The Commissioner of Internal Revenue (Commissioner) appeals from the tax court's valuation of Medtronic, Inc. and its consolidated subsidiaries' (Medtronic) true income for the 2005 and 2006 tax years.

The Commissioner characterizes this dispute as involving "the classic case of a U.S. multinational taxpayer (Medtronic) shifting income from its highly profitable U.S. operations and intangibles to an offshore subsidiary operating in a tax haven (Medtronic [Puerto Rico] ), by charging an artificially low rate for the intangibles." Appellant's Reply Br. 1. Medtronic's view of the case is that because its Puerto Rico subsidiary bears the lion's share of potential liability arising from any defectively manufactured products, it was entitled to a commensurate rate of return on its operations there. Appellee's Br. 21-26.

The Commissioner argues that the tax court erred in not applying the correct transfer pricing method when calculating the arm's length royalty rates for Medtronic's intercompany licenses. We vacate the tax court's order and remand for further proceedings consistent with this opinion.

I. Background

Medtronic is a medical device company that produces and markets class III devices, which include implantable cardiac pulse generators and neurological stimulators (devices), as well as other medical therapy devices (leads). Medtronic's parent company, Medtronic US, and its distributor, Medtronic USA, Inc. (Med USA), are located in the United States, and its class III device manufacturer, Medtronic Puerto Rico Operations Co. (Medtronic Puerto *612Rico), is located in Puerto Rico. Medtronic allocates the profit earned from its devices and leads between Medtronic US, Med USA, and Medtronic Puerto Rico through its intercompany licensing agreements.

Medtronic's 2002 consolidated tax return used the comparable uncontrolled transactions (CUT) transfer pricing method to determine the royalty rates paid on its intercompany licences. The Internal Revenue Service's (IRS) audit of the return left it with the concern that Medtronic was shifting too much profit from its devices and leads to Puerto Rico in an attempt to avoid taxation in the United States. Using the residual profit split transfer pricing method, the IRS concluded that 90% of Medtronic's devices and leads profit should be allocated to the United States operations and 10% to the Medtronic Puerto Rico operations. To resolve the audit, Medtronic and the IRS entered into a Memorandum of Understanding (Memorandum) in which Medtronic Puerto Rico agreed to pay royalty rates of 44% for devices and 26% for leads on its intercompany sales. The IRS in return agreed to apply the Memorandum's royalty rates in future years "as long as there [were] no significant changes in any underlying facts." Neither party considered the Memorandum's royalty rates to be an arm's length price, but rather as only a compromise in an effort to resolve the audit.

The IRS and Medtronic could not agree on how the Memorandum should apply to Medtronic's royalty income for the 2005 and 2006 tax years. After completing an initial audit of Medtronic's transfer pricing method, the IRS determined that the comparable profits method-not the CUT method-was the best way to determine an arm's length price for Medtronic's intercompany licensing agreements for those two years.1 Using the comparable profits method to determine the royalty rates for intangibles under the intercompany licensing agreements, the IRS concluded that the rate paid by Medtronic Puerto Rico was too low, resulting in tax deficiencies for 2005 and 2006. Accordingly, the Commissioner proposed an initial adjustment of $84 million based on his revised calculations under the Memorandum. Medtronic contested the IRS's determinations, arguing that the CUT method should instead be used to calculate an arm's length price. Medtronic further claimed an overpayment of its taxes based on its original royalty rates under the intercompany licenses.

After completing the audit, the Commissioner proposed to increase the royalty payments paid by Medtronic Puerto Rico to Medtronic US by an additional $455 million. Following Medtronic's appeal to the IRS's Appeals Office, the Commissioner requested that the case be returned to the IRS for reexamination. Thereafter, the Commissioner again used the comparable profits method to calculate the arm's length royalty rates, following which he issued Medtronic a notice of deficiency totaling $198,232,199 for 2005 and $759,383,578 for 2006. Approximately seven months later, the Commissioner amended the notice, asserting that the initial adjustments were understated and that Medtronic's deficiencies as related to devices *613and leads were actually $548,180,115 and $810,301,695 for 2005 and 2006, respectively.

Medtronic filed suit in United States Tax Court, arguing that the CUT method, not the comparable profits method, was the best method for determining an arm's length price for the intercompany licenses.2 After a nearly six-week trial, the tax court rejected both parties' royalty rate valuations. In doing so, the tax court held that the Commissioner's "allocations were arbitrary, capricious, or unreasonable." The court also found that the comparable profits method "downplayed" Medtronic Puerto Rico's role in ensuring the quality of the devices and leads, that it did not reasonably attribute a royalty rate to Medtronic's profits, that it used an incorrect return on assets approach, that it improperly aggregated the transactions, and that it ignored the value of licensed intangibles. Similarly, the tax court concluded that Medtronic's CUT method did not produce an accurate arm's length adjustment because it did not distinguish between devices and leads and therefore produced a result that was unconvincing and overly broad.

The tax court then engaged in its own valuation analysis. It ultimately decided that Medtronic's CUT method was the best way to determine an arm's length royalty rate for intercompany agreements, but made a number of adjustments. In doing so, it found that the arm's length royalty rate for the device licenses was 44% and the rate for the lead licenses was 22%. It thereafter issued an order concluding that Medtronic had an income tax deficiency of $26,711,582.00 in 2005, but that it had an income tax overpayment of $12,459,734.00 in 2006. The Commissioner then filed this appeal, seeking a reversal and a remand for a reevaluation of the best transfer pricing method and a recalculation of the arm's length royalty rate.

II. Discussion

We review a tax court's decision in the same manner as a district court's civil bench ruling-legal conclusions and mixed questions of law and fact are reviewed de novo , and factual findings are reviewed for clear error. Clajon Gas Co., L.P. v. C.I.R., 354 F.3d 786, 789 (8th Cir. 2004).

Section 1.482 of the Treasury Regulations states that "there is no strict priority of methods" when determining an arm's length result of a controlled transaction. Treas. Reg. § 1.482-1(c)(1). Instead, "[a]n arm's length result may be determined under any method without establishing the inapplicability of another method, but if another method subsequently is shown to produce a more reliable measure of an arm's length result, such other method must be used." Id. When more than one method is available, the two primary factors to consider are "the degree of comparability between the controlled transaction (or taxpayer) and any uncontrolled comparables, and the quality of the data and assumptions used in the analysis." Treas. Reg. § 1.482-1(c)(2).

As set forth above, the tax court concluded that the CUT method would produce the most reliable arm's length return rate. This method "evaluates whether the amount charged for a controlled transfer of intangible property was arm's length by reference to the amount charged in a comparable *614uncontrolled transaction." Treas. Reg. § 1.482-4(c). If uncontrolled transactions involve the same or comparable intangible property, then the CUT method will generally yield the most reliable arm's length measurement. Treas. Reg. § 1.482-4(c)(2)(ii). Intangible property is considered comparable if it was created under similar circumstances and was "used in connection with similar products or processes within the same general industry or market; and [it has] similar profit potential." Treas. Reg. § 1.482-4(c)(2)(iii)(B). Other factors to consider when evaluating comparability include relevant functions, contract terms, risks, economic conditions, and property or services. Treas. Reg. § 1.482-1(d)(1).

In using this method, the tax court applied the Pacesetter agreement as the best CUT to calculate the arm's length result for intangible property. The Pacesetter agreement was entered into by Pacesetter's parent company and Medtronic US in 1992 in an effort to settle several lawsuits regarding patent and license use. As part of the agreement, the parties cross-licensed their pacemaker and patent portfolios. They additionally agreed that Medtronic would receive a $75 million lump sum payment plus a 7% royalty for all future sales of cardiac stimulation devices or components covered under Medtronic's patents in the United States.

The tax court determined that the Pacesetter agreement was an appropriate CUT because it involved similar intangible property and had similar circumstances regarding licensing. We conclude that the tax court's factual findings are insufficient to enable us to conduct an evaluation of that determination.

The tax court did not address in sufficient detail whether the circumstances of the settlement between Pacesetter and Medtronic US were comparable to the licensing agreement between Medtronic and Medtronic Puerto Rico. The Pacesetter agreement resolved litigation between the parties, and the tax court did not decide whether it was one created in the ordinary course of business. See Treas. Reg. § 1.482-1(d)(4)(iii)(A)(1) (stating that transactions that were not made in the ordinary course of business will not generally be considered reliable for arm's length purposes).

Additionally, the tax court did not analyze the degree of comparability of the Pacesetter agreement's contractual terms and those of the Medtronic Puerto Rico licensing agreement. See Treas. Reg. § 1.482-1(d)(3)(ii)(A)(1) ("Determining the degree of comparability between the controlled and uncontrolled transactions requires a comparison of the significant contractual terms that could affect the results of the two transactions."). For example, the tax court acknowledged that the Pacesetter agreement included a lump sum payment and a cross-license, but it did not address how Pacesetter's additional terms affected the degree of comparability with Medtronic Puerto Rico's licensing agreement, which did not include a lump sum payment or cross-license. In the absence of findings regarding the degree of comparability between the controlled and uncontrolled transactions, we cannot determine whether the Pacesetter agreement constituted an appropriate CUT. See Treas. Reg. § 1.482-4(c)(2)(iii)(B)(2)(vii) ("In evaluating comparability of the circumstances of the controlled and uncontrolled transactions, ... specific factors that may be particularly relevant include ... [t]he existence and extent of any collateral transactions or ongoing business relationships between the transferee and transferor.").

The tax court also did not evaluate how the different treatment of intangibles affected *615the comparability of the Pacesetter agreement and the Medtronic Puerto Rico licensing agreement. The Pacesetter agreement was limited to patents and excluded all other intangibles, including "any technical know-how or design information, manufacturing, marketing, and/or processing information or know-how, designs, drawings, specifications, software source code or other documents directly or indirectly pertinent to the use of the Licensed patents." The Medtronic Puerto Rico licensing agreement, on the other hand, did not exclude such intangibles. Although we recognize that the tax court made a 7% adjustment for the "know how" that Medtronic Puerto Rico received from Medtronic, as well as a 2.5% adjustment to account for the differences in licensed products (the Pacesetter agreement licensed only cardiac "patent portfolios" whereas Medtronic's agreements also licensed neurological products), we cannot determine that appropriateness of using the Pacesetter agreement as a CUT without additional findings regarding the comparability of the remaining intangibles.

Finally, the tax court did not decide the amount of risk and product liability expense that should be allocated between Medtronic US and Medtronic Puerto Rico. The Commissioner contends that Medtronic Puerto Rico bore only 11% of the devices and leads manufacturing costs, which included its share of the product liability expense, and that therefore Medtronic Puerto Rico's allocation of profits should be a similar percentage based on its economic contribution. The tax court rejected the Commissioner's 11% valuation, concluding that it was unreasonably low because it did not give enough weight to the risks that Medtronic Puerto Rico incurred in its effort to ensure quality product manufacturing. Accordingly, the tax court allocated almost 50% of the device profits to Medtronic Puerto Rico. In doing so, the tax court also rejected the Commissioner's comparable profits methods because it found that the comparable companies used by the Commissioner under this method did not incur the same amount of risk incurred by Medtronic Puerto Rico. Yet the tax court reached these conclusions without making a specific finding as to what amount of risk and product liability expense was properly attributable to Medtronic Puerto Rico. In the absence of such a finding, we lack sufficient information to determine whether the tax court's profit allocation was appropriate.

We deem such findings to be essential to our review of the tax court's determination that the Pacesetter agreement was a CUT, as well as necessary to our determination whether the tax court applied the best transfer pricing method for calculating an arm's length result or whether it made proper adjustments under its chosen method. Accordingly, we vacate the tax court's January 25, 2017, order and remand the case for further consideration in light of the views set forth in this opinion. See Centron DPL Co. v. Tilden Fin. Corp., 965 F.2d 673, 676 (8th Cir. 1992) ("In the absence of ... critical factual determinations, we must vacate the judgment of the district court and remand for reconsideration with instructions to make more complete factual findings.").

I concur in full with Judge Wollman's opinion. As it recounts, when selecting the Pacesetter-Medtronic US agreement as a comparable uncontrolled transaction ("CUT"), the tax court did not sufficiently address: (1) the fact it arose out of litigation; (2) the lump sum payment that was a part of it; (3) the cross-licenses that were a part of it; and (4) certain intangibles that *616were not part of it.3 I write separately to make two additional points. First , not only are those factors important to ensure adequate appellate review, but the applicable Treasury Guidelines mandate that they be considered. And second , when searching for CUTs to assess damages in patent infringement actions, courts routinely reject patent licenses that are different in even one of the four ways that was not adequately addressed by the tax court. Simply put, the Treasury Department and courts in patent cases deem these factors significant. At the very least, the taxpayer deserves an explanation why they are insignificant in this case.

The Treasury Guidelines operate with a mix of "mandatory" and "discretionary words." See Murphy v. Smith, --- U.S. ----, 138 S.Ct. 784, 789, 200 L.Ed.2d 75 (2018). And it is a well-worn principle of reading legal texts that "mandatory words impose a duty; permissive words grant discretion." See Antonin Scalia & Bryan A. Garner, Reading Law: The Interpretation of Legal Texts 112 ( West 2012). In this case, the Treasury Guidelines "create[ ] a mandate, not a liberty" when it comes to engagement with the four factors not addressed by the Tax Court. Smith, 138 S.Ct. at 787. When speaking generally about comparability, the Treasury Guidelines state that, regardless of the comparability test deployed, "each method requires analysis of all of the factors that affect comparability." Treas. Reg. § 1.482-1(d)(1) (emphasis added). The Treasury Guidelines go on to say that "[s]uch factors include ... functions ... [and] contractual terms." Id. § 1.482-1(d)(1) (i)-(ii). All four of the factors identified by Judge Wollman's opinion touch on either "functions" or "contractual terms." The "require[d] analysis" was missing from the Tax Court's discussion.4

Courts assessing damages in patent cases find these factors decisive as well. In determining damages in a patent infringement case, the goal is to get to a number which would have been arrived at during "a hypothetical negotiation between the patentee and the infringer when the infringement began." ResQNet.com, Inc. v. Lansa, Inc., 594 F.3d 860, 868 (Fed. Cir. 2010). The standard is essentially the same as the one set forth by the Treasury Guidelines. See 12 James. J. Hall, Mertens Law of Federal Income Taxation § 45I:25 (noting "Section 482" is meant to determine an "arm's-length price" which "is the price an unrelated party would have paid under the same circumstances for the property involved in the controlled transaction"). In the patent context, previous patent licenses are used as proxies for the "hypothetical negotiation." But in conducting this analysis, courts often shy away from comparisons that differ on even one of the four planes the tax court failed to analyze here.

For example, take lump sum payments. As one academic has noted, "courts generally *617frown upon the use of one type of license-for instance, a lump sum license-to calculate a different type of license, such as a running royalty in which the defendant pays per unit sold over time." Jonathan S. Masur, The Use and Misuseof Patent Licenses, 110 Nw. U. L. Rev. 115, 124 (2015). Indeed, the Federal Circuit has held that "certain fundamental differences exist between lump-sum agreements and running-royalty agreements." Wordtech Sys., Inc v. Integrated Networks Solutions, Inc., 609 F.3d 1308, 1320 (Fed. Cir. 2010) (internal quotation marks omitted) (rejecting comparison between lump-sum and royalty licenses and remanding for new trial on damages). Here, as Judge Wollman's opinion notes, the Pacesetter-Medtronic agreement contained a $75 million lump-sum payment whereas the Medtronic US-Medtronic Puerto Rico agreement was a royalty-only one. The tax court failed to grapple with this difference.

Next, consider cross licenses. Courts have held that agreements which include cross licenses are inadequate comparisons for "hypothetical negotiation[s]"-damage assessments-where they are not involved. See, e.g., ePlus, Inc. v. Lawson Software, Inc., 764 F.Supp.2d 807, 813 (E.D. Va. 2011), aff'd, 700 F.3d 509 (Fed. Cir. 2012). Indeed, in a striking parallel to this case, the Lawson Software court held that comparison agreements which involve "lump[-]sum payments ... and extensive cross-licensing agreements ... differ considerably from the factual predicates ... where the hypothetical negotiation does not involve a lump[-]sum payment or cross-licensing of a wide variety of patents." Id.

The same mismatch problem is found when attempting to use settlements. As Judge Easterbrook has noted: "The terms of a settlement reflect [litigation] costs as well as the parties' estimates about the probable outcome on the merits if the case proceeds. It is risky to use the parties' predictions as a reason to decide some other case on the merits." In re Mahurkar Double Lumen Hemodialysis Catheter Patent Litig., 831 F.Supp. 1354, 1379 (N.D. Ill. 1993) (Easterbrook, J., sitting by designation), aff'd, 71 F.3d 1573 (Fed. Cir. 1995). That said, the Federal Circuit has recognized that sometimes the "most reliable license" for comparison may "ar[i]se out of litigation." Lansa, Inc., 594 F.3d at 872 ; but see id. at 880 (Newman, J., concurring in part and dissenting in part) (noting that "unpredictability of patent litigation remains notorious" and that "particular litigation settlements may be based on unique considerations"). Regardless, Judge Easterbrook's exact warning is borne out here: the Pacesetter-Medtronic settlement agreement recitals note that the parties entered into the agreement to reduce future litigation costs. And, again, this was not accounted for by the tax court.

Finally, some intangibles were not accounted for. Failing to do so is reversible error in the patent context. Wordtech Sys., Inc., 609 F.3d at 1320 ("We stressed that comparisons of past patent licenses to the infringement must account for the technological and economic differences between them." (internal quotation marks omitted) ). Here, as Judge Wollman's opinion notes, the intangibles not included in the Pacesetter-Medtronic agreement, but included in the Medtronic-Medtronic Puerto Rico, are varied-and valuable. Without a doubt, "additional findings regarding the comparability" of the intangibles are needed. Maj. Op. 615.

To conclude, "any search for a 'comparable uncontrolled [transaction]' " is undoubtedly "quixotic." Michael J. Graetz & Rachael Doud, *618Technological Innovation, International Competition, and the Challenges of International Income Taxation, 113 Colum. L. Rev. 347, 416 (2013). But, I harbor serious doubts that the Medtronic-Pacesetter agreement can serve as an appropriate CUT for the reasons stated above. Cf. South Dakota v. Wayfair, Inc., --- U.S. ----, 138 S.Ct. 2080, 2086, --- L.Ed.2d ---- (2018) ("It is essential to public confidence in the tax system that [courts] avoid creating inequitable exceptions."). In the first instance, however, the tax court should conduct the "require[d] analysis" mandated by the Treasury Regulations in order ensure meaningful appellate review. See Treas. Reg. § 1.482-1(d)(1).