
665 F.3d 60 (2011)
PPL CORPORATION and Subsidiaries
v.
COMMISSIONER OF INTERNAL REVENUE, Appellant.
No. 11-1069.
United States Court of Appeals, Third Circuit.
Argued September 22, 2011.
Opinion filed: December 22, 2011.
*61 Thomas J. Clark, Esquire, Gilbert S. Rothenberg, Esquire, Francesca U. Tamami, Esquire (Argued), United States Department *62 of Justice, Tax Division, Washington, DC, for Appellant.
Mark B. Bierbower, Esquire, Timothy L. Jacobs, Esquire, Richard E. May, Esquire (Argued), Hunton & Williams LLP, Washington, DC, for Appellee.
Alan I. Horowitz, Esquire, Miller & Chevalier Chartered, Washington, DC, for Amicus Appellee.
Before: AMBRO, CHAGARES and [*] GARTH, Circuit Judges.

OPINION OF THE COURT
AMBRO, Circuit Judge.
The Commissioner of Internal Revenue appeals a decision of the United States Tax Court holding that PPL Corporation was entitled to a foreign tax credit for the 1997 tax year under § 901 of the Internal Revenue Code. We agree with the Commissioner that the foreign tax before us does not qualify for a foreign tax credit, and thus reverse.

I. Background
PPL is a Pennsylvania corporation. In 1997, it held a 25% stake in SWEB (formerly South Western Electricity Board), a utility in the United Kingdom. SWEB was one of 32 United Kingdom companies subject to a one-time "windfall tax." After it paid that tax, PPL claimed under I.R.C. § 901 a foreign tax credit on its United States tax return. We must decide whether the U.K. windfall tax is an "income, war profits, [or] excess profits" tax within the meaning of § 901(b)(1).
The windfall tax emerged from a backlash against the privatization of British utilities and transit operators. The U.K.'s Government, then controlled by the Conservative Party, sold SWEB and 31 other state-owned companies to private investors between 1984 and 1996. Though privately owned, the utilities remained regulated. In particular, the U.K. Government set the rates at which the utilities would sell electricity to customers. With the pricing scheme, it induced the new private owners to provide electricity more efficiently; every pound sterling that the owners could save would go to them as profit rather than to customers as lower prices. Most of the utilities, including SWEB, increased efficiency to a greater degree than the U.K. Government had expected. As a result, the utilities' profits and their share prices increased. Executive compensation also increased, as it was tied in many cases to share prices. These high profits and compensation packages, coupled with the fixed costs that customers paid under the regulatory scheme, left the public unhappy with the utilities and their executives.
The opposition Labour Party sought to capitalize on this public discontent by introducing a new tax. Party leaders promised a "windfall levy on the excess profits of the privatised utilities," in the words of Labour's 1997 Election Manifesto. They put Geoffrey Robinson, a Labour Member of Parliament, in charge of the plan. He hired accounting firm Arthur Andersen to develop a series of proposals. Robinson and the Andersen team rejected simpler proposals, including taxes on gross receipts or on profits, and instead selected the "windfall tax" now at issue. Gordon Brown, then the Shadow Chancellor of the Exchequer, approved Robinson's windfall tax proposal, and Parliament enacted it without substantive change after Labour won the 1997 elections.
In concept, the windfall tax was a one-time 23% tax on the difference between each company's "profit-making value" and *63 its "flotation value," the price for which the U.K. Government had sold it. (The public believed that the Government had sold the companies too cheaply, hence the "windfall.") The tax statute defined each company's "profit-making value" as its average annual profit multiplied by its price-to-earnings ratio. It defined average annual profit as the company's average profit per day over a statutorily defined "initial period" (which for SWEB and most others was the first four years after privatization) multiplied by 365. Rather than using the companies' actual price-to-earnings ratios, the statute imputed a ratio of 9 for all companies. This "ratio," a U.K. Government document explained, "approximates to the lowest average sectoral price-to-earnings ratio of the companies liable to the tax." J.A. at 264. We may express the tax algebraically in this way:

Tax = 23% × [ (365 × (P / D) × 9)  FV],
where 23% is the tax rate, P is the company's total profit over the "initial period," D is the length of the initial period in days, and FV is the company's flotation value (to repeat, the price for which the U.K. Government sold the company).
SWEB paid the windfall tax, and PPL filed with the IRS a claim for refund seeking a foreign tax credit for PPL's share of the windfall tax paid. In 2007, the IRS denied PPL's claim for refund and issued a notice of deficiency. PPL then filed a petition in the Tax Court to challenge the IRS's determination that it was not entitled to a credit under I.R.C. § 901 for PPL's share of SWEB's windfall tax. The Tax Court held a trial and, after post-trial briefing and further testimony, agreed with PPL that it was entitled to a foreign tax credit. The Commissioner timely appealed to our Court, asserting that § 901 does not cover the windfall tax.
The Tax Court had jurisdiction under I.R.C. §§ 6213 and 6214, and our Court has jurisdiction under I.R.C. § 7482(a)(1). "We have plenary review over the Tax Court's legal conclusions, and may set aside findings of fact if they are clearly erroneous." Capital Blue Cross v. Comm'r, 431 F.3d 117, 123-24 (3d Cir. 2005).

II. Discussion

A. The Applicable Test
To determine whether the U.K. windfall tax is a creditable foreign tax, we start with I.R.C. § 901(b)(1). That subsection provides a tax credit for "the amount of any income, war profits, and excess profits taxes paid or accrued during the taxable year to any foreign country." Congress first enacted these words in 1918, and it has not changed them since. See Phillips Petroleum Co. v. Comm'r, 104 T.C. 256, 284 (1995) (discussing legislative history). In the decades that followed, "the word `income' in section 901(b)(1) [became] the subject of a long and tortuous history" in case law that was "permeated" with "vagaries, confusion, and seeming contradictions." Bank of Am. Nat'l Trust & Sav. Ass'n v. Comm'r, 61 T.C. 752, 759 (1974).
The Treasury Department explained and clarified § 901(b)(1) in a 1983 regulation, Treasury Regulation 1.901-2, which the parties agree governs our case. We follow our sister Courts of Appeals in according it the force of law. See, e.g., Texasgulf, Inc. v. Comm'r, 172 F.3d 209 (2d Cir.1999); Amoco Corp. v. Comm'r, 138 F.3d 1139 (7th Cir.1998).
The regulation's purpose is to define "income, war profits, [or] excess profits tax" within the meaning of I.R.C. § 901(b)(1). The regulation combines those statutory terms into the single concept *64 of an "income tax." Treas. Reg. § 1.901-2(a)(1). It provides that a foreign assessment is an "income tax" if it has the "predominant character . . . of an income tax in the U.S. sense." Id. § 1.901-2(a)(1)(ii). (It also requires that the foreign tax be a "tax," which is not at issue here.) The regulation then provides that a foreign assessment has a tax "character" if it is "likely to reach net gain in the normal circumstances in which it applies." Id. § 1.901-2(a)(3)(i). And it is "likely to reach net gain . . . if and only if the tax, judged on the basis of its predominant character,"[1] satisfies each of three requirements: the "realization" requirement, the "gross receipts" requirement, and the "net income" requirement. Id. § 1.901-2(b)(1) (emphases added).
The realization requirement is that the tax is imposed on or after the occurrence of events that would result in the realization of income under U.S. tax law. Id. § 1.901-2(b)(2). The gross receipts requirement is that the tax is imposed on gross receipts or an amount not greater than gross receipts. Id. § 1.901-2(b)(3). The net income requirement is that computing the tax demands deducting from gross receipts the costs and expenses incurred in earning those receipts. Id. § 1.901-2(b)(4). We determine whether each requirement is met "judged on the basis of [the] predominant character" of the tax. Id. § 1.901-2(b)(2), (b)(3), (b)(4). We do so mindful that "[b]ecause § 901's exemption from taxation is `a privilege extended by legislative grace,' it is strictly construed." Texasgulf, 172 F.3d at 214 (quoting Inland Steel Co. v. United States, 677 F.2d 72, 79 (Ct.Cl.1982) (per curiam)).
The three requirements concern the timing and the base of the foreign tax. The realization requirement, one of timing, ensures that the taxpayer has received income before being obligated to pay taxes on it. See Helvering v. Horst, 311 U.S. 112, 115, 61 S.Ct. 144, 85 L.Ed. 75 (1940) ("`[R]ealization' is not deemed to occur until the income is paid."). The main effect of this requirement is to exclude from "income" the appreciation in value of property that its owner has not yet sold. The gross receipts and net income requirements present questions about the tax base, the amount on which the tax is levied. The amount that a particular corporation *65 owes is the product of its tax base multiplied by its tax rate.

B. The Tax Base
The parties offer dueling perspectives on the base of the windfall tax. In the Commissioner's view, the tax base is what the U.K. statute says it is: the difference between two imputed values of each affected company. The first value is the company's "profit-making value," defined as its average annual profit during its "initial period" (that is, average profit per day over the initial period, multiplied by 365) times 9, the assumed price-to-earnings ratio. The second value is the company's "flotation value," the amount for which the U.K. Government sold the company to investors. Neither value represents the company's gross receipts, nor does the tax base account for recognizable costs and expenses such as employee costs. Thus, the Commissioner contends, the "windfall tax" fails to meet either the gross receipts or the net income requirement under the U.S. regulation.
In PPL's view, looking through the form of the tax to its substance reveals that "the [t]ax [i]s, in substance, a tax on profits, specifically on excess profits." PPL Br. at 43 (citation and internal quotation marks omitted). Our classification of a foreign tax hinges on its economic substance, not its form. See Boulware v. United States, 552 U.S. 421, 429, 128 S.Ct. 1168, 170 L.Ed.2d 34 (2008) ("[T]ax classifications. . . turn on `the objective economic realities of a transaction rather than. . . the particular form the parties employed'; a `given result at the end of a straight path is not made a different result. . . by following a devious path.'") (citations omitted). PPL's expert testimony purports to establish that initial-period profit would satisfy the gross receipts and net income requirements.
In our view, PPL's formulation of the substance of the U.K. windfall tax is a bridge too far. No matter how many of PPL's proposed simplifications we may accept, we return to a fundamental problem: the tax base cannot be initial-period profit alone unless we rewrite the tax rate. Under the Treasury Department's regulation, we cannot do that.
PPL's proposal and its fatal flaw are best understood in algebraic terms. Once again, the U.K. statute computes each company's tax thus:

Tax = 23% × [ (365 × (P / D) × 9)  FV],
where 23% is the tax rate, P is the company's initial-period profit, D is the length of the initial period in days, and FV is the company's flotation value. Were this a tax on initial-period profit, as PPL contends that it is in substance, the tax base would be simply P, so that we could express the tax thus:

Tax = 23% × P.

No amount of emphasis on substance over form can take us from the first equation to the second.
If profit is in essence the only variable in the tax base, we would first need to explain away the other two variables that the U.K. statute puts there. For the sake of argument, we do so as PPL suggests. First, we assume that the "initial period" for all companies is 1,461 days longin other words, that D equals 1,461. Twenty-nine of the 32 affected companies had initial periods of 1,461 daysfour years (4 x 365) plus one day for leap yearor just shy of it. Second, we assume that each company's flotation value (the variable FV) is not relevant for the purpose of satisfying the regulation's three requirements. PPL contends that we should do so because the flotation value in the U.K. *66 windfall tax merely gives that tax the form of historical "excess profits" taxes.[2]
These two modifications would make the tax base appear to be quite different. Rather than the statutory formula, that is,

Tax = 23% × [ (365 × (P/D) × 9)  FV],
we would confront this new formula:

Tax = 23% × [ (365 × (P / 1,461)) × 9],
because we have substituted 1,461 for D and eliminated FV. And because P is the only variable left, we may combine the remaining numbers in the tax base. Multiplying 365 by 9, then dividing by 1,461, equals roughly 2.25. Thus, we could express the U.K. windfall tax even more simply:

Tax = 23% × [2.25 × P].
PPL's two proposed simplifications boil down to this formula.
Even accepting those simplifications, this tax base would violate the gross receipts requirement under the following logic:
 The tax base that PPL's two simplifications produce is 2.25 times profit;
 Profit equals gross receipts minus expenses;
 Thus the tax base that PPL's two simplifications produce is 2.25 times gross receipts minus 2.25 times expenses;
 The gross receipts requirement addresses the income portion of a tax base, whereas the net income requirement addresses the expense portion of a tax base; and
 Hence the income portion of this tax base2.25 times gross receiptsviolates the gross receipts requirement, which limits the basis of a tax to gross receipts or an approximation thereof "likely to produce an amount that is not greater than [their] fair market value." Treas. Reg. § 1.901-2(b)(3)(B) (emphasis added).
PPL attempts to skirt this logic by changing the tax rate. A 23% tax on 2.25 times profit, PPL observes, is mathematically identical to a 51.75% tax on profit, because 23% times 2.25 equals 51.75%. PPL Br. at 25-26. In other words, returning to our formula, PPL would make one last modification:

Tax = 23% × [2.25 × P] = 51.75% × P.

Rewritten in this way, the tax base is profit alone. This tax base, PPL posits, would not offend the gross receipts requirement *67 because the starting point for calculating profit is gross receipts.
However, changing the tax rate in this way to avoid a problem with the tax base would read the gross receipts requirement out of the regulation. This we decline to do. An example from the Treasury regulation illustrates why our law does not tolerate such a mathematical maneuver. In the example, another country imposes a tax on the extraction of petroleum. Treas. Reg. § 1.901-2(b)(3)(ii), Ex. 3. The country deems "gross receipts" to equal 105% of the market value of the petroleum extracted. That is, the starting point for the tax base is 105% of each affected company's gross receipts from petroleum. The regulation disallows a credit for the tax because it "is designed to produce an amount that is greater than the fair market value of actual gross receipts." Id. As the tax would not even be creditable up to the amount imposed on 100% of gross receipts, less associated costs, the entirety of the tax fails to satisfy the requirement. This all-or-nothing result is so because the regulation mandates that "a tax either is or is not an income tax, in its entirety, for all persons subject to the tax." Id. § 1.901-2(a)(1)(ii) (emphasis added). If 105% of gross receipts (barely more than actual receipts) does not satisfy the requirement, then 225% is in the same boat but another ocean.
In this example, as with the U.K. windfall tax, manipulating the tax rate could in theory fix the problem. Say that the tax rate on the hypothetical extraction tax is 20%. It is true that a 20% tax on 105% of receipts is mathematically equivalent to a 21% tax on 100% of receipts, the latter of which would satisfy the gross receipts requirement. PPL proposes that we make the same move here, increasing the tax rate from 23% to 51.75% so that there is no multiple of receipts in the tax base. But if the regulation allowed us to do that, the example would be a nullity. Any tax on a multiple of receipts or profits could satisfy the gross receipts requirement, because we could reduce the starting point of its tax base to 100% of gross receipts by imagining a higher tax rate. The regulation forbids that outcome.[3]

III. Conclusion
Even if we accept PPL's contention that the U.K. windfall tax is in substance a 23% tax on 2.25 times profits, that tax fails to satisfy at least the gross receipts requirement. Without changing the tax rate, the calculation of the tax base begins with an *68 amount greater than gross receipts. And we may not manipulate the tax rate to address a question about the tax base.
Thus, we hold that the windfall tax is not creditable and reverse the decision of the Tax Court.
NOTES
[*]  Participated in Video Conference
[1]  Because the regulation repeats the phrase "predominant character" throughout its definitions, both the Tax Court and PPL on appeal suggest that it applies a "predominant character standard" independent of the three requirements. That is incorrect. We must assess whether a foreign tax satisfies each of the regulation's three requirements "judged on the basis of its predominant character." Treas. Reg. § 1.901-2(b)(1), (b)(2), (b)(3), (b)(4). We may not, however, simply ask whether the "predominant character" of a foreign tax is that of a U.S. income tax without addressing the requirements. The Court of Claims did essentially that in a pair of cases that predated the Treasury regulation governing our case. See Inland Steel Co. v. United States, 677 F.2d 72, 80 (Ct.Cl.1982) (per curiam); Bank of Am. Nat'l Trust & Sav. Ass'n v. United States, 459 F.2d 513, 519 (Ct.Cl.1972).

A single paragraph in the Treasury regulation's preamble purports to adopt both the Court of Claims' approach and the three-requirement test. Creditability of Foreign Taxes, 48 Fed. Reg. 46,272, 46,273 (Oct. 12, 1983). Those two approaches to § 901 are, at the least, in tension with one another. We resolve this tension in favor of the text of the regulation, which does not include the preamble. In doing so, we follow the Second Circuit's decision in Texasgulf, which considered the same foreign tax that the Court of Claims had in Inland Steel but reached the opposite result, the former deciding that the Ontario Mining Tax was creditable under § 901, Texasgulf, 172 F.3d at 216-17, and the latter ruling that it was not, Inland Steel, 677 F.2d at 87.
[2]  Section 901(b)(1) establishes a credit for "any income, war profits, and excess profits taxes" paid to a foreign nation. As we noted above, the relevant Treasury regulation treats those three taxes as though they are identical. Treas. Reg. § 1.901-2(a)(1). PPL protests that the regulation "does not address the elements necessary to [distinguish] `excess profits' from `normal profits.'. . . . One must search [beyond the regulation] to determine the predominant character of an excess profits tax." PPL Br. at 36. In other words, PPL submits, the regulation cannot tell us what an "excess profits" tax is because it does not define that term specifically. Instead, we are invited to look to World War I-era "excess profits" taxes, which, we are told, would render flotation value irrelevant to our analysis.

But this argument merely suggests that the regulation misinterprets the statute. The regulation expressly defines an excess profits tax as an "income tax," which for the purposes of the regulation is a tax that satisfies the realization, gross receipts, and net income requirements. PPL could have argued that the Treasury Department's regulation was arbitrary or capricious because it mingles "excess profits taxes" with the other statutory terms. But it did not. Instead, PPL agrees with the Commissioner that Treasury Regulation 1.901-2 governs this case. See id. at 30-33, 35, 52. We nonetheless indulge for the sake of argument PPL's contention that historical practice allows us to cast flotation value aside. Doing so does not affect our holding.
[3]  To repeat, a tax must satisfy the regulation's three requirements to be creditable. A tax's failure to satisfy any one of the three tests renders it not creditable, regardless whether it satisfies the other two tests. Because the U.K. tax fails to satisfy the gross receipts requirement, it is not creditable. Nonetheless, we also believe that (laying aside any discussion of the net income requirement) the tax fails to satisfy the realization requirement. To meet that test, the tax must be imposed "[u]pon or subsequent to the occurrence of events (`realization events') that would result in the realization of income. . . ." Treas. Reg. § 1.901-2(b)(2)(i)(A). The "income" that PPL asserts is at issue here is initial-period profit. But as we have explained, the amount being taxed (the "income") was greater than initial-period profit. The U.K. windfall tax did not ensure that the companies had actually realized the amount being taxed. In SWEB's case, for example, initial-period profit was £306.2 million, but the taxable amount was approximately £393.1 million after subtracting flotation value. SWEB did not realize the full latter amount as profit over its initial period. See Eisner v. Macomber, 252 U.S. 189, 211, 40 S.Ct. 189, 64 L.Ed. 521 (1920) (holding that income is not realized unless it "is available for actual distribution"). Putting aside the Commissioner's other arguments, this alone belies PPL's claim that the windfall tax meets the realization requirement, as the tax was not imposed on past profit (and certainly not on excess profit, which of course is less than total profit).
