Mr. Justice Pitney

delivered the opinion of the court.

These cases áre an appeal and a cross-appeal from a final decree of the District Court in a suit that was commenced by the Louisville & Nashville Railroad Company, a Kentucky corporation, against Henry M. Bosworth and others, then constituting the Board of Valuation and Assessment of that State (Bosworth being also Auditor of Public Accounts), and against the Attorney General of the State and his assistants, seeking to restrain the taking of any steps toward enforcing state and local taxes upon the basis of an "assessment of the “franchise” of the company for the year 1913 made by the Board of Valuation and Assessment at the sum of $45,658,630, or upon the basis of any greater valuation than $22,899,200; and this upon the ground that the assessment was unlawful and not in accordance with the statute, was the result of an abuse of power by the Board of Valuation and Assessment, and if enforced would result in a taking *526 of plaintiff’s property without due process of. law and a denial of the equal protection of the laws, contrary to § 1 of the Fourteenth Amendment.. By a supplemental bill, Robert L. Greene and others were brought in as successors in office of the original defendants. There being no. diversity of citizenship, the jurisdiction was rested upon the ground that the suits arose under the cited provisions of the Federal Constitution; but plaintiff relied also upon the provisions of the constitution and laws of the State. A chief ground of complaint, based upon the equal protection provision of the Fourteenth Amendment, and also upon the requirement of equal taxation prescribed by §§ 171, 172, and 174 of the state constitution, 1 was that the plaintiff had been subjected to illegal discrimination, in that its property had been assessed at more than its actual value, whereas the property of all other taxpayers in the State was assessed uniformly and intentionally at much less than actual valúe, in fact at not exceeding 60 per cent, thereof. It was alleged, besides, that the method of assessment followed by the Board of Valuation was inconsistent with the provisions of the statutes of Kentucky, and for that further reason the assessment was illegal.

A previous suit of the same character had been brought by the same plaintiff in the same court for relief against the assessment for the year 1912, in which, after a hearing on motion for preliminary injunction and demurrer to the bill, the court delivered a very elaborate opinion, allowing a temporary injunction upon condition that plaintiff should pay franchise taxes to the State and subordinate taxing districts upon a valuation of $22,899,200. Louisville & N. R. Co. v. Bosworth, 209 Fed. Rep. 380, 465.

Following this precedent, the court, upon the filing of *527 the bill in the present case, allowed a preliminary injunction upon the payment of taxes based upon the same valuation. ■ The cause proceeded to final hearing, and the court, having found plaintiff to have been subjected to discrimination by the valuing'of other property at approximately 60 per cent, of actual values, but having overruled the other grounds of relief asserted, applied an equalizing factor to the valuation of plaintiff’s franchise, with the result of finding $25,808,493.60 to be the amount at which it was legally taxable, or $2,909,293.60 in excess of the amount upon which payment was made at the inception of the suit. Therefore a final decree was made enjoining defendants from enforcing the assessment complained of, on condition that plaintiff should pay taxes, state and local, on the excess amount named. 230 Fed. Rep. 191, 232.

Plaintiff appealed to this court upon the ground that it ought not to be required to pay franchise taxes upon any amount in excess of $22,899,200. Defendants took a cross appeal upon the ground that plaintiff was entitled to no relief. The cases were argued together with kindred cases this day decided, viz., Nos. 617 and 618, Greene v. Louisville & Interurban R. R. Co., ante, 499, and Nos. 642-645, Illinois Central R. R. Co. v. Greene, post, 555.

There are numerous assignments of error by each party, but, without specifying these, the questions raised will be disposed of in the order of convenience. Of course, the federal jurisdiction, having been invoked upon substantial grounds of federal law, extends to the determination of all questions involved in the case, whether resting upon state or federal law. Siler v. Louisville & Nashville R. R. Co., 213 U. S. 175, 191; Ohio Tax Cases, 232 U. S. 576, 586.

It may be premised that plaintiff owns and operates a great system of railroads extending throughout Kentucky and twelve other States, embracing (in the year in question) roads operated on its own account to the extent of *528 4,478.61 miles, of which 1,574.47 miles, or 35.15 per cent., were in Kentucky, and an aggregate of roads owned, operated, and controlled, extending to 7,907.83 mile’s, of which 1,952.45 miles, or 24.69 per cent., were in Kentucky. It is subject to taxation in Kentucky upon its tangible property as assessed by the State Railroad Commission, and, in addition, to taxation state and local upon its intangible property or “franchise” under § 4077, Ky. Stats., and succeeding sections (set forth below in the margin), the valuation to be fixed by the Board of Valuation and Assessment.

(1) Defendants contend that the District Court was without jurisdiction because the suit was in effect a suit against the State of Kentucky. It is said that the sole basis of a suit to enjoin state officers from the performance of duties pursuant to a statute must be that the statute itself is unconstitutional; that, since the statute in question here is constitutional, an action may not be maintained in a court of the United States (there being no diversity of citizenship) for what is done by subordinate officers of the State in executing the statute in an unconstitutional manner; and that for misconduct of this sort there is no remedy except in the state courts. These contentions are disposed of adversely in Greene v. Louisville & Interurban R. R. Co., ante, 499.

(2) It is contended that the plaintiff has an adequate remedy at law under § 162, Ky. Stats. This likewise is negatived by the case just mentioned.

(3) It is urged that, although it be true that the local assessors in each county assessed other property at less than its cash value, plaintiff is not entitled to relief for this reason if its property was not assessed at more than its fair cash value, even though it was assessed at a higher percentage than other property. To this the same answer may be made. • The facts found in this case bring it within the ruling that, in the case last mentioned, was made upon *529 admitted facts, because of the provisions of the constitution and laws of the State. In this case, as in that, we find it unnecessary to pass upon the merits of the question whether a like result would be reached by the application of the “equal protection” clause of the Fourteenth Amendment.

(4) It is contended that although there be jurisdiction to enjoin the apportioning of the assessment among the counties, cities, and towns for the purpose of local taxation, it was erroneous to enjoin state taxation based upon the same assessment. So far as this is bottomed upon the theory that the suit is a suit against the State, it is disposed of by the decision cited. It is argued, however, that while this court has held that in a proper case a bill may be brought to restrain apportionment and certification to the counties of a tax imposed by a state board in violation of federal rights (Fargo v. Hart, 193 U. S. 490), yet Coulter v. Weir, 127 Fed. Rep. 897, 906, 912—a case that arose out of the same provisions of the Kentucky statutes that are here involved — is an authority in opposition to granting relief against the state taxes, and that it was approved by this court in Coulter v. Louisville & Nashville R. R. Co., 196 U. S. 599, 608. What was Said upon the subject in the case last mentioned was not a part of the matter decided, as a reference to the opinion clearly shows; for the decision in favor of defendants proceeded upon the ground that the evidence was insufficient to sustain the bill. Coulter v. Weir, supra, is easily distinguishable. There,- the Auditor of Public Accounts was the sole defendant. The Circuit Court of Appeals, after citing Poindexter v. Greenhow, 114 U. S. 270, 286-288; Reagan v. Farmers’ Loan & Trust Co., 154 U. S. 362, 390; Scott v. Donald, 165 U. S. 107, 112; Smyth v. Ames, 169 U. S. 466, 518; Fitts v. McGhee, 172 U. S. 516, 529; and Taylor v. Louisville & Nashville R. R. Co., 88 Fed. Rep. 350, and quoting from the opinion in the Taylor Case to the effect *530 that a suit against individuals seeking to enjoin them from doing certain acts which they assert to be by authority of the State, but which complainants aver to be without lawful authority, is not a suit against the State, and from Fitts v. McGhee to the effect that a suit against state officers not holding any special relation to the particular statute alleged to be unconstitutional nor charged with its enforcement, is a suit merely to test the constitutionality of a state statute and therefore is a suit against- the State, proceeded (p. 906) to sustain the action only so far as it sought to enjoin the defendant from certifying to the county clerks the assessment complained of. The contrary result reached with respect to the tax due to the State went solely upon the ground that as to this tax the Auditor had no act to perform under the statute and no authority to enforce collection; the court proceeding to say further (p. 907): “If the defendant had been about to take some step under color of the law tending to complete the assessment, or if he had been authorized to seize property and was about to do so, then he was, assuming the case to be with the complainants on the merits, about to commit a trespass for which he would be individually liable, and in a proper case equity might enjoin his proposed action upon the ground of his want of legal authority. But this is not the case made in respect to the tax due the state, and the bill, so far as it sought relief against the state tax, must be dismissed without regard to the merits.” It would seem that the court overlooked §§ 144, 145, and 152, Ky. Stats., which require the Auditor to keep account of taxes collected, keep a correct list of balances due by individuals to the Commonwealth, audit and enter in account all demands payable at the treasury, report to the Attorney General all public debtors who fail to render their accounts at the proper time or to pay the money in their hands due the Commonwealth into the treasury, and grant written authority to the Treasurer to receive money *531 from public officers or other persons due to the Commonwealth. However, we need not rest upon this point, since in the present case the Attorney General and his assistants are joined as parties, and the final decree under review restrains all of the defendants from taking any steps to collect the excessive taxes due to the State or to any of its subdivisions, and from instituting or prosecuting any proceedings against the plaintiff, either by indictment or civil action, because of any alleged delinquency or failure of the plaintiff to pay taxes upon its franchise on a valuation above the amount found by the court to be proper. The decree, with respect to the state as well as the local taxes, is clearly within the authority of Ex parte Young, 209 U. S. 123, 156, where Fitts v. McGhee, 172 U. S. 516, 530, was distinguished upon the ground that in that case no state officer who was made a party had to do with the enforcement of the statute alleged to be unconstitutional.

If what was said in Coulter v. Louisville & Nashville R. R. Co., 196 U. S. 599, 608, imports that an injunction can under no circumstances be awarded with respect to state taxes, it must be deemed to have been overruled by Raymond v. Chicago Union Traction Co., 207 U. S. 20, where the collection of taxes based upon an unconstitutional assessment was enjoined, a part of these being state taxes, as appears by the report, pp. 22, 27.

(5) It is contended by defendants that the evidence was insufficient to warrant the conclusion of the learned District Judge that in fact property in general in the State of Kentucky was systematically undervalued. A similar question of fact was involved in Coulter v. Louisville & Nashville R. R. Co., and this court (p. 609) held the evidence to be insufficient. In the present case, besides much to the same effect as that presented in the Coulter Case, a mass of additional evidence was introduced, including extracts from the United States Census Report for the year 1910; reports of the State Board of Equaliza *532 tion for the years 1910,1911,1912, and 1913; report of the ■ State Tax Commission of 1913; testimony of a member of the State Board of Equalization who served in the years 1908 to 1911, inclusive; affidavits of nearly 200 individuals from 47 counties in different parts of the State; and much besides. The evidence is too voluminous to be adequately reviewed within reasonable limits of space, and we content ourselves with saying that it comprises a body of official admissions and direct and circumstantial evidence from private and public sources that are unimpeached, fully sustaining the finding of the trial court that the great mass of property in the State, so far as assessed by the county assessors under the review of the county boards of supervisors and the State Board of Equalization — and this embraces all tangible property except railroad property and distilled spirits — during a period of years prior to and including the year 1913, was intentionally, systematically, and notoriously assessed far below its actual value, and at certainly not exceeding 60 per cent, of its fair cash value. There is little to the contrary except the general presumptions arising from the statutory duty of assessors to assess at fair cash value and from the oath customarily required of individual taxpayers, and a large number of stereotyped affidavits made by former assessors to the effect that they endeavored to follow the law and assess all property at its fair cash value, and if any property was otherwise assessed it was unintentional and not pursuant to any agreement between the assessor and the taxpayer. In our judgment this does not materially detract from the convincing effect of plaintiff’s proofs. The evidence is analyzed briefly in the opinion of the District Judge, 230 Fed. Rep. 227-231, and nothing more need be added to his comments upon it.

This disposes of all the points raised by defendants.

(6) It is contended by plaintiff that the Board of Valuation and Assessment, in assessing plaintiff’s franchise, *533 proceeded upon erroneous principles and adopted an improper method, not only in failing to equalize the assessment so as to make it conform to the basis generally adapted by other assessing officers in assessing other kinds' of property, but also in failing to follow the course prescribed by the Kentucky statute; and that with respect to its complaint in this regard the decree of the District' Court gave inadequate relief.

In order to pass upon this contention, we must consider the nature of the so-called “franchise tax,” the method prescribed by the statute for valuing the franchise, the method that was pursued by the Board, and the manner in which the District Court dealt with it.

The statutory provisions are in §§ 4077-4081, Ky. Stats., the material portions of which are set forth in the margin. 1 *534 They originated in the first General Assembly after the new Constitution, being §§ 1 to 5 of Article III of Chap. 103 (November 11, 1892; Acts 1891-1893, p. 299), which were amended by Chap. 217 of the same session (June 9, 1893, p. 990), by Act of March 29,1902 (c. 128, Acts 1902, pp. 281, 305-309), and by Act of March 15, 1906 (c. 22, Laws 1906, pp. 88, 126-130). One of the amendments, having to do with one of the questions we are to' consider, will be mentioned below.

It will be observed that the values of franchises (except as to turnpike companies, otherwise provided for), are to be determined by the Board of Valuation and Assessment, which board, upon a consideration of information furnished to it by the corporation, and from such other *535 evidence as it may have, is to “fix the value of the capital stock of the corporation . . . and from the amount thus fixed shall deduct the assessed value of all tangible property assessed in this State, or in the counties where situated. The remainder thus found shall be the value of its corporate franchise subject to taxation as aforesaid.” It has been held by the Kentucky Court of Appeals, and by this court, that the “capital stock of the corporation” includes its entire property of every kind and description, tangible and intangible, and that what is called its “corporate franchise” is the intangible property of the company in Kentucky. Henderson Bridge Co. v. Commonwealth, 99 Kentucky, 623, 639, 641; Henderson Bridge Co. v. Kentucky, 166 U. S. 150, 154; Adams Express Co. *536 v. Kentucky, 166 U. S. 171, 180; Louisville Tobacco Warehouse Co. v. Commonwealth, 106 Kentucky, 165, 167; Marion National Bank v. Burton, 121 Kentucky, 876, 888.

• The findings of an official body such as the Board of Valuation and Assessment, made — as was the case here— after a hearing and upon notice to the taxpayer, are quasi- judicial in their character, and are not to be set aside or disregarded by the courts unless it is made to. appear that the body proceeded upon an erroneous principle or adopted an improper mode of estimating the value of the franchise, or unless fraud appears. Pittsburgh &c. Railway Co. v. Backus, 154 U. S. 421, 435-436; Chicago, Burlington & Quincy Ry. Co. v. Babcock, 204 U. S. 585, 596. In this case there is no showing of fraud, the contention being that the Board departed from .the mode prescribed by the statute. If they did this, or if they proceeded in disregard of rights secured to the taxpayer by the state or federal Constitution, of course they proceeded upon an *537 erroneous principle. Henderson Bridge Co. v. Commonwealth, 99 Kentucky, 623, 645; Hager v. American Surety Co., 121 Kentucky, 791, 800. It appears that the Board, having received a report from the plaintiff, and having made a tentative assessment of its franchise for taxation for the year 1913, had a hearing upon the matter in the presence of counsel for plaintiff, and as a result made up its assessment in a manner summarized by the District Court (230 Fed. Rep. 193) as follows:

“The details of the assessment, showing the manner in which the board arrived at $45,658,630 as the value of the franchise, are these: The board first found the fair cash value of plaintiff’s capital stock, hereafter termed its unit, to be $262,252,566. This valuation it arrived at by capitalizing at 6 per cent, what it took to be plaintiff’s net income from operations on its own account for the year ending June 30, 1912, as of which date the assessment speaks-, less what it took .to be its net income from certain property which it took to be nontaxable. Plaintiff’s reports to the Kentucky Railroad Commission and to the Interstate Commerce Commission as of that date state plaintiff’s net income for that year to have been $18,052,905.12. This included the net income from the operation by plaintiff of three railroads, two in and one out of Kentucky, on account of the owners, which amounted to $1,439,604. The board deducted this sum from the total, leaving a balance of $16,613,301.12 of net income from operations on its own account. It then deducted from this balance the sum of $878,147 on account of its net income from such nontaxable property. This left a balance of $15,735,154, which capitalized at 6 per cent, gave the sum of $262,252,566, at which it valued the unit. The nontaxable property, the income from which was thus deducted, consisted of stocks in other corporations which owned property in this state and which had'paid the taxes thereon. The deduction was based on *538 sections 4085 and 4086, Kentucky Statutes, and the construction thereof by the Court of Appeals in the cases of Com. v. Walsh’s Trustee, 133 Kentucky, 103, 117 S. W. Rep. 398, and Com. v. Fidelity Trust Co., 147 Kentucky, 77, 143 S. W. Rep. 1037. It then apportioned $92,181,766 of this sum to Kentucky. The sum so apportioned was 35.15 per cent, thereof. The percentage which it took was the percentage which the mileage operated by plaintiff in Kentucky on its own account was of the entire mileage so operated by it. The entire mileage so operated by it was 4,478.61, of which 1,574.41 was in Kentucky. It then added to the sum so apportioned $2,468,612, the excess in the value which it took that the portion of the unit in Kentucky was over such mileage proportion of the value thereof,' It found this excess in value to be in the intangible part of the portion of the unit in Kentucky, and that in this way: The value of the tangible part it took to be $177,038,113, and that of the intangible $85,214,453. The proportion of the gross income derived from Kentucky of the entire gross income it took to be 38 per cent., or 2.85 per cent, in excess of such mileage proportion. It took it that this showed that the value of the portion of the intangible part of the unit in Kentucky was 2.85 per cent, of the value of such part, or the sum of $2,468,612, in excess of such mileage proportion thereof. Adding this sum to such mileage proportion of the value of the unit, to wit, $92,181,766, made the value of the portion of the unit in Kentucky $94,650,388. It then reduced this sum to that of $94,500,000 as the value. This reduction is not to be accounted for, except on the ground that it wanted to place the value of such portion in round numbers. This lessened the addition to such mileage proportion of the value of the unit on account of the excess in value of the portion of the intangible part of the unit in Kentucky over such mileage proportion thereof from the sum of $2,468,612 to $2,318,244, which latter sum was the dif *539 ference between $94,500,000 and $92,181,766. But the board had no sooner made this reduction than it made a further reduction from this sum in round numbers to another sum, not in round numbers, to wit $75,139,402, as the value of the portion of the unit in Kentucky, and there it stayed. On the assumption that this sum was reached by reducing from $94,500,000, there is no accounting for how it reached it, rather than any other sum. The only account of it which it gave was that it so did ‘to be conservative, and out of an abundance of caution, to the end that no injustice may be done respondent in arriving at the value of the corporate franchise of respondent in this state.’ And it noted the fact that this-sum was ‘less than 80 per cent, of that which it believes to be the fair cash value of Kentucky’s proportion of the entire capital stock of respondent.’ It then deducted from this last sum the assessed value of the tangible property in Kentucky, to wit, $29,500,772, which left the sum of $45,658,630 as the value of the franchise.. Such is what the board did on the face of things.”

Plaintiff being an interstate carrier whose lines of railroad extend both within and without the limits of the State, it comes within §4081, Ky. Stats., which requires that “the said board will fix the value of the capital stock as hereinbefore provided, and that proportion of the value of the capital stock which the length of the lines operated, owned, leased, or controlled in this State, bears to the total length of the lines owned, leased or controlled in this State and elsewhere, shall be considered in fixing the value of the corporate franchise of such corporation liable for taxation in this State.” The only previous provision to satisfy the reference “will fix the value of the capital stock as hereinbefore provided,” is the provision of § 4079 that the Board shall fix it “from said statement, and from such other evidence as it may have.”

Under this system it is obvious that there are three *540 principal steps in the process of ascertaining the value of the intangible property, taxable in Kentucky, of companies operating lines of railroad extending within and beyond the limits of the State. These are: (1) The fixing of the value of “the capital stock of the corporation”; which, as construed in previous cases, means the total value of all its net assets, tangible and intangible, within and without the State; (2) the apportionment to Kentucky; and (3) the elimination of the value of the tangible assets. Whet'her the second step shall precede the third, or vice versa, is one of the matters in dispute.

No specific method being prescribed by the statute for fixing the value of the “capital stock” of the entire system, except a requirement to the effect that the Board shall have before it, with other evidence, a statement by the corporation setting forth the kind of business engaged in, the amount of capital stock, the number of shares, the par and real value thereof, with the highest price at which it has sold recently, the amount of surplus and undivided profits, the value of all assets, the total amount of indebtedness, the gross and net earnings or income, the amount and kind of tangible property within the State, and its location and fair cash value, it. follows that the particular method to be pursued in ascertaining from this and other evidence the aggregate capital value is left to the sound judgment and discretion of the Board. In such cases there are (at least) two recognized methods, known as the stoek-and-bond plan and the capitalization-of-income plan. In the present case the latter was followed.

(7) The application of this method by the Board is attacked in two respects, first, in the manner of deducting non-taxable assets, and, second, in the rate of percentage used in capitalizing the income. As to the first point, the insistence is that as the tax under consideration is merely an intangible-property tax, it results that if *541 among the assets of the corporation going to make up its total capital value there were some that were non-taxable, it was necessary to deduct these before arriving at the taxable capital. It is pointed out that under § 4085, Ky. Stats., the property of all corporations is to be assessed in the name of the corporation, and “so long as said corporation pays the tax on all its property of every kind, the individual stockholders shall not be required to list their shares in said corporation;” the argument being that, to the extent that plaintiff held the stock of other corporations having property in Kentucky and paying taxes thereon in that State, this stock in plaintiff’s hands was non-taxable, and its value should have been deducted from the total value of its capital stock previously ascertained; citing Commonwealth v. Fidelity Trust Co., 147 Kentucky, 77, 84. As the record shows, the Board of Valuation and Assessment recognized plaintiff’s right to deduction upon this account, and for this reason, in applying the capitalization-of-income method, deducted from $16,613,301.12, net income from operated roads, the sum of $878,147, the net income from non-taxable securities as reported by plaintiff to the Auditor and the Railroad Commission, taking the balance only, or $15,735,154, as the income to be capitalized in order to arrive at the value of the entire system. The criticism is that adopting this method had the effect of deducting only such stock in other corporations as paid dividends, whereas plaintiff insists that much of its stock thus held, although paying no dividends, or dividends at a low rate, had large intrinsic value by reason of the control it gave over other lines of railroad and the increment it brought , to the aggregate income of the company. There was evidence that these non-taxable securities amounted to upwards of $30,000,000 in value, whereas the capitalization at 6 per cent, of their income of $878,147 produced a value of only $14,469,113. In our opinion, it is a sufficient answer to this contention *542 to say that the Board merely carried out the capitalization-of-income plan of valuation, perhaps to its logical extreme, but certainly not in a manner that enables this court to say that they pursued a fundamentally wrong method.

(8) The second point, the adoption of a 6 per cent, interest rate as the basis of capitalization, instead of the higher rate, called'in the testimony the “composite percentage,” reached by taking plaintiff’s mileage in each of the thirteen States in which it operates, multiplying this by the legal rate of interest in that State, and dividing the total of the products by the total mileage, is, like the first, a criticism merely of the conclusion of the Board upon a question of fact which is not properly subject to review by the courts.

Therefore we concur in the opinion of the District Judge that, upon this record, the value of the capital stock must be taken to be at least as great as $262,252,566, the amount found by the Board.

(9) The Board’s next step was to apportion to Kentucky a certain part of this total value, which of course included both tangible and intangible assets; after which it proceeded to deduct the assessed value of the tangible assets in Kentucky. Plaintiff insists that these steps should have been reversed; that the Board, having valued the total capital stock of the company, including assets tangible and intangible, should first have deducted the entire tangible assets wherever situate, and next have assigned a proper portion of the intangible to Kentucky.

What the statute requires, in this respect, is a question of state law, upon which we must follow the Kentucky Court of Appeals if that court has passed upon it. It is true that the only authority of the Board was to assess intangible property, and, whether it followed the local statute or not, it could not, consistently with the due process provision of the Fourteenth Amendment, include, at least as against any foreign corporation, any part of its *543 tangible property lying without the State; and it is not to be supposed that the statute intended to prescribe a different rule with respect to Kentucky corporations, since domestic and foreign corporations are dealt with in the same section (§ 4081). That section, .according to its terms, first provides that the Board shall “fix the value of the capital stock as hereinbefore provided,” there being, as already shown, no provision respecting the method except that the ascertainment shall be based upon the statement of the corporation and such other' evidence as the Board may have. The section proceeds to declare that “that proportion of the value of the capital stock which the length of the lines operated, owned, leased, or controlled in this State bears to the total length of the lines owned, leased, or controlled in this State and elsewhere, shall be considered in fixing the value of the corporate franchise' of such corporation liable for taxation in this State.” Referring now to the mode of procedure, these words evidently contemplate an apportionment, as an aid in reaching the ultimate result (valuation of franchise taxable in Kentucky); but it is an apportionment of “the value of the capital stock,” which includes both tangibles and intangibles, within and without the State. This is not to say that' any property without the State- may be taxed. It requires state mileage valuation to be considered and compared with system mileage valuation, but it does not make this comparison conclusive. As the section was enacted originally, the words, “considered in fixing” were not contained in it, so that upon the face of things the mileage pro-rate was conclusive in ascertaining the State’s proportion of the value of the corporate franchise, — just as county and district mileage was and still is conclusive as to apportionment between those taxing districts. 'But by the Act of June 9, 1893, the words “considered in fixing” were inserted, the necessary effect of which was to make the relation of state *544 mileage to system mileage a factor that must be considered, ■but not necessarily given conclusive weight. Section 4081 says nothing about deducting the value of tangible property, and the preceding sections speak of deducting only such tangible property as is located within the State. Indeed, there is no provision requiring the corporation to re- ■ port its tangibles outside of .the State. And, if all tangibles were deducted before apportionment, then the deduction of “all tangible property assessed in this State,” specifically required by the proviso to § 4079, obviously would result in a double deduction. The sections are inartificially drawn in this as in some, other respects. The District Court, upon elaborate consideration in the case of the 1912 assessment (209 Fed. Rep. 418-429), reached the conclusion that by the proper construction the entire value of capital stock should be first apportioned, having •regard to the mileage, and that from Kentucky’s portion of the whole the assessed value of the tangibles within the State should then be deducted; and-that the Kentucky Court of Appeals had so decided in Commonwealth v. Covington & Cincinnati Bridge Co., 114 Kentucky, 343.

Plaintiff relies upon two cases, the first being Adams Express Co. v. Kentucky, 166 U. S. 171, 180, where this court, by Mr. Chief Justice Fuller, after referring to the statutory provisions now under consideration, and the use in the several sections of the words “franchise” and “corporate franchise,” said: “But taking the whole act together, and in view of the provisions of sections 4078, 4079, 4080 and 4081, we agree with the Circuit Court that it is evident that the word ‘franchise’ was not employed in a technical sense, and that the legislative intention is. plain that the entire property, tangible and intangible, .' . . should be valued as an entirety, the value of the tangible property be deducted, and the value of the intangible property thus ascertained be taxed under these provisions; and as to railroad . . . companies, whose lines ex *545 tend beyond the limits of the State, that their intangible property should be. assessed on the basis of the mileage of their lines within and without the State. But from the valuation on the mileage basis the value of all tangible property is deducted before the taxation is applied.” The matter of apportionment was not there involved, nor what method or order was prescribed by the statute; the question at the moment being whether the tax was a true franchise tax, or merely a property tax upon' intangible property. The significant thing was that the value of tangibles was to be deducted; whether before or after apportionment was a matter of no present significance. And the last sentence quoted, in the expression “valuation on the mileage basis,” indicates an apportionment of the entire capital stock, mile for mile, prior to the deduction of tangibles.

The second case referred to is Coulter v. Weir, 127 Fed. Rep. 897, 907-908, where the Circuit Court of Appeals for the Sixth Circuit, in dealing with the question whether the law was repugnant to the commerce clause or the Fourteenth Amendment, used this language: “Neither is the injunction in reference to a deduction of the value of tangible taxable property from the gross value of the whole corporate property limited to such as is situated within the state of Kentucky. If tangible property having a situs outside the state be included in the valuation of the company’s intangible property, the purpose of the law, being to tax only intangible property, is defeated. We therefore read the act, as the- Supreme Court seems to have read it in Adams Express Co. v. Kentucky, as requiring the deduction of tangible property from the gross value of all corporate assets, whether such tangible property be within or without the state.” The question of apportionment, or of the particular method to be pursued in making the assessment, was not involved in this case, any more than in Adams Express Co. v. Kentucky, supra. *546 It is true, as the court said, that if tangible property having a situs outside the State were included in the valuation, the purpose of the law to tax only intangible property would be defeated. The same result would follow if tangible property within the State were included in the valuation. But it does not follow that tangibles, within or without the State, are to be included in the valuation because included in the apportionment. Any excess of tangibles, ■ without or within the State, properly may be given its due weight as a factor modifying the tentative result reached by mere mileage apportionment. In the absence of special circumstances, this is not of itself necessarily an unjust method of apportioning such a tax. Western Union Telegraph Co. v. Massachusetts, 125 U. S. 530, 552-553; Western Union Telegraph Co. v. Taggart, 163 U. S. 1, 18, 20, 22, 26.

However, the decision of the Kentucky Court of Appeals in the Covington & Cincinnati Bridge Co. Case, supra, is directly in point, and, being so, is conclusive upon the question of the proper statutory method. There the company’s “capital stock,” valued "by the stock-and-bond method, amounted to $1,330,000. It owned an interstate bridge, 59 per cent, of the length thereof being in Kentucky, the remainder in Ohicj; and it had tangible property in Kentucky assessed at $452,000. The State of Ohio assessed the portion of the bridge lying in that State at $237,984, and the company paid the taxes thereon. The Kentucky Board of Valuation and Assessment fixed the value of its entire property or capital stock at $730,349,. and, deducting from this the assessment of tangibles in Kentucky ($452,000), took the difference, or $278,349, as the franchise valuation. The company, insisting that the correct valuation was $180,489, paid to Kentucky the tax on this amount, reserving the question of its liability for a claimed balance of $464.84, and of the method or basis upon which its franchise should be valued for taxa *547 tion by the Board, to be determined by the courts. The matter was submitted to the Circuit Court as an agreed case presenting two questions, (1) whether the company owed to the Commonwealth the sum of $464.84, or any part thereof, on account of the tax of its franchise, and (2) what method or basis should be adopted by the State Board of Valuation and Assessment for fixing the value of defendant’s franchise for taxation in the Commonwealth of Kentucky. That court held that the Board had adopted an improper method, and that the company, by the payment it had made, had fulfilled its obligation to the State; reaching this conclusion by taking the aggregate market value of its capital stock and bonded indebtedness ($1,330,000), deducting the assessed value of the Ohio tangibles ($237,984), and apportioning the balance of $1,092,016 on the basis of 59 per cent, to Kentucky and 41 per cent, to Ohio. From 59 per cent, of $1,092,016, namely $664,289, it deducted the tangible property assessed in Kentucky, $452,000, which left a balance of $192,289 as the value of the Kentucky franchise. The State appealed to the Court of Appeals, where it insisted that by the method adopted by the Circuit Court the company was not taxed upon its entire property. The report of the case states (pp. 348, 349): “It is insisted for the State that the proper way to arrive at the valuation of the franchise is to take the total value, $1,330,000, and get 59 per cent, of it, which is $782,700, and that, this presents the total of the tangible property and of the franchise in Kentucky. Therefore, if we deduct from this total $782,700, the assessment of the tangible property in Kentucky, $452,000, the balance, $330(700, is the value of the franchise. The board fixed the value of the franchise at $278,349, or considerably less than the result thus obtained.” It was insisted for the Bridge Company that the Circuit Court had followed Henderson Bridge Co. v. Commonwealth, 99 Kentucky, 623, but the Court of Ap *548 peals pointed out that in that case the Board had followed the method claimed by the Company, that as the action was brought by the State to recover taxes upon the assessment made by the Board, the State was not in a position to question the propriety of the assessment, and that there was nothing in that case, or in any subsequent case approving it, to prevent the Board from adopting a different basis. To a criticism that the Board had adopted an erroneous basis in the instant case, the court conceded the point, arguendo, but sustained the assessment upon the ground that it was no more onerous than it would have been had a correct method been adopted; and, in conclusion, declared (pp. 350-351): “We therefore conclude that the basis urged by appellant [the State] is the proper one for the assessment of the property under the agreed facts, and the board having fixed a lower assessment than this would make, the court erred in not enforcing the collection of the tax on the assessment made by the board.” This was a precise answer to the equally precise contention urged in behalf of the State affecting each of the two questions that were submitted for decision, and it seems to us that it is binding upon the federal courts as a construction of the statute.

This, we repeat, does not necessarily result in including in the Kentucky franchise valuation tangible or intangible property not located within that State. It does permit the Kentucky officials tó take into consideration extra-state tangibles,- as well as intangibles, constituting portions of the unit of which they are valuing a part. This is permissible, even in applying the statute to non-resident corporations. It is settled that total stock or total assets, situate partly within and partly without the State but organically related, may be taken into consideration as a means of reaching the true cash value of property within the State, -and that the mileage relation may be given its proper weight. State Railroad Tax Cases, 92 U. S. 575, *549 608; Pullman’s Palace Car Co. v. Pennsylvania, 141 U. S. 18, 26; Pittsburgh &c. Railway Co. v. Backus, 154 U. S. 421, 430-431; Western Union Telegraph Co. v. Taggart, 163 U. S. 1, 26, 27; Fargo v. Hart, 193 U. S. 490, 499.

(10) Plaintiff’s next point is that the Board, took into consideration a mileage proportion of. 35.15 per cent., which was the ratio borne by the roads operated by plaintiff within the State of Kentucky to its total operated mileage; whereas it should have included the controlled mileage within and without the State, which would have yielded to Kentucky a proportion of only 24.69 per cent. In this the District Court yielded to plaintiff’s contention, and, we think, rightly so. By § 4079, Ky. Stats., where the company’s lines extend beyond the limits of the State, the report to the Auditor shall in addition to other facts show “the length of entire lines operated, owned, leased or controlled in this State, and in each county, incorporated city, town or taxing district, and the entire line operated, controlled, leased or owned elsewhere.” And, by §4081, “that proportion of the value of the capital stock which the length of the lines operated, owned, leased, or controlled in this State, bears to the total length of the lines owned, leased or controlled in this State and elsewhere, shall be considered in fixing the value of the corporate franchise of such corporation liable for taxation in this State.” In Commonwealth v. L. & N. R. R. Co., 149 Kentucky, 829, 838, the very point was considered by the Court of Appeals, which declared: “If the railroad com.pany owns a majority of the stock of any company, so that it may elect its directors and dictate its policy, there can be no doubt that it controls it within the meaning of the statute, and that such other railroad should be included in the report required to be made to the Auditor. If required to be reported, the Board of Valuation and Assessment may take them into consideration in fixing *550 the value of the franchise of the controlling company in the State of Kentucky.”

(11) The District Court (230 Fed. Rep. 199, et seq.) acceded to the contention of the plaintiff that the action of the Board in adding at first $2,468,612, and, finally, $2,318,244, to the Kentucky proportion of the value of the unit, on account of the excess value of the portion of the Kentucky intangibles over the mileage proportion thereof was not warranted; basing this decision upon the ground that the Board did not follow the only possible method that would have determined this excess with any certainty, and did not have before it the data that would have enabled it to do so. The point perhaps is covered by one of defendants’ assignments of error; but no argument- has been addressed to it, and we express no opinion upon it.

(12) The District Court, having found that the value of plaintiff’s entire capital stock must be taken to be at least as much as $262,252,566, the amount found by. the Board, and that the apportionment must be upon the basis not of the operated mileage only, but of all mileage operated, owned, leased, and controlled within and without the State, was led to the further conclusion, as a corollary (230 Fed. Rep. 202-204), that the valuation of the total capital stock should include an item that the Board had overlooked, viz., the value of so much of the controlled mileage as Was not represented by plaintiff’s holdings. (Of course, in adopting the capitalization-of-income method of valuation, no account was taken of the interests of others than plaintiff in the controlled roads.) Plaintiff contends that the statute does not justify this procedure; that it is beyond the power of the State because it results in taxing property not belonging to the plaintiff; and that a more logical and consistent method would be to arrive at the operated, owned, leased, or controlled mileage by treating as controlled mileage not the *551 total, but only a proportion corresponding to the amount of stock held by plaintiff in the controlled roads. The matter is not free from doubt ; but we concur in the view of the District Judge that it was the legislative intent that, in fixing the percentage apportionable to Kentucky and to be taken into consideration in valuing the taxable franchise, the whole of the controlled mileage within and without the State was to be treated as a part of the aggregate “capital stock,” not only in fixing the mileage, but also in fixing the valuation, upon which the apportionment is to be .based. It is not to be supposed that the legislature intended to require that, in making the mileage apportionment, which as already shown is not conclusive but evidential upon the valuation of the taxable franchise, fractional interests in the controlled roads should be taken into the account, but rather that a controlled road should be treated the same as a road owned.

In order to avoid a double assessment of the franchise of so much of the controlled mileage as was within the State, the court found it necessary to deduct from the Kentucky apportionment of the “capital stock” the value of the Kentucky portion of the controlled mileage (in addition to the assessed value of the tangible property there situate) since these local franchises would be assepsed against each of the separate organizations. In this view we concur.

But the court was unable to apply the proper correction to the Board’s valuation (p. 232), because of there being nothing in the record to show either the value of the portion of plaintiff’s total capital stock not considered by the Board (that is,’the value of the outstanding interests in the controlled roads), or the value of that portion of the controlled mileage which was in Kentucky.

After the court delivered its opinion to this effect, and before the entering of the final decree, plaintiff tendered what is called a supplemental bill, which the court allowed to be filed, purporting to show all the facts respecting the *552 controlled roads, and to demonstrate that the result of adopting the process indicated by the court’s opinion would be to reduce the assessment below the amount upon which the company already had paid taxes, and this whether the valuation were made on the stock-and-bond plan or on the eapitalization-of-ineome plan. It appears that defendants never filed any answer to this, and it is urged that because of their failure to do so its allegations must be taken as confessed. But there is nothing to show that defendants were ordered to answer; and inasmuch as this supplemental bill was filed after the hearing and decision of the cause, and the record contains nothing to show why its averments were ignored, we are not able to say either that defendants were in the position of admitting those averments, or that the court erred in failing to give effect to them. But at least it can be. said that plaintiff was not in default for omitting to introduce evidence at the hearing respecting these matters, they not having been considered by the Board, nor set up in the original pleadings, nor so far as appears deemed by any of the parties to be material until the court rendered its decision. Yet, as will appear presently, the court in effect decided the case against plaintiff because there was nothing in the record to show the facts concerning the controlled mileage.

(13) In attempting to carry into effect its conclusions upon the facts and the law, the District Court pursued the following process of reasoning (p. 231): Assuming $262,252,566 to be the true cash value of plaintiff’s entire capital stock, as the Board found it to be, and 24.6901 (in the opinion this is misprinted as “24.9601”) to be the true percentage of the fair cash value apportionable to Kentucky, and that Kentucky’s portion was not of greater value than the mileage proportion, the fair cash value of the portion of plaintiff’s capital stock attributable to Kentucky would be $64,750,418.79. Sixty per cent, of *553 this — the 'factor of equalization — was taken to be $38,850,251.12. Deducting $29,500,772, the assessed value of the tangible property, would leave $11,349,479.27 as the value of the franchise — this being less than half of the amount upon which payment had been made. (There appear to be some additional misprints, or trifling errors of calculation, but not sufficient to affect the result.) But since the Board had omitted to include in the value of the capital stock that interest in the controlled mileage not represented by the stock and bonds owned by plaintiff, and since there was nothing in the record to show the value of this interest, or the value of that portion of the controlled mileage located in Kentucky, the court assumed that the result of considering these two matters might be to make the value of the Kentucky portion of plaintiff’s capital stock as much as $92,181,766, the sum at which the Board fixed it, instead of $64,750,418.79, the amount computed by the court. The court proceeded to say (p. 232):

“The board has found the fair cash value of the portion of plaintiff’s unit in this state to be $92,181,766, without any excess yalue. They have not gone at it in the right way. But they have in fact found such to be its valué. It is possible that, if they had gone at it in the right way, they would have found such to be the value thereof. . ... I will therefore dispose of the case on the basis that it was that much. This is not such an exactness as I always like to attain, but the case is one where exactness is not, and only approximation is, attainable. Taking 60 per cent, of $92,181,766' would give $55,309,059.60 as the value of the portion of plaintiff’s unit in Kentucky. Deducting $29,500,566, the assessed value of the tangible property, leaves $25,808,493.60 as the value of the franchise. And deducting from this balance $22,899,300, the amount on which payment has been made, leaves $2,909,192.60 on which payment should yet be made.”

*554 This rough-and-ready reasoning had the effect of depriving plaintiff of the benefit of having controlled mileage taken into consideration in making the apportionment, instead of operated mileage only; and this because of the assumption that the same valuation reached by the Board through an erroneous method possibly might have been reached had they pursued a correct method. We think the court here fell into error. It being shown that the valuation made by the Board was the result of following a method substantially erroneous because not in accordance with the statute, there is no presumption that a like valuation would have been reached by following a correct method. As the difference is so great — more than. $27,000,000 — there is a strong presumption to the contrary. If any of the facts necessary to enable the court to determine what result would have been reached by the application of a correct method were absent from the record, the court might have opened the proofs, in its discretion; otherwise it should have proceeded to base its judgment upon such proofs as already were in the record. The result of the method adopted in making up the decree was to deprive plaintiff of the relief it was entitled to, upon the basis of the facts as found, because of a surmise that, upon other facts not shown by the record, a conclusion sustaining the Board’s action might have been reached.

The decree under review, so far as defendants’ assignments of error are concerned, should be affirmed. Upon plaintiff’s assignments of error, it should be reversed, and the cause remanded to the District Court for further proceedings in conformity with this opinion.

No. 778, reversed.

No. 779, affirmed.

Me. Justice Holmes, Mr. Justice Brandéis, and Mr. Justice Clarke dissent.

Notes

Set forth in full in the opinion in Greene v. Louisville & Interurban R. R. Co., ante, p. 499.

§ 4077. (1) Franchise — assessment' of. Every railway company or corporation, . . . also every other corporation, company or association having or exercising any special or exclusive privilege or franchise not allowed by law to natural persons, or performing any public service, shall, in addition to the other taxes imposed on it by law, annually pay a tax on its franchise to the State, and a local tax thereon to the county, incorporated city, town or taxing district, where its franchise may be exercised. The Auditor, Treasurer and Secretary of State are hereby constituted a board of valuation and assessment for fixing the value of said franchise, except as to turnpike companies, which are provided for in § 1 [4095] of subdivision 4 of this article, . . . The Auditor shall be chairman of said board, and shall convene the same from time to time, as the business of the board may require. It shall be the duty of the Attorney-General, when requested by the board of valuation and assessment, to attend said board at its meetings and advise with samé in its proceedings.

§ 4078. (2) Corporations to report to Auditor to determine value of franchise. In order to determine the value of the franchises mentioned in the next preceding section, shall, annually, between the thirtieth day of June and the first day of October, make and deliver to the Auditor of Public Accounts of this State a statement, verified by its president, cashier, secretary, treasurer, manager, or other chief officer or agent, in such form as the Auditor may prescribe, showing the following facts, viz.: the name and principal place of business of the cor *534 poration, company or association; the kind of business engaged in; the amount of capital stock, preferred and common; the number of shares of each; the amount of stock paid up; the par and real value thereof; the highest price at which such stock was sold at a bona fide sale within twelve months next before the thirtieth day of June of the year in which the statement is required to be made; the amount of surplus funds and undivided profits and the value of all other assets; the total amount of indebtedness as principal, the amount of gross or net earnings or income, including interest on investments, and incomes from all other sources for twelve months next preceding the thirtieth day of June of the year in which the statement is required; the amount and kind of tangible property in this State, and where situated, assessed, or liable to assessment in this State, and the fair cash value thereof, estimated at the price it would bring at a fair voluntary sale, and such other facts as the Auditor may require.

§ 4079. (3) Value of franchise — how determined — lines extend beyond State or county. Where the line or lines of any such corporation, company or association extend beyond the limits of the State or county, the statement shall, in addition to the other facts hereinbefore required, show the length of entire lines operated, owned, leased or controlled in this.State, and in each county, incorporated city, town or taxing district, and the entire line operated, controlled, leased or owned elsewhere. If the corporation, company or association be organized under the laws of any , other State or government or organized and incorporated in this State, but operating and conducting its business in *535 other States as well as in this State, the statement shall show the following facts in addition to the facts hereinbefore required: The gross and net income or earnings received in this State and out of this State, on business done in this State, and the entire gross receipts of the corporation, company or association in this State and elsewhere, during the twelve months next before the'thirtieth day of June of the year in which the assessment is required to be made. . . . Provided, That said board, from said statement, and from such other evidence as it may have, if such corporation, company or association be organized under the laws of this State, shall fix the value of the capital stock of the corporation, company or association, as provided in the next succeeding section, and from the amount thus fixed shall deduct the assessed value of all tangible property assessed in. this State, or in the counties where situated. The remainder thus found shall be the value of its corporate franchise subject to taxation as aforesaid.

§ 4080. (4) Foreign corporations — franchise—how determined. If the corporation, company or association be organized under the laws of any other State or government, except as provided in the next section, the board shall fix the capital stock in this State by capitalizing th.e net income derived in this State, or it shall fix the capital stock as hereinbefore provided; and will determine from the amount of the gross receipts of such corporation, company.or association in this State and elsewhere, the proportion which the gross receipts of this State, within twelve months next before the thirtieth day of June of the year in which the assessments were made, bears to the entire gross *536 receipts of the company, the same proportion of the value of the entire capital stock or the capitalizing of the net earnings in this State, less the assessed value of the tangible property assessed, or liable to assessment, in this State, shall be the correct value of the corporate franchise of such corporation, company or association for taxation in this State.

§4081. (5) Interstate carrier — franchise—how fixed. If the corporation organized under the laws of this State, or of some other State government, be a railroad . . . company or a corporation performing any other public service, the lines of which extend beyond the limits of the State, the said board Will fix the value of the capital stock as hereinbefore provided, and that proportion of the value of the capital stock which the length of the lines operated, owned, leased, or controlled in this State, bears to the total length of the lines owned, leased or controlled in this State and elsewhere, shall be considered in fixing the value of the corporate franchise of such corporation liable for taxation in this State; and such corporate franchise shall be liable to taxation in each county, incorporated city, town or district through or into which such lines pass, or are operated, in the same proportion that the length of the line in such county, city, town or district bears to the whole length of lines in this State; . . .