delivered the opinion of the' Court.
This suit was brought in the federal district court for North Dakota by petitioner against the state tax commissioner and the auditors and treasurers of 30 counties, to enjoin collection of about 40% of 1933 taxes laid upon its railroad properties in each county. The assessed value of all petitioner’s, railroad property in the State is $78,-832,888. The total of the tax is $1,508,352.34, of which petitioner has paid about 60%. The suit is grounded upon the claim that the taxes are based on a valuation that *138includes properties located outside the State and in other respects are so excessive and arbitrary as to be repugnant to the due process and equal protection clauses of the Fourteenth Amendment to, and the commerce clause of, the Federal Constitution. Issues were joined, the casé was tried, the court made findings of fact, concluded that petitioner was not entitled to relief and dismissed the bill. The Circuit Court of Appeals affirmed. 77 F. (2d) 405.
The state law requires that all property subject to taxation be assessed at its true and full value in money. Comp. Laws 1913, § 2122. The state board of equalization is required in August of each year to assess at its actual value every railroad within the State and it is governed by the rules that apply to township assessors in valuing other property. § 2242. 1925 Supp.,- § 2141a3. The average values per -mile of main and branch lines, respectively, constitute the bases for assignment of value to counties. § 2243. And on like mileage basés the value given to each county is distributed to its cities, towns, townships and districts, through which the railroad extends. § 2244. The railroad property is taxed, as is personal property, by applying the local rate to 50% of the assessed value.1 Petitioner did not allege that other property was not assessed at its full and true value as required by state law, and does not seek relief on the ground of discrimination.
Petitioner claims that the board made the assessment by attributing to North Dakota too great a proportion of a grossly excessive system- valuation. More specifically its contentions are: (1) That, by reason of the methods employed for the ascertainment of the percentage of system value to be assigned to North Dakota, the assessment *139includes the value of property located in other States to the extent of approximately $20,-000,000, and (2) that, even if the factors used to make the allocation be not condemned, the assessment must nevertheless be held arbitrary and excessive to the extent of $15,000,000.
The full and true value of the property is the amount that the owner would be entitled to receive as just compensation upon a taking of that property by the State or the United States in the exertion of the power of eminent domain. That value is the equivalent of the property, in money paid at the time of the taking. Olson v. United States, 292 U. S. 246, 254. The principles governing the ascertainment of. value for the purposes of taxation, are the same as those' that control in condemnation cases, confiscation cases and generally in controversies involving the ascertainment of just compensation. West v. C. & P. Telephone Co., 295 U. S. 662, 671.
In determining the amount of the assessment the board was not bound by any formula, rule or method, but for guidance to right judgment it was free to consider ¿11 pertinent facts, estimates and forecasts and to give to them such weight as reasonably they might be deemed to have. Courts decline to disturb assessments for taxation unless shown clearly to transgress reasonable limits. Overvaluation is not of itself sufficient to warrant injunction against any part of the taxes based on the challenged assessment; mere error of judgment is not enough; there must be something that in legal effect is the equivalent of intention or fraudulent purpose to overvalue the property and so to set at naught fundamental principles that safeguard the taxpayer’s rights and property. Rowley v. Chicago & N. W. Ry., 293 U. S. 102, 109-111. The assessment is presumed to have been rightly made on the basis of actual value. Its validity, must be tested upon consideration of the facts established by the evidence and of those of which judicial notice may be taken. ,
*140There is controversy between the parties as to whether the evidence discloses how the assessment was made. Petitioner maintains that the record shows that the board found system value and apportioned it to North Dakota and also shows the methods by which these determinations were made. The district court refused to find, and the Circuit Court of Appeals held that petitioner failed to prove, that the board made the valuation by methods which petitioner claims that it employed.
As to methods employed by the board. Respondents called as a witness Mr. Lyman A. Baker, who had been with the North Dakota tax commissioner for 19 years and during the last 13 years, ending January 1,1933, had been deputy commissioner in charge of the valuation of railroads and other utilities. He was engaged in this litigation in behalf of respondents and spent much time in making computations and in the preparation of exhibits that were put in evidence by respondents. In substance he testified:
The first step in the valuation of railroad property within-a State is.to determine the value of the entire system. There are two classes of evidence ordinarily considered: The average market price of stock and bonds, and the past- earnings over a period of years. As the stock and bond prices reflect value of the entire railroad, it is necessary to eliminate the value of non-operating property. The method requires a definite period ■ over which to average price quotations and that must of necessity be somewhat arbitrarily-fixed. It assumes that the average price reflects value, but rarely is controlling interest bought or sold on the exchange. Where control is sought prices advance sharply. - The method also assumes that purchasers act on accurate knowledge of conditions; it ignores the influence of pure speculation. In applying the method, taxing boards, economists and railroad men have always adopted five-year periods immediately pre*141ceding the assessment in order to give stability to the tax value. The -depression resulted in a collapse in the stock and bond market. Forced selling brought prices down to a figure that did not fairly represent the value of the property. “Despite all these objections to the stock and bond method of valuation, I still consider it as one of the best indices of value obtainable.”
He further testified: Capitalization of net railroad operating income is generally recognized as an important element in estimating the value of railroad operating property. The average net income, usually for five years, is capitalized at a reasonable .rate of return. The method assumes the amount so ascertained to be the value of the property. The income qf .a single year is seldom, if ever, used. As 1931 and 1932 were the worst years in railroad history since the panic of 1893, the use of the three-year period ending in 1932 has but little justification. The five-year period has been given the same weight by the state board for a good many years. It is generally considered that the rate of return that a company is allowed to earn under state and federal law is a fair rate to use. A rate of six .percent, is justifiable under present conditions. Economic return from farm property, being about 65% of all that is taxable in North Dakota, decreased-about 75% from the 1924-1928 average. Assessments on values indicated by capitalization of average net income for the five years ending in 1932 would result in giving preferential treatment to railroads as compared with other properties. Where properties have been operated at a loss over a period of years, there are no earnings to capitalize. Yet they have present and prospective value which would be reflected by use of the stock and bond valuation method. The criticisms made of these methods are not sufficient to render them valueless. “On the contrary the two methods are universally approved as the two best evidences of the value of a-railroad which are available.”
*142The answer alleges: In 1932 the tax commissioner made and presented to the board computations based upon a determination of system value by the use of a composite of the average stock and bond values of the petitioner for a period of five years preceding the assessment and the average value ascertained by capitalizing net earnings for the same period; by apportioning the system value to North Dakota upon the basis of the average of five factors: (1) miles of all track, (2) physical property, (3) car and locomotive miles, (4) ton and. passenger miles, (5) gross earnings, there was produced a value of $76,-115,715; another apportionment on-the basis of the three use factors, viz. car and locomotive miles, ton and passenger, miles, and gross earnings, produced $79,417,825, and a third apportionment by the average of track miles and the three use factors produced $80,671,790. The answer further alleged that “upon this evidence and upon all other evidence and matters of common knowledge before it the Board did in the year 1932 fix the valuation of plaintiff’s property in North Dakota at $78,850,024”; that, in 1933 the commissioner and the railway company presented to the board the financial a'nd .operating statistics of the plaintiff’s railroad and reports and computations based upon the formulas used in 1932 and other evidence of value, and that the board after full consideration of them and all other evidence of value and matters of . common knowledge fixed the assessment for 1933 at $78,832,888 “which said amount represented the honest judgment” of the board “and the full and true value of the plaintiff’s North Dakota property in money.”
The average of'the valuations computed for 1932 as alleged in the answer is $78,735,110; the assessment was $78,850,024. The difference is less than one-sixth of one per cent. The trial court found that for 1933 the board assessed the property at “the sum of $78,832,888, which sum was the same as the 1932 . assessment except for a *143deduction, of $17,136 for certain trackage of the plaintiff which had been removed.”
It is clear that the computations prepared by the tax commissioner for the use of the board served as guides to, if indeed they were not used as the measure of, value for the assessments made by the board for 1932 and 1933. Respondents’ answer and evidence require a finding that' these computations were in fact the controlling bases and constituted the very foundation of the 1932 and 1933 assessments. In view of the relatively small differences between the 1933 assessment and the figures produced by the methods approved by respondents and universally as the best available evidence of value of a railroad, the latter rightly may be used in testing the validity of the former.
Petitioner’s claim that the board’s apportionment of system value to North Dakota operated to assess and tax property in other States cannot be upheld.
Petitioner maintains .that the amount attributed. to that State was found by the use of the factors above referred to. More fully described, they are: 1. Miles of all track (as of December 31, 1931) — 20.19%. 2. Physical property as measured by cost of reproduction less depreciation (as of December 31, 1931) — 13.84%. 3.- Car and locomotive miles (average for five years ending with 1931) — 19.90%. 4. Ton and passenger miles (average for five years ending with 1931) — 18.65%. 5. Gross •earnings (average for five years ending with 1931)— 18.45.%; the amount assigned to North Dakota was found by adding to the intrastate revenue earned in that .State its mileage proportion of revenue derived from traffic moving partly within and partly outside her boundaries. The average of these percentages is 18.206%.
The principal grounds on which petitioner assails the board’s apportionment are: Petitioner’s railroad in North Dakota consists largely of relatively cheaper branch lines. *144The most valuable terminals and costly construction are in other States and, while these include little mileage, they contribute as much to system value in proportion to cost as do the cheaper stretches of the road where the same investment is spread over much greater mileage.
The problem of apportionment is a difficult one. It is impossible to formulate a rule generally applicable. Controlling conditions vary greatly from time to time. Allocations to be sufficiently accurate for practical purposes must be arrived at by the exercise of sound judgment based on facts that fairly reflect the relation between value of the system as a whole and value of the part within a State. Rowley v. Chicago & N. W. Ry., supra, 109, 110.
The methods proposed by petitioner discredit its objections to the apportionment made by the board. While the board had the 1933 assessment under consideration, petitioner submitted to it a brief in which it proposed two methods of apportionment. One was by use of the above described factors 1, 3, 4 and .5, and the other by use of' 3, 4 and 5,- producing, respectively, as calculated by petitioner, 19.35% and 19.14%. These percentages are higher than the average of those that petitioner says the board used. There is no evidence that the assessment was arrived at by use of apportioning percentages higher than those then used by petitioner.
Petitioner’s bill suggests a method of apportionment that would assign to North Dakota less than 12%% of system value. Briefly, the method is this: To the revenue derived from North Dakota intrastate traffic add a part of the revenue received from the interstate moving in North Dakota that is equal to its proportion of the property used in, and the cost of, carrying that traffic; deduct the operating expenses incurred in moving it from the total revenue, The relation of the state net earnings *145so found to the net for .the system will' be the same as that existing between North Dakota value and system value. As petitioner gives this method scant, if any, support here and as it was rejected by the lower courts, we need not consider it. United States v. State Investment Co., 264 U. S. 206, 211. Texas & N. O. R. Co. v. Railway Clerks, 281 U. S. 548, 558. United States v. Commercial Credit Co., 286 U. S. 63, 67.
And here petitioner argues that the apportionment, should be made on the basis of physical property, i. e. factor 2 above described. That would assign to North Dakota less than 15% of the system value. Petitioner did not submit it to the board as the measure or even include it in the group of factors upon which it based the calculations included in its brief. It is not sustained by evidence.
When regard is had to the size of the Great Northern system and the variety of" things that affect values to be attributed to its railroad in different States, and the numerous matters as to which there may be wide difference of opinion, it must be held that percentages lower than, or substantially the same as, those petitioner itself used and submitted to the board are not -confiscatory or arbitrary. Helvering v. Taylor, 293 U. S. 507, has no bearing.
There remains to consider whether the assessment may be sustained against petitioner’s claim that, assuming validity of apportionment, the valuation was arbitrarily made and is grossly excessive. .
No testimony was given- by the tax commissioner or any other member of the board. They 'could not be compelled to submit to examination as to the operation of their minds in making the challenged assessment. Chicago, B. & Q. Ry. Co. v. Babcock,. 204 U. S. 585, 593. Bolder v. Callaway, 267 U. S. 479, 491. It results that resort must be had to determinations of the board, find.*146ings of the lower courts, the evidence and the facts judicially known.
From the answer and evidence it unquestionably appears that the board valued petitioner’s system and made apportionment to North Dakota. The assessments for the years 1929-1933 are: $83,294,677, $83,294,688, $82/-999,997, $78,850,024 and $78,832,888. The trial judge found no overassessment for 1932 but refused to find the value of the property in 1933 or whether the assessment for that year was excessive,; and he found' that there is no evidence, other than that offered to show overvaluation, that the assessment was fraudulent or made with intent to defraud petitioner. The Circuit Court of Appeals held that petitioner failed to prove the method employed by the board to make the assessment or that it was grossly excessive and arbitrary.
Respondents’ witness prepared tabulations which were put in evidence as Exhibit P. It shows: 1. The value for each- year, based on averages for .preceding five years, from 1929 to 1933, inclusive, of the system operating property as indicated by: (a) stock and bond value less value of non-operating property; (b) net operating income capitalized at six per cent; (c) the average of (a) and (b). 2. Apportionment of system value to North Dakota by percentages reflected by average of: (a) 'three use factors, i. e. transportation service, traffic units and gross operating revenue; (b) mileage of tracks operated and the three use factors; (c) mileage of tracks owned and operated and leased and operated and the three use factors; (d) mileage of track operated, physical property and the three use factors; (e) mileage of track operated, physical property, the three use factors and net revenue. 3. Apportionment to North Dakota of: (a) stock and bond value; f(b) capitalized value; (c) average of (a) and (b). 4. The North Dakota assessments. Ratio of assessments to apportionments made on (a) stock and *147bond value; (b) capitalized value; (c) average of (a) and (b).2
The composite of the five year.average of stock and bond value and of net operating income capitalized for 1932 was $415,278,961; admittedly that was produced by the use of the two methods shown by respondents’ witness to be universally approved 'as the best methods for finding system value. The 1932 assessment is 99.93% of that figure apportioned on the basis of the three use fac*148tors, 98.39% apportioned on the basis of track mileage operated and three use factors; 96.02% apportioned on tracks owned and operated and leased and operated and the three use factors, 104.29% apportioned on track mileage, physical property and the three use factors; 101.40% apportioned on track operated, physical property, three use factors and net revenue.
If the system value for 1933 had been computed on the basis of the stock and bond and capitalized income methods used for 1932, it would have been $345,188,820, about 83% of the corresponding figure for 1932, less than 76% of like figures for 1931 and 1930 and about 79% of that for 1929. See footnote 2. The 1933 assessment exceeds what would have been made on system valuation based/ on the five-year average of stock and bond values, apportioned by use of the five factors above described (advocated by the State as “the fairest basis of allocation”) by 19.97%, exceeds that based on net operating income capitalized by 29.44%, on the composite of both by 24.52%. The testimony and computations made by respondents’ witness show that the 1933 assessment could not have *149been arrived at by any calculation based on the principles and methods governing the tax commissioner in his computations submitted to the board through a period of years and constituting the controlling bases of the assessments made by it. The five-year average of the composite of the stock and bond and capitalized income values, held by all to be the best method, produced for 1932 á valuation within one-sixth of one per cent, of the assessment for that year. The board arbitrarily adopted that •assessment, less value of a short stretch of track removed, as the assessment for 1933.' If the assessment for that year had been based on the principles governing in 1932 and preceding years, it would have been less by about $13,000,000 than the amount, fixed by the board and here in controversy.
The long period through which, even in 1933, the depression had extended compelled the conclusion that it was not temporary. Judicial notice must be taken of the fact that late in 1929 there occurred a great collapse of values of all classes of-property — railroads, other utilities, commodities and securities, and that the depression then commenced progressively became greater. In making assessments in that period, the board was bound to take into account and give due. weight to the sudden, progressive and enormous declines of value.'
Respondents’ witness testified: The purchasing power of money greatly increased and correspondingly values decreased from 1929' to 1933. The Dow-Jones & Company average of 30 industrial stocks fell from 383.17 in September, 1929, to 41.22 in July, 1932. The average of 20 railroad stocks fell between the same dates from 189.11 to 13.23; total 'market value of all common and preferred stocks listed on the New York Stock Exchange fell from eighty-nine and' one-half billion do fifteen arid one-half billion dollars. Assessing officials and equalizing boards were confronted with a very difficult situation. *150“Values which had been more or less stable for a generation have melted rapidly away. If all assessments had been reduced to conform to actual market value, • the State and its subdivisions would have ceased to function, as the revenue would not even approximate necessary expenses.”
Changed business conditions affecting petitioner’s traffic, coupled with competition from.new methods of transportation, precluded belief that prospective improvement in petitioner’s business and earnings would within a reasonable time, if ever, be sufficient to justify the assessment in question. Cf. Nashville, C. & St. L. Ry. v. Walters, 294 U. S. 405, 423. But from 1929 to and including 1933 the board reduced assessments of petitioner’s North Dakota railroad'properties by less than six per cent. It is everywhere known that the general decline in values in that period was very much greater than that. The evidence conclusively shows that the value of petitioner’s system and of its North Dakota railroad properties declined several times six per cent. Its traffic, gross earnings and net income from operation fell off enormously.3 The 1929 collapse and the decline progressively following it resulted in much lower levels of prices and values which at least as early ,as 1933 were to be regarded *151not as temporary but as at least relatively permanent. Atchison, T. & S. F. Ry. Co. v. United States, 284 U. S. 248, 260-261. Los Angeles Gas Co. v. Railroad Comm’n, 289 U. S. 287, 311-312.
In eases such as this, courts are not permitted to weigh evidence of value. They may not substitute their opinions for the findings of assessing officers or boards. ' But, when the jurisdiction of the district court is appropriately invoked, it is its duty, to decide upon the merits of the taxpayer’s claim that the assessment of his property was arbitrarily made and is grossly excessive. It clearly appears; that the board failed to give reasonable weight to the falling off of petitioner’s traffic, gross earnings, operating income,'the extraordinary shrinkage in values of railroad properties, the prices of commodities and securities generally. The. value óf petitioner’s property varied with the profitableness of its use, present and prospective. Cleveland, C., C. & St. L. Ry. Co. v. Backus, 154 U. S. 439, 445. Southern Ry. Co. v. Kentucky, 274 U. S. 76, 81-82. Petitioner’s system net operating income was for 1929 in round figures $32,457,000; in the following years $21,912,000, $12,669,000, $1,290,000. The board persistently disregarded known conditions essential to the just ascertainment of value. While the vanishing of values described by respondents’ witness, the reduction of the tax base from 75% to 50%, and the established limitations upon rates of taxation, justify diligence on the part of the assessing authorities that taxable property be assessed at full value, neither these nor any other conditions warrant or excuse arbitrary or excessive valuations.
The . facts alleged in respondents’ answer, and those shown by the testimony of their witness and his computations above described, compel the conclusion that, by reason of changed conditions affecting value, the methods or system by which the board arrived at the 1933 value of petitioner’s railway as a whole were plainly calculated *152to produce a grossly excessive assessment of • its North Dakota property for. that year. That assessment ■ being shown to have been arbitrarily made ■ and grossly excessive, petitioner’s right io relief was not conditioned upon overassessment or upon its submission to overtaxation in 1932 or any prior year. It follows that the lower courts erred in holding that petitioner was not entitled to any relief. The evidence persuasively supports petitioner’s claim that by reason of system overvaluation the North Dakota assessment was too high by $15,000,000. And, resolving all doubts in favor of validity, the evidence must be held conclusively to show that the challenged assessment exceeds the true and full value of petitioner’s North Dakota railroad properties in 1933 by $10,000,000. See footnote 2. The board’s failure to consider the enormous diminution in value of petitioner’s, property caused by the 1929 collapse and the progress of the depression is, within the principles of our- decisions, the equivalent in law of intention to make a grossly excessive assessment for 1933 in disregard of petitioner’s rights under the due process clause of the Fourteenth Amendment. 'We need not consider whether the assessment is repugnant to the equal protection or commerce clause. Unquestionably, the assessment was made in plain violation of established principles that govern property valuation. Fargo v. Hart, 193 U. S. 490, 502. Rowley v. Chicago & N. W. Ry., supra, 109-110. Southwestern Bell Tel. Co. v. Public Service Comm’n, 262 U. S. 276, 287-288. Bluefield Waterworks Co. v. Public Service Comm’n, 262 U. S. 679, 692. McCardle v. Indianapolis Water Co., 272 U. S. 400, 408-412. Monongahela Navigation Co. v. United States, 148 U. S. 312.
The judgment of the Circuit Court of Appeals will be reversed. The case will be remanded to the district court with directions to enter a decree for petitioner, the plaintiff below, that ■ respondents, the defendants below, be *153enjoined from collecting on account of the taxes levied against petitioner on the basis or because of the challenged assessment any amount in excess of suGh propor-: tion of .the taxes levied as the value above indicated, $68,832,888, is to the assessment, $78,832,888, being 87.3149+%; the injunction will be conditioned upon payment by petitioner of that proportion of the taxes. And the decree shall declare that it is without prejudice to the authority of the state board Of equalization, if any it has, again to assess petitioner’s properties for 1933.
Reversed.
Comp. Laws, 1913, § 2244. Initiated measure, approved June 29, 1932, Laws 1933, p. 493, amending 1925 Supp., § 2122a, reduced the percentage of assessed value to be used in calculating the tax from 75%. to 50%.
Exhibit P need not be given in full. The following statement shows by years, 1929-1933, inclusive:
Column 1, system value according to average of stock and bond value and capitalized value.
Column 2, percentage of system value in North Dakota as reflected by the apportionment factors 'used in the exhibit.
Column 3, values apportioned to North Dakota according to average of stock and bond values and capitalized values.
Column 4, the North Dakota assessments.
Column 5,- ratio of assessments to assigned values on the basis of stock and bond values.
Column 6, ratio of assessments to assigned values on the basis of capitalized values.
Column 7, ratio of assessments to assigned values on the basis of composite of both.
*148
The tabulation, follows :