This case brings before us, once again, troublesome problems arising from state taxation of an interstate commercial enterprise. At issue is a tax assessment pursuant to a Missouri statute specifying the manner in which railroad rolling stock is to be assessed for the State's ad valorem tax on that property.1

In 1964 the Norfolk & Western Railway Co. (N & W), a Virginia corporation with interstate rail operations, leased all of the property of appellant Wabash Railroad Company. The Wabash owned substantial fixed property and rolling stock, and did substantial business in Missouri as well as in other States. Prior to the lease, N & W owned no fixed property and only a minimal amount of rolling stock in Missouri. N & W is primarily a coal-carrying railroad. Much of its equipment and all of its specialized coalcarrying equipment are generally located in the coal regions of Virginia, West Virginia, and Kentucky, and along the coalferrying routes from those regions to the eastern seaboard and the Great Lakes. Scarcely any of the specialized equipment ever enters Missouri. According to appellants, the Wabash property in Missouri was leased by N & W in order to diversify its business, not to provide the opportunity for an integrated through movement of traffic.

By the terms of the lease, the N & W became obligated to pay the 1965 taxes on the property of the Wabash in Missouri and elsewhere.2 Upon receiving notice of the 1965 assessment from the appellee Missouri Tax Commission, the N & W filed a request for an adjustment and hearing before the Commission. The hearing was held, and the Commission sustained its assessment against the taxpayer's challenge. On judicial review, the Commission's decision was affirmed without opinion by the Circuit Court of Cole County, and then by the Supreme Court of Missouri. Appellants filed an appeal in this Court, contending that the assessment in effect reached property not located in Missouri and thus violated the Due Process Clause and the Commerce Clause of the United States Constitution. We noted probable jurisdiction. 389 U.S. 810, 88 S.Ct. 84, 19 L.Ed.2d 63 (1967).

The Missouri property taxable to the N & W was assessed by the State Tax Commission at $31,298,939. Of this sum, $12,177,597 relates to fixed property within the State, an assessment that is not challenged by appellants. Their attack is aimed only at that portion of the assessment relating to rolling stock, $19,981,757.3

With respect to the assessment of rolling stock, the Commission used the familiar mileage formula authorized by the Missouri statute. In relevant part, this provides (§ 151.060, subd. 3):

'* * * when any railroad shall extend beyond the limits of this state and into another state in which a tax is levied and paid on the rolling stock of such road, then the said commission shall assess, equalize and adjust only such proportion of the total value of all the rolling stock of such railroad company as the number of miles of such road in this state bears to the total length of the road as owned or controlled by such company.'

The Commission arrived at the assessment of rolling stock by first determining the value of all rolling stock, regardless of where located, owned or leased by the N & W as of the tax day, January 1, 1965. Value was ascertained by totaling the original cost, less accrued depreciation at 5% a year up to 75% of cost, of each locomotive, car, and other piece of mobile equipment. To the total value, $513,309,877, was applied an 'equalizing factor' of 47%, employed in assessing all railroad property in an attempt to bring such assessments down to the level of other property assessments in Missouri. The Commission next found that 8.2824% of all the main and branch line road (excluding secondary and side tracks) owned, leased, or controlled by the N & W was situated in Missouri. This percentage was applied to the equalized value of all N & W rolling stock, and the resulting figure was $19,981,757.

There is no suggestion in this case that the Commission failed to follow the literal command of the statute. The problem arises because of appellants' contention that, in mechanically applying the statutory formula, the Commission here arrived at an unconscionable and unconstitutional result. It is their submission that the assessment was so far out of line with the actual facts of record with respect to the value of taxable rolling stock in the State as to amount to an unconstitutional attempt to exercise state taxing power on out-of-state property.

Appellants submitted evidence based upon an inventory of all N & W rolling stock that was actually in Missouri on tax day. The equalized value of this rolling stock, calculated on the same cost-less-depreciation basis employed by the Commission, was approximately $7,600,000, as compared with the assessed value of $19,981,000. Appellants also submitted evidence to show that the tax-day inventory was not unusual. The evidence showed that, both before and in the months immediately after the Wabash lease, the equalized value of the N & W rolling stock actually in Missouri never ranged far above the $7,600,000 figure. In the preceding year, 1964, the rolling stock assessment against the Wabash was only $9,177,683, and appellants demonstrated that neither the amount of rolling stock in Missouri nor the Missouri operations of the N & W and Wabash had materially increased in the intervening period.4 The assessment of the fixed properties (for which no mileage formula was applied) hardly increased between 1964 and 1965. In 1964, prior to the lease, the fixed properties in Missouri were assessed at $12,092,594; in 1965, after the lease, the assessment was $12,177,597.

The Supreme Court of Missouri concluded that the result reached by the Commission was justifiable. It pointed out that the statutory method used by the Commission proceeds on the assumption that 'rolling stock is substantially evenly divided throughout the railroad's entire system, and the percentage of all units which are located in Missouri at any given time, or for any given period of time, will be substantially the same as the percentage of all the miles of road of the railroad located in Missouri.' It then held that the valuation found by the Commission could be justified on the theory of 'enhancement,' although the Commission had not referred to that principle. The court described the theory as follows:

'The theory underlying such method of assessment is that rolling stock regularly employed in one state has an enhanced or augmented value when it is connected to, and because of its connection with, an integrated operational whole and may, therefore, be taxed according to its value 'as part of the system, although the other parts be outside the State;—in other words, the tax may be made to cover the enhanced value which comes to the property in the State through its organic relation to the system.' Pullman Co. v. Richardson, 261 U.S. 330, 338, 43 S.Ct. 366, 67 L.Ed. 682.'

The court correctly noted, however, that 'even if the validity of such methods be conceded, the results, to be valid must be free of excessiveness and discrimination.' It concluded that in the present case, the result reached by the Commission was justifiable. We disagree. In our opinion, the assessment violates the Due Process and Commerce Clauses of the Constitution.

Established principles are not lacking in this much discussed area of the law. It is of course settled that a State may impose a property tax upon its fair share of an interstate transportation enterprise. Marye v. Baltimore & Ohio R. Co., 127 U.S. 117, 123 124, 8 S.Ct. 1037, 1039—1040, 32 L.Ed. 94 (1888); Pullman's Palace-Car Co. v. Commonwealth of Pennsylvania, 141 U.S. 18, 11 S.Ct. 876, 35 L.Ed. 613 (1891); Ott v. Mississippi Valley Barge Line Co., 336 U.S. 169, 69 S.Ct. 432, 93 L.Ed. 585 (1949); Braniff Airways, Inc. v. Nebraska State Board of Equalization and Assessment, 347 U.S. 590, 74 S.Ct. 757, 98 L.Ed. 967 (1954). That fair share may be regarded as the value, appropriately ascertained, of tangible assets permanently or habitually employed in the taxing State, including a portion of the intangible, or 'going-concern,' value of the enterprise. Railway Express Agency v. Commonwealth of Virginia, 347 U.S. 359, 364, 74 S.Ct. 558, 561, 98 L.Ed. 757 (1954); Cudahy Packing Co. v. State of Minnesota, 246 U.S. 450, 455, 38 S.Ct. 373, 375, 62 L.Ed. 827 (1918); Adams Express Co. v. Ohio State Auditor, 166 U.S. 185, 218—225, 17 S.Ct. 604, 605, 607, 41 L.Ed. 965 (1897). The value may be ascertained by reference to the total system of which the intrastate assets are a part. As the Court has stated the rule, 'the tax may be made to cover the enhanced value which comes to the (tangible) property in the State through its organic relation to the (interstate) system.' Pullman Co. v. Richardson, 261 U.S. 330, 338, 43 S.Ct. 366, 368, 67 L.Ed. 682 (1923). Going-concern value, of course, is an elusive concept not susceptible of exact measurement. Rowley v. Chicago & N.W.R. Co., 293 U.S. 102, 109, 55 S.Ct. 55, 58, 79 L.Ed. 222 (1934); Nashville, C. & St. L.R. Co., v. Browning, 310 U.S. 362, 365—366, 60 S.Ct. 968, 970, 84 L.Ed. 1254 (1940). As a consequence, the States have been permitted considerable latitude in devising formulas to measure the value of tangible property located within their borders. Union Tank Line Co. v. Wright, 249 U.S. 275, 282, 39 S.Ct. 276, 278, 63 L.Ed. 602 (1919). Such formulas usually involve a determination of the percentage of the taxpayer's tangible assets situated in the taxing State and the application of this percentage to a figure representing the total going-concern value of the enterprise. See, e.g., Rowley v. Chicago & N.W.R. Co., 293 U.S. 102, 55 S.Ct. 55, 79 L.Ed. 222 (1934); Pittsburgh, C., C. & St. L.R. Co. v. Backus, 154 U.S. 421, 14 S.Ct. 1114, 38 L.Ed. 1031 (1894). A number of such formulas have been sustained by the Court, even though it could not be demonstrated that the results they yielded were precise evaluations of assets located within the taxing State. See, e.g., Nashville, C. & St. L.R. Co. v. Browning, 310 U.S. 362, 365—366, 60 S.Ct. 968, 970, 84 L.Ed. 1254 (1940).

On the other hand, the Court has insisted for many years that a State is not entitled to tax tangible or intangible property that is unconnected with the State. Delaware Railroad Tax, 18 Wall. 206, 229, 21 L.Ed. 888 (1874); Fargo v. Hart, 193 U.S. 490, 499, 24 S.Ct. 498, 500, 48 L.Ed. 761 (1904). In some cases the Court has concluded that States have, in fact, cast their tax burden upon property located beyond their borders. Fargo v. Hart, 193 U.S. 490, 499—503, 24 S.Ct. 498, 500, 501, 48 L.Ed. 761 (1904); Union Tank Line Co. v. Wright, 249 U.S. 275, 283—286, 39 S.Ct. 276, 278, 279, 63 L.Ed. 602 (1919); Wallace v. Hines, 253 U.S. 66, 69—70, 40 S.Ct. 435, 436, 64 L.Ed. 782 (1920); Southern R. Co. v. Commonwealth of Kentucky, 274 U.S. 76, 81—84, 47 S.Ct. 542, 544—545, 71 L.Ed. 934 (1927). The taxation of property not located in the taxing State is constitutionally invalid, both because it imposes an illegitimate restraint on interstate commerce and because it denies to the taxpayer the process that is his due.5 A State will not be permitted, under the shelter of an imprecise allocation formula or by ignoring the peculiarities of a given enterprise, to 'project the taxing power of the state plainly beyond its borders.' Nashville, C. & St. L.R. Co. v. Browning, 310 U.S. 362, 365, 60 S.Ct. 968, 970, 84 L.Ed. 1254 (1940). Any formula used must bear a rational relationship, both on its face and in its application, to property values connected with the taxing State. Fargo v. Hart, 193 U.S. 490, 499—500, 24 S.Ct. 498, 500, 48 L.Ed. 761 (1904).6

Applying these principles to the facts of the case now before us, we conclude that Missouri's assessment of N & W's rolling stock cannot be sustained. This Court has, in various contexts, permitted mileage formulas as a basis for taxation. See, e.g., Pittsburgh, C., C. & St. L.R. Co. v. Backus, 154 U.S. 421, 14 S.Ct. 1114, 38 L.Ed. 1031 (1894). A railroad challenging the result reached by the application of such a formula has a heavy burden. See Butler Brothers v. McColgan, 315 U.S. 501, 507, 62 S.Ct. 701, 704, 86 L.Ed. 991 (1942); Norfolk & Western R. Co. v. State of North Carolina ex rel. Maxwell, 297 U.S. 682, 688, 56 S.Ct. 625, 628, 80 L.Ed. 977 (1936). It is confronted by the vastness of the State's taxing power and the latitude that the exercise of that power must be given before it encounters constitutional restraints. Its task is to show that application of the mileage method in its case has resulted in such gross overreaching, beyond the values represented by the intrastate assets purported to be taxed, as to violate the Due Process and Commerce Clauses of the Constitution. Cf. Capitol Greyhound Lines v. Brice, 339 U.S. 542, 547, 70 S.Ct. 806, 809, 94 L.Ed. 1053 (1950). But here the appellants have borne that burden, and the State has made no effort to offset the convincing case that they have made.

Here, the record shows that rigid application of the mileage formula led to a grossly distorted result. The rolling stock in Missouri was assessed to N & W at $19,981,757. It was practically the same property that had been assessed the preceding year at $9,177,683 to the Wabash. Appellants introduced evidence of the results of an actual count of the rolling stock in Missouri. On the basis of this actual count, the equalized assessment would have been less than half of the value assessed by the State Commission. The commission's mileage formula resulted in postulating that N & W's rolling stock in Missouri constituted 8.2824% of its rolling stock. But appellants showed that the rolling stock usually employed in the State comprised only about 2.71% by number of units (and only 3.16% by cost-less-depreciation value) of the total N & W fleet.

Our decisions recognize the practical difficulties involved and do not require any close correspondence between the result of computations using the mileage formula and the value of property actually located in the State, but our cases certainly forbid an unexplained discrepancy as gross as that in this case.7 Such discrepancy certainly means that the impact of the state tax is not confined to intrastate property even within the broad tolerance permitted. The facts of life do not neatly lend themselves to the niceties of constitutionalism; but neither does the Constitution tolerate any result, however distorted, just because it is the product of a convenient mathematical formula which, in most situations, may produce a tolerable product.

The basic difficulty here is that the record is totally barren of any evidence relating to enhancement or to going-concern or intangible value, or to any other factor which might offset the devastating effect of the demonstrated discrepancy. The Missouri Supreme Court attempted to justify the result by reference to 'enhanced' value, but the Missouri Commission made no effort to show such value or to measure the extent to which it might be attributed to the rolling stock in the State. In fact, N & W showed that it is chiefly a coal-carrying railroad, 70% of whose 1964 revenue was derived from coal traffic. It demonstrated that its coal operations require a great deal of specialized equipment, scarcely any of which ever enters Missouri. It showed that traffic density on its Missouri tracks was only 54% of traffic density on the N & W system as a whole. Finally, it proved that the overwhelming majority of its rolling stock regularly present in Missouri was rolling stock it had leased from the Wabash. As long ago as Pittsburgh, C., C. & St. L.R. C. v. Backus, 154 U.S. 421, 14 S.Ct. 1114, 38 L.Ed. 1031 (1894), we indicated that an otherwise valid mileage formula might not be validly applied to ascertain the value of tangible assets within the taxing State in exceptional situations, for example, 'where, in certain localities, the company is engaged in a particular kind of business, requiring for sole use in such localities an extra amount of rolling stock.' Id., at 431, 14 S.Ct. at 1119.

The Missouri Supreme Court did not challenge the factual data submitted by the N & W. Its decision that these data did not place this case within the realm of 'exceptional situations' recognized by this Court was apparently based on the conclusion that the lease transaction between Wabash and the N & W had increased the value of tangible assets formerly belonging to the two separate lines. This may be true, but it does not follow that the Constitution permits us, without evidence as to the amount of enhancement that may be assumed, to bridge the chasm between the formula and the facts of record. The difference between the assessed value and the actual value as shown by the evidence to which we have referred is too great to be explained by the mere assertion, without more, that it is due to an assumed and nonparticularized increase in intangible value. See Wallace v. Hines, 253 U.S. 66, 69, 40 S.Ct. 435, 436, 64 L.Ed. 782 (1920).

As the Court recognized in Fargo v. Hart, 193 U.S. 490, 499 500, 24 S.Ct. 498, 500, 48 L.Ed. 761 (1904), care must be exercised lest the mileage formula

'be made a means of unlawfully taxing the privilege, or property outside the state, under the name of enhanced value or good will, if it is not closely confined to its true meaning. So long as it fairly may be assumed that the different parts of a line are about equal in value a division by mileage is justifiable. But it is recognized in the cases that if for instance a railroad company had terminals in one state equal in value to all the rest of the line through another, the latter state could not make use of the unity of the road to equalize the value of every mile. That would be taxing property outside of the state under a pretense.'

We repeat that it is not necessary that a State demonstrate that its use of the mileage formula has resulted in an exact measure of value. But when a taxpayer comes forward with strong evidence tending to prove that the mileage formula will yield a grossly distorted result in its particular case, the State is obliged to counter that evidence or to make the accommodations necessary to assure that its taxing power is confined to its constitutional limits. If it fails to do so and if the record shows that the taxpayer has sustained the burden of proof to show that the tax is so excessive as to burden interstate commerce, the taxpayer must prevail.

Accordingly, we conclude that, on the present record, Missouri has in this case exceeded the limits of her constitutional power to tax, as defined by the Due Process and Commerce Clauses. It will be open to the Missouri Supreme Court, so far as our action today is concerned, to remand the case to the appropriate tribunal to reopen the record for additional evidence to support the assessment. We vacate the judgment of the Supreme Court of Missouri and remand the cause to it for further proceedings not inconsistent with our decision.

Vacated and remanded.

Mr. Justice BLACK, dissenting.

It is established law, as the Court apparently recognizes in its opinion, that an interstate company challenging a state apportionment of the company's property taxable in the State has the heavy burden of proving by 'clear and cogent evidence' that the apportionment is grossly and flagrantly excessive. See, e.g., Railway Express Agency v. Commonwealth of Virginia, 358 U.S. 434, 444, 79 S.Ct. 411, 417, 3 L.Ed.2d 450, and cases cited. I agree with the Supreme Court of Missouri that appellant railroad failed to meet that burden and would therefore affirm its judgment. See its opinion at Mo., 426 S.W.2d 362.

It is true that most of the cars used in Missouri by N & W were owned by the Wabash Railroad and that before transfer to N & W they had been assessed at $9,177,683 as against the assessment here of $19,981,757. But this, of course, does not prove that the higher assessment was too much. For, as the Supreme Court of Missouri pointed out, this Court has held that 'a mere increase in the assessment does not prove that the last assessment is wrong. Something more is necessary before it can be adjudged that the assessment is illegal and excessive * * *.' Pittsburgh, C., C. & St. L.R. Co. v. Backus, 154 U.S. 421, 432, 14 S.Ct. 1114, 1119, 38 L.Ed. 1031. The court below held, and this Court agrees, that in pricing the value of the rolling stock the Commission was authorized to consider intangible values, such as goodwill and values added because of the enhancement to the property in Missouri brought about by being merged into the entire N & W system. This consideration of enhanced value is not new (see, e.g., Pullman Co. v. Richardson, 261 U.S. 330, 338, 43 S.Ct. 366, 368, 67 L.Ed. 682), and, as the Court points out, it is because of this intangible factor of enhancement that States are allowed wide discretion in determining the value of tangible property located within their borders. Thus, mileage formulas, such as the one used here, have generally been upheld. As this Court said in Nashville, C. & St. L.R. Co. v. Browning, 310 U.S. 362, 60 S.Ct. 968, 84 L.Ed. 1254, 'In basing its apportionment on mileage, the Tennessee Commission adopted a familiar and frequently sanctioned formula (cases cited).' 310 U.S. at 365, 60 S.Ct. at 970. It has never been contended that mileage formulas are completely accurate, but because States must consider such intangibles as enhancement value, these formulas are allowed except where the taxpayer can show, as the Court puts it, 'that application of the mileage method in its case has resulted in such gross overreaching, beyond the values represented by the intrastate assets purported to be taxed, as to violate the Due Process and Commerce Clauses of the Constitution.' I do not believe that appellants have made such a showing here. The fatal flaw with the appellants' case is that they have not proved that the tax is excessive when possible enhancement of value due to the merger is considered. The Court's opinion admits as much when it says that 'the record is totally barren of any evidence relating to enhancement or to going-concern or intangible value, or to any other factor * * *.' Where I differ with the Court is that I believe the burden of proof is on the railroad to show that the tax is excessive under all considerations rather than on the Commission to show sufficient enhancement of value to justify the tax.

¢This Court has recognized before, and indeed the majority pays lip service to the fact today, that it is impossible for a State to develop tax statutes with mathematical perfection. Indeed, as was stated in International Harvester Co. v. Evatt, 329 U.S. 416, 67 S.Ct. 444, 91 L.Ed. 390: 'Unless a palpably disproportionate result comes from an apportionment, a result which makes it patent that the tax is levied upon interstate commerce rather than upon an intrastate privilege, this Court has not been willing to nullify honest state efforts to make apportionments.' 329 U.S., at 422—423, 67 S.Ct., at 447. And the 'burden is on the taxpayer to make oppression manifest by clear and cogent evidence.' Norfolk & Western R. Co. v. State of North Carolina ex rel. Maxwell, 297 U.S. 682, 688, 56 S.Ct. 625, 628, 80 L.Ed. 977. Since appellants here did not prove that the enhanced value* of the rolling stock was less than the tax assessment, or that the State was imposing on N. & W. taxes that were exorbitant on the full value of all its property, cf. Capitol Greyhound Lines v. Brice, 339 U.S. 542, 70 S.Ct. 806, 94 L.Ed. 1053, I would affirm the decision of the Missouri Supreme Court.