, permitting Ampco to reap the benefits of the over $50 million in dividends from Greenlease without being held accountable for Greenlease's conduct is an injustice. But Trinity overlooks that Pennsylvania requires a plaintiff seeking to pierce the corporate veil to make "a threshold showing that the controlled corporation acted robot- or puppet-like in mechanical response" to the controlling shareholder's demands. E. Minerals & Chem. Co. v. Mahan , 225 F.3d 330 , 333 n.6 (3d Cir. 2000) (citation omitted). Trinity has not made that showing here. Pennsylvania law is also clear that courts are not to disregard the legal fiction of separate corporate entities if it would render "the theory of the corporate entity ... useless." Ashley , 393 A.2d at 641 ; see also Wedner , 296 A.2d at 795 ("Care should be taken on all occasions to avoid making the entire theory of the corporate entity ... useless." (internal quotation marks omitted) (quoting Zubik , 384 F.2d at 273 ) ). To permit Trinity to pierce the corporate veil in this instance, in the face of all the objective criteria favoring Ampco, would, in essence, result in rendering useless Ampco's legitimate use of the corporate form when setting up Greenlease as a subsidiary. The record is devoid of evidence that Ampco misused separate corporate entities for some nefarious purpose. To pierce the corporate veil would thus fly in the face of Pennsylvania's "strong presumption ... against piercing the corporate veil." Lumax , 669 A.2d at 895 . d. Public Policy Considerations Do Not Favor Trinity. Finally, Trinity argues that the District Court failed to consider public policy justifications for piercing the corporate veil to ensure that the "polluter pays." (Trinity Opening Br. at 74.) As discussed above, however, both federal and Pennsylvania law favor maintaining the legal fiction of separate corporate entities. Because the evidence does not suggest that there was fraud or an attempt to use a corporate façade as an alter ego, public policy first favors upholding the integrity of the corporate form. Trinity has not presented any public policy consideration sufficiently compelling to overcome the strong presumption against veil piercing. IV. CONCLUSION For the foregoing reasons, we will affirm in part but will vacate the District Court's cost allocation determination and remand for further proceedings consistent with this opinion. Footnotes [1] Greenlease was known first as the Greenville Metal Products Company and then as the Greenville Steel Car Company. For purposes of this opinion, we refer to all Greenlease and Greenville entities as "Greenlease." [2] The facts recounted here are taken from the District Court's post-trial findings of fact or from facts in the record that are undisputed. [3] Greenlease's stock was first acquired in 1937 by another company, the Pittsburgh Forging Co. Ampco then acquired all of the stock of the Pittsburgh Forging Co., and, through a series of transactions, became the sole shareholder of Greenlease. [4] In 2008, that reserve was $150,000, and in 2009, it was $282,500. [5] According to the District Court's findings of fact, the work includes maintaining the asphalt caps and continued ground water monitoring. [6] A court may equitably allocate among the parties before it the share of hazardous waste contamination belonging to responsible third-party entities not before it (such allocated amounts being known as "orphan shares"). But it can typically only do so if such orphan shares belong to entities that are unknown, insolvent, or immune from suit. See Litgo N.J. Inc. v. Comm'r N.J. Dep't of Envtl. Prot. , 725 F.3d 369 , 380 n.4 (3d Cir. 2013) (permitting equitable allocation of orphan shares among liable parties at the court's discretion). As found by the District Court, that is not the case here. [7] The District Court had jurisdiction over Trinity's federal law claims under 42 U.S.C. §§ 6972 (a) and 9613(b) and 28 U.S.C. § 1331 . It had supplemental jurisdiction over Trinity's state law claims under 28 U.S.C. § 1367 . We have jurisdiction pursuant to 28 U.S.C. § 1291 . [8] As cited earlier, those sections of CERCLA are codified at 42 U.S.C. §§ 9607 (a) and 9613(f), respectively. [9] The National Contingency Plan provides a set of standards governing environmental cleanup activities, including " 'methods and criteria for determining the appropriate extent of removal, remedy, and other measures,' 42 U.S.C. § 9605 (a)(3), and 'means of assuring that remedial action measures are cost-effective.' [42 U.S.C.] § 9605(a)(7)." United States v. E.I. Dupont De Nemours & Co. Inc. , 432 F.3d 161 , 168 (3d Cir. 2005) (en banc). [10] The case law that has developed around CERCLA has interpreted the term "necessary" to refer to a more elastic concept than how the word is typically understood. For example, CERCLA case law defines a "necessary" cost as one that has some "nexus" to the cleanup of environmental harm, not as a cost without which the cleanup would not have been possible. Compare Young v. United States , 394 F.3d 858 , 863 (10th Cir. 2005) (interpreting the term "necessary cost" in the CERCLA context to refer to a cost that has a "nexus" to an environmental cleanup), with NECESSARY, Black's Law Dictionary (10th ed. 2014) (defining "necessary" as something "[t]hat is needed for some purpose or reason; essential"). We have undertaken our analysis of what costs were or were not necessary in this case in light of CERCLA precedent. Our opinion does not address how the term "necessary" should be interpreted in contexts outside of CERCLA. [11] The site-specific standard also required Trinity and Golder to engage the local community and to accept public comments about the cleanup efforts. [12] Certain contaminated soil was amenable to chemical treatment that rendered it nonhazardous; other soil was not amenable to such treatment and remained hazardous prior to disposal. The soil that was chemically treated could be transported to a nonhazardous waste landfill, which was two to four times cheaper than disposal at a hazardous waste landfill. The soil remaining hazardous had to be transported to a hazardous waste landfill. [13] Even if Greenlease's argument had merit, and the matter were in equipoise, we might yet be inclined to affirm the District Court's finding that the costs Trinity incurred were reasonable. That is because Trinity incurred those costs in furtherance of the Consent Decree. Although we need not, and do not, decide here whether costs incurred by a private party in compliance with a state consent decree are presumed reasonable under CERCLA, we note that similar costs incurred by a government party are presumed reasonable. For example, it is black letter CERCLA law that when a government's actions are not inconsistent with the National Contingency Plan, its costs are presumed reasonable, E.I. Dupont , 432 F.3d at 178 , and are recoverable against PRPs, 42 U.S.C. § 9607 (a)(4)(A). Since compliance with a consent decree entered pursuant to state law "establishe[s] ... compliance with the National Contingency Plan," Niagara Mohawk Power Corp. v. Chevron U.S.A., Inc. , 596 F.3d 112 , 137 (2d Cir. 2010), costs incurred by a government party in compliance with such a decree should be presumed reasonable. There may be a related principle warranting a similar presumption in a context like this. [14] Greenlease's expert incorporated Gormley's cost allocation methodology into his own cost allocation analysis, so Gormley's methodology was the only one presented to the District Court. [15] While the report did not break the methodology into the six discrete steps we describe here, it did have each of the steps, and identifying them separately is, we believe, helpful. [16] The District Court interpreted Gormley's trial testimony as establishing that "[e]ach of the three methods used by [him] could be used on its own-without considering the other two methods-to allocate responsibility for the contamination at the North Plant." (App. at 249.) Although that conclusion was understandable based on Gormley's testimony, it was mistaken. While Gormley agreed that "someone who was trying to develop their own logical or fair means to allocate responsibility" could incorporate any one of his stages into an allocation methodology, (D.I. 340 at 111), he never testified that someone could separate out one stage, and then use that stage's allocation methodology alone to allocate all cleanup costs for remediating contamination at the North Plant. [17] We find no error in the Court's underlying factual findings with regard to the contamination in each specific impact area. [18] Although we determine that the District Court erred in utilizing the cost allocation methodology that it did, the Court's use of volumetric data and a focus on major remediation activity as a means to determine the allocation of response costs was reasonable and within the Court's discretion. [19] "Cubic measures and square measures represent fundamentally different things. A cubic measure is always a three-dimensional unit of volume: length times width times height. A square measure is always a two-dimensional unit of area: length times width." Chris Magyar, Cubic Yards to Square Feet Conversion , SCIENCING (Mar. 13, 2018), https://sciencing.com/cubic-yards-square-feet-conversion-8641439.html (last visited Aug. 21, 2018). [20] We reiterate that any cost allocation methodology must differentiate between major remediation activities and account for the varying costs across those activities. Exactitude is not required. Indeed, at this late date it is probably not even possible. It is enough for the Court to make a reasonable estimate of costs based on an appropriate record. See Scully , 238 F.3d at 515 (explaining that the law only requires that district courts "arrive at an intelligent estimate" of CERCLA damages "without speculation or conjecture"; it does not require courts to arrive at a "mathematical[ly] precise[ ]" figure (citations omitted) ). [21] Because we must remand this case, we do not address whether Trinity met its burden to prove damages. However, if the Court chooses to reopen the record on remand, we encourage it to permit the parties to address whether some South Plant costs were impermissibly included in the Court's prior allocation of costs at the North Plant. It may also allow the parties to introduce evidence quantifying the costs incurred in remediating contamination caused by third parties. [22] Trinity argues that "substantial factual similarities" between Bestfoods and the facts here support its argument that Ampco is directly liable for Greenlease's operation of the North Plant. (Trinity Opening Br. at 78.) It contends that "[e]very fact referenced by the Supreme Court in Bestfoods has a parallel in this case." (Trinity Reply Br. at 20.) We disagree. In Bestfoods , the Supreme Court vacated a judgment in favor of a parent corporation because one of its employees "played a conspicuous part in dealing with the toxic risks emanating from the operation of the [subsidiary's] plant." 524 U.S. at 72 , 118 S.Ct. 1876 . Here, by contrast, Trinity has not pointed to record evidence that any officer, director, or employee of Ampco played a significant, let alone conspicuous, role in the operation of the North Plant. [23] Factors considered by Pennsylvania state courts include "undercapitalization, failure to adhere to corporate formalities, substantial intermingling of corporate and personal affairs and use of the corporate form to perpetrate a fraud." Lumax , 669 A.2d at 895 . [24] See also Advanced Tel. Sys., Inc. v. Com-Net Prof'l Mobile Radio, LLC , 846 A.2d 1264 , 1281 (Pa. Super. Ct. 2004) (looking to the "totality of circumstances" when conducting corporate veil piercing analysis). [25] See also E. Minerals & Chem. Co. v. Mahan , 225 F.3d 330 , 333 n.6 (3d Cir. 2000) (explaining that Pennsylvania law "require[s] a threshold showing that the controlled corporation acted robot- or puppet-like in mechanical response to the controller's tugs on its strings or pressure on its buttons" before allowing a plaintiff to pierce the corporate veil (citation omitted) ); Culbreth v. Amosa (Pty) Ltd. , 898 F.2d 13 , 14 (3d Cir. 1990) (interpreting Pennsylvania law to require that "the party seeking to pierce the corporate veil on an alter-ego theory establish[ ] that the controlling corporation wholly ignored the separate status of the controlled corporation and so dominated and controlled its affairs that its separate existence was a mere sham"). [26] Trinity presents three arguments for why the District Court erred by applying the clear and convincing evidence standard to its alter-ego analysis: that it is always improper for a district court to apply that standard to a motion for summary judgment, that federal law does not incorporate the clear and convincing standard when the plaintiff does not allege fraud, and that Pennsylvania applies a preponderance of the evidence standard to its alter-ego analysis. First, Trinity is incorrect as a matter of law that "under no circumstances" is a clear and convincing standard "appropriate for summary judgment purposes." (Trinity Opening Br. at 68.) "[T]he determination of whether a given factual dispute requires submission to a jury must be guided by the substantive evidentiary standards that apply to the case." Anderson v. Liberty Lobby, Inc. , 477 U.S. 242 , 255, 106 S.Ct. 2505 , 91 L.Ed.2d 202 (1986). "Consequently, where the clear and convincing evidence standard applies, the trial judge [at summary judgment] must inquire whether the evidence presented is such that a jury applying that evidentiary standard could find only for one side." Justofin v. Metro. Life Ins. Co. , 372 F.3d 517 , 522 (3d Cir. 2004). Second, our precedent is clear, as a matter of federal common law in this Circuit, that "[b]ecause alter ego is akin to and has elements of fraud theory, ... it ... must be shown by clear and convincing evidence." Lutyk , 332 F.3d at 192 (citation omitted). Trinity has not presented any compelling argument to revisit that longstanding proposition. Third, we do not need to address the standard of proof we think Pennsylvania applies to its alter-ego analysis because, whether we apply a preponderance of the evidence standard or a clear and convincing evidence standard to the state law analysis, our ultimate conclusion is the same-no reasonable fact-finder could justify piercing the corporate veil on this record.