In a prior appeal of this tax case, we affirmed the district court’s decision to *285disregard the partnership form of Chem-tech Royalty Associates, L.P. (“Chemtech I”), and Chemtech II, L.P. (“Chemtech II”), for tax purposes but vacated and remanded as to the penalty award. On remand, the court reinstated the vacated penalty award and further held that a tax penalty for gross-valuation misstatement applied to Chemtech II. Through its wholly-owned subsidiary Dow Europe, S.A., which was the tax matters partner for Chemtech I, real party in interest The Dow Chemical Company (“Dow”) now appeals the penalty award solely as to Chem-tech I. We find no error and affirm.
I.
The underlying facts are set out in detail in the opinions of this court and the district court,1 so we only summarize the most relevant facts. In the early 1990s, Dow decided to engage in a tax shelter transaction that became Chemtech I. After forming Chemtech I as a limited partnership, Dow contributed seventy-three patents, which it then leased back in return for royalty payments.
Dow took valuable tax deductions on its royalty payments to Chemtech I. Dow, however, was allocated only a small fraction of Chemtech I’s taxable income, which instead was allocated mainly to Chemtech I’s tax-exempt investors, foreign banks2 that invested $200 million in return for a priority return of interest-like payments of 6.947% per year. In theory, the foreign banks had minimal participation (1%) in Chemtech I’s residual profits. But Dow was able to control the extent of the foreign banks’ profit participation through a contractual provision that enabled it to remove' profitable patents from Chemtech I’s patent portfolio. See Chemtech, 766 F.3d at 464. Other provisions also insulated the foreign banks from almost all risk of loss by effectively guaranteeing that they would receive their investment back regardless of Chemtech I’s financial performance. See id.
In 1998, Dow terminated Chemtech I in response to changes in U.S. tax laws. Dow bought out the shares of the foreign banks, then reorganized the partnership as Chemtech II. The details of Chemtech II are irrelevant for purposes of this appeal.
After conducting a partnership-level audit, the Internal Revenue Service issued Final Partnership Administrative Adjustments (“FPAAs”) to the tax matters partner for Chemtech I for tax years 1993 through 1997 and to the tax matters partner for Chemtech II for tax years 1998 through 2006. The FPAAs asserted adjustments for tax years 1993 through 2006, resulting in the disallowance of $1 billion of tax deductions to Dow and also asserted accuracy-related penalties for tax years 1997 through 2006 under 26 U.S.C. § 6662.3
Through the tax matters partners for Chemtech I and Chemtech II, which are both Dow subsidiaries, Dow filed a part*286nership-level proceeding in district court under the Tax Equity and Fiscal Responsibility Act of 1982 (“TEFRA”), challenging the FPAAs. After- a bench trial, the court affirmed the FPAAs’ adjustments of partnership items, basing its decision on three grounds: (1) The alleged partnerships were shams; (2) the contribution-leaseback transactions at the heart of Chemtech I and Chemtech II lacked economic substance; and (3) the banks’ interests in Chemtech I and Chemtech II were debt rather than equity. The .court then held that the 20% accuracy-related penalties for negligence and substantial understatement applied but that substantial-valuation and gross-valuation misstatement penalties were foreclosed under Todd v. Commissioner, 862 F.2d 540 (5th Cir.1988), and Heasley v. Commissioner, 902 F.2d 380 (5th Cir.1990).
In our 2014 opinion, we affirmed the district court’s decision to disregard the partnership form of Chemtech I and Chemtech II for tax purposes, reasoning that they were sham partnerships. Despite that affirmance, however, we vacated and remanded as to the penalty award in light of the intervening decision in United States v. Woods, — U.S. —, 134 S.Ct. 557, 564, 187 L.Ed.2d 472 (2013), which effectively overruled Todd and Heasley. We instructed the district court to reconsider the applicability of the substantial-valuation and gross-valuation misstatement penalties and to “consider the extent to which imposing [the negligence and substantial-understatement] penalties remains consistent with this opinion.” Chemtech, 766 F.3d at 465.4
On remand, the district court amended its final judgment. It held that the gross-valuation misstatement penalty applied to Chemtech II and that the substantial-understatement and negligence penalties vacated in the first appeal applied to both Chemtech I (tax years 1997 through mid-1998) and Chemtech II (tax years mid-1998 through 2006). Because penalties under Section 6662 do not stack,5 the result of the district court’s decision was to hold applicable a 20% penalty for tax years 1997 to mid-1998 and a 40% penalty for tax years mid-1998 to 2006.
II.
Section 6662 of the Internal Revenue Code (“IRC”) imposes a penalty of 20% of the portion of any underpayment of tax attributable to, inter alia, negligence and substantial understatement of income. Negligence “includes any failure to make a reasonable attempt to comply with the provisions” of the IRC. 26 U.S.C. § 6662(c). A substantial understatement occurs when the amount by which a corporate taxpayer understates its tax obligation exceeds the lesser of $10,000,000 or 10% of the tax actually owed. Id. § 6662(d)(1)(B).
At issue here is whether, on remand, the district court erred in holding that penalties for negligence and substantial understatement applied to the last year and a half of Chemtech I, i.e., tax years 1997 through mid-1998. Dow asserts that the answer is yes, for essentially two reasons.6 First, it maintains, our *287mandate from the first appeal required the district court to justify any tax penalty solely on the ground that Chemtech I was a sham partnership. Second, penalties for negligence and substantial understatement cannot be justified on the basis that Chem-tech I was a sham partnership, because Dow had a reasonable basis and substantial authority for its contrary position that Chemtech I was a valid partnership. A taxpayer may reduce or eliminate the negligence penalty by establishing that it had a “reasonable basis” for its tax treatment of an item, 26 C.F.R. § 1.6662 — 3(b)(1), and may reduce or eliminate the substantial-understatement penalty by showing that it had “substantial authority,” id. § 1.6662-3(b)(3).7
A.
We review a district court’s interpretation of a remand order de novo. 8 Review of a determination that the negligence penalty applies as a factual matter is for clear error,9 and whether the reasonable-basis defense applies as a legal matter is reviewed de novo. 10 Where the facts are essentially undisputed, the applicability of the substantial-authority defense is a question of law reviewed de novo. 11
B.
In the first appeal, we vacated the penalties for negligence ánd substantial understatement and directed the district, court to “consider the extent to which imposing those penalties remains consistent with this opinion.” Chemtech, 766 F.3d at 465. On remand, the court readopted “the factual findings and conclusions of law [from its original opinion] on the issues of negligence and substantial-understatement penalties,” then reinstated the negligence and substantial-understatement penalties.12 It gave two reasons: (1) The underlying facts remained unchanged; and (2) the “imposition of those penalties does not contravene the Fifth Circuit’s opinion in this *288matter.”13
Dow contends that the district court failed to implement our mandate. According to Dow, we vacated that court’s original penalty determinations in light of the “narrow” ground for our affirmance of tax deficiency in the first appeal. Whereas the district court gave three grounds for affirming the deficiencies assessed by the IRS, we affirmed the deficiency determinations on only one ground, namely, that Chemtech I was a sham-partnership. Dow maintains that we vacated and remanded as to the tax penalties so that the district court could reconsider whether the negligence and substantial-understatement penalties could be justified on the basis of our sham-partnership holding, an inquiry that the district court never undertook. Again according to Dow, in its original order the district court justified the negligence penalty based solely on the finding that the “artificial tax benefits [of Chemtech I and Chemtech II] would seem ‘too good to be true’ to a reasonable and prudent person, let alone to a highly sophisticated Fortune 100 company and its numerous lawyers and tax professionals.” Chemtech v. U.S., 2013 WL 704037, at *28. The district court did not consider whether Dow had a reasonable basis for any of its tax positions, and it considered Dow’s substantial-authority defense only with regard to Dow’s economic-substance position.14
We reject Dow’s theory that our mandate required the district court to consider whether Dow had a reasonable basis and substantial authority for its sham-partnership position. As stated at the beginning of our opinion in the first appeal, we vacated and remanded as to the penalty award in light of Woods, which overruled the line of cases on which the district court had precluded substantial-valuation and gross-valuation misstatement penalties. Although Woods did not directly pertain to the penalties for negligence and substantial understatement, we nevertheless deemed it appropriate to vacate those penalties in case, on remand, the district court determined that application of Woods might indirectly affect the applicability of negligence and substantial-understatement penalties. We stated that we were “expressing] no opinion on whether the [district] court erred in imposing the negligence and substantial-understatement penalties.” Chemtech, 766 F.3d at 465. Dow’s suggestion that our vacatur of those penalties reflects some disapproval of or dissatisfaction with the district court’s original grounds for finding them applicable is therefore untenable.
C.
The district court did not err in failing to justify the negligence and substantial-understatement penalties on the basis of our sham-partnership holding, but it could have done so. We affirm the applicability of the negligence and substantial-understatement penalties on the ground that the district court would have been correct to do so.15 Dow lacked substantial authority *289for its position that Chemtech I was a valid partnership. And Dow lacked a reasonable basis for the same reasons that its substantial-authority defense fails: The cited authorities are materially distinguishable on their facts.16
1.
The government contends that Dow may not assert the substantial-authority defense because it made no attempt to show that it “reasonably believed” its tax treatment of Chemtech I was “more likely than not correct.” For years before 2004, the IRC prohibited corporate taxpayers such as Dow from invoking the substantial-authority defense for items attributable to a tax shelter. 26 U.S.C. § 6662(d)(2)(C)(ii) (2000) (amended 2004). The Treasury Regulations, however, grandfathered in transactions occurring before December 9, 1994. 26 C.F.R. § 1.6662 — 4(g)(l)(ii)(B). For such transactions, a corporate taxpayer may invoke the substantial-authority defense if it can show that it “reasonably believed that the tax treatment of such item by the taxpayer was more likely than not the proper treatment.” 26 U.S.C. § 6662(d)(2)(C)(i)(II) (1997) (amended 2004).
We agree with the government that Dow is subject to the reasonable-belief requirement because it began Chemtech I in 1993 and because Chemtech I was a tax shelter. During the years at issue, a tax shelter was defined as a partnership, entity, plan, or arrangement “if the principal purpose of the entity, plan or arrangement, based on objective evidence, is to avoid or evade Federal income tax.” 26 C.F.R. § 1.6662-4(g)(2)(i) (1997). The principal purpose is tax avoidance or evasion “if that purpose exceeds any other purpose.” Id. The district court found that Dow’s only business purpose in forming Chemtech I was to obtain tax benefits. Chemtech, 2013 WL 704037, at *18. Because that finding is not clearly erroneous, we affirm the district court’s determination that Chemtech I was a tax shelter. Id. at *30. Dow is therefore subject to the reasonable-belief requirement.
Nonetheless, we disagree with the government’s notion that Dow was required to make its reasonable-belief showing in the district court. In a recent decision, we expressed uncertainty over whether the reasonable-belief requirement can be determined in a partnership-level proceeding such as this.17 The government draws attention to the decisions of several out-of-circuit district courts that considered reasonable belief in partnership-level rather than partner-level proceedings.18 But the government cites no authority that requires litigation of reasonable belief in a partnership-level proceeding, and we decline to impose such a requirement, particularly where, as here, the government failed to raise any objection to the availability of the substantial-authority defense in the district court. We may therefore *290consider the substantial-authority defense in this partnership-level proceeding.19
2.
In addition to rejecting the government’s claim that the substantial-authority defense is unavailable to Dow, we likewise decline its insistence that Dow waived its substantial-authority argument by failing to brief the issue in the first appeal. In its original decision, the district court failed to justify the negligence and substantial-understatement penalties on the basis of its sham-partnership holding. Under those circumstances, Dow sufficiently preserved its substantial-authority argument in the first appeal through its general assertion that it possessed a reasonable basis and substantial authority for all of its challenged tax positions. Dow was under no obligation to brief in extenso issues not addressed by the district court.
3.
On the merits of Dow’s appeal, in order for there to be substantial authority, the weight of the authorities supporting treatment of an item must be substantial in relation to the weight of those supporting contrary treatment. 26 C.F.R. § 1.6662—4(d) (3) (i). This standard is more stringent than the reasonable-basis standard but less stringent than the more-likely-than-not standard. Id. § 1.6662-4(d)(2). For purposes of the substantial-authority inquiry, an authority’s weight “depends on its relevance and persuasiveness, and the type of document providing the authority.” Id. § 1.6662—4(d)(B)(ii). An authority is not particularly relevant if it is materially distinguishable on its facts. Id. Moreover, it is relevant for purposes of the substantial-authority inquiry only if it existed at the time the return containing the item was filed or the last day of the taxable year to which the return relates.. See id. § 1.6662-4(d)(3)(iv)(C).
Under these criteria, Dow lacked substantial authority for its position that Chemtech I was a valid partnership. Dow points to only two authorities in existence at the time' of the filing of Chemtech I’s tax returns as allegedly supporting treatment of Chemtech I as a valid partnership. In Morris v. Commissioner, 13 T.C. 1020 (1949), the Tax Court held that the petitioner’s wife was a true limited partner in her husband’s brokerage partnership even though she received only a fixed 6% return on her investment plus 2% of any profits earned in excess of expenses and charges. And in Hunt v. Commissioner, T.C. Memo. 1990-248, 59 T.C.M. (CCH) 635 (1990), the Tax Court held that a partnership was. not a sham in which one of the partners was entitled to a cumulative return of 18%, followed by a return of its capital contribution, before any of the other partners began receiving returns of their capital contributions. According to Dow, both decisions treated an interest with minimal sharing in profits and losses as a partnership interest and the holder of such an interest as a valid partner.
We deny Dow’s interpretation of Morris and Hunt, which would eliminate any intent element from the sham-partnership doctrine. Under the totality-of-the-circumstances test in Commissioner v. Culbertson, 337 U.S. 733, 741-42, 69 S.Ct. 1210, 93 L.Ed. 1659 (1949), a partnership is a sham if the putative partners do not possess the intent to share profits and losses. Morris and Hunt explicitly recognize and purport to apply Culbertson’s holding and thus cannot be read in the way that Dow proposes, as authority that the *291owner of an equity instrument automatically satisfies Culbertson. To the contrary, Morris and Hunt show that an interest with minimal sharing in profits and losses can qualify as a partnership interest only if the owner of that interest intends to share profits and losses.
The government urges that Morris and Hunt are entirely inapposite because, as found by the district court and affirmed by us, Dow lacked the intent to share profits' and losses with the foreign banks, Chemtech, 766 F.3d at 464-65, and no authority supports the recognition of a partnership in which the putative partners lacked the intent to share profits and losses. We might find the government’s position persuasive if there were direct evidence that Dow lacked the intent to share profits and losses. Given the lack of direct evidence of intent, however, Dow can satisfy the substantial-authority standard if it produces authority for the view that the circumstantial evidence in this case would permit a not-clearly-erroneous finding that Dow possessed the intent to share profits and losses. That test is essentially the same as the one adopted by the Sixth Circuit, though our reasoning differs.20 That test also accords with how at least one district court in this circuit has handled the substantial-authority inquiry.21
Because Morris and Hunt can be interpreted as providing some support for the view that Dow possessed the intent to share profits and losses with the foreign banks, we disagree with the government’s contention that those decisions are entirely inapposite. Nevertheless, they are not “substantial authority,” because they are materially distinguishable on their facts. In contrast to the entities here, the partnerships in Morris and Hunt did not make use of any contribution-leaseback transactions. Nor did they possess a mechanism that would have allowed the managing partner or real party in interest to make the sharing of profits illusory, as the district court found was the case with Chem-tech I.22
Even if Morris and Hunt were not materially distinguishable on their facts, they would fail to constitute substantial authority in light of Merryman v. Commissioner, 873 F.2d 879 (5th Cir.1989). There, we affirmed, as not clearly erroneous, the finding that a partnership was a sham and should be disregarded for tax purposes. The partnership in Merryman contained many of the same features as does Chem-tech I: a partner that retained complete control over the property contributed to the partnership; a circular flow of funds; minority partners’ total lack of risk with respect to partnership property; and the partnership’s lack of employees and failure to hold itself out as being engaged in a business.
Because Merryman is more apposite than are Morris and Hunt, and because Merryman is published circuit authority, whereas Morris and Hunt are Tax Court *292cases (one old and the other unpublished), Dow lacked substantial authority for its position that Chemtech I was a valid partnership. For substantially the same reasons, Dow fails to meet the lesser reasonable-basis standard.
The judgment is AFFIRMED.