
293 U.S. 102 (1934)
ROWLEY, TREASURER OF CONVERSE COUNTY, WYOMING, ET AL.
v.
CHICAGO & NORTHWESTERN RAILWAY CO.
No. 9.
Supreme Court of United States.
Argued October 10, 1934.
Decided November 5, 1934.
CERTIORARI TO THE CIRCUIT COURT OF APPEALS FOR THE TENTH CIRCUIT.
*103 Mr. Ray E. Lee, Attorney General of Wyoming, and Mr. James A. Greenwood, with whom Mr. George A. Weedell was on the brief, for petitioners.
Mr. Robert R. Rose, with whom Messrs. Samuel H. Cady, William T. Faricy, and Vincent Mulvaney were on the brief, for respondent.
MR. JUSTICE BUTLER delivered the opinion of the Court.
This suit was brought in the district court for Wyoming by the company against the treasurers of four counties to enjoin collection of a part of the taxes for 1931 levied upon its railroad property therein. The laws of that State required all taxable property to be assessed on the basis of its actual value. See State Constitution, Art. XV, § 11. Wyoming Compiled Statutes, 1931, §§ 115-119, 115-511, 115-1804. The complaint rests upon the *104 claim that for a number of years, including the one here involved, the State acting through its board of equalization and other taxing authorities systematically and intentionally discriminated against respondent's railroad and in favor of all other property, in violation of the equal protection clause of the Fourteenth Amendment, in that it regularly taxed the railroad at about 133 1/3% while taxing all other property at about 60% of actual value. Respondent tendered and paid to the treasurer of each county the amount it claimed would have been levied against it if all taxable property had been assessed upon the same basis of valuation. The total claimed by the four counties was $168,606.12; respondent paid $101,163.67, leaving in controversy $67,442.45.
Petitioners' answer denied discrimination. There was a trial at which much evidence was introduced. The district court upon specific findings of fact concluded that respondent's railroad property in Wyoming had been substantially and arbitrarily overvalued. It found that, with exceptions that are here immaterial, all other property had been assessed at its actual value. It entered a decree requiring respondent to pay additional taxes amounting in all to $33,519.46 and enjoining collection of any part of the balance.
Petitioners seek reversal upon the ground that respondent failed to exhaust an administrative remedy open to it by appeal from the determination of the state board of equalization to the district court under § 115-512, Wyoming Compiled Statutes, 1931. They also maintain that under § 115-311 respondent had an adequate remedy at law and therefore was not entitled to relief in equity. These contentions depend upon serious questions of Wyoming law which have not been decided by its highest court. This court is reluctant, in advance of decision thereon by the state courts of last resort, to construe state *105 statutes of doubtful meaning or to decide other questions of state law as to which there may be substantial controversy.
In this case it is not necessary, for, upon an analysis of the grounds of the decision below, it is clear that respondent was not entitled to an injunction. Respondent does not challenge the finding that other property was assessed at actual value, and so there remains only the claim that its railroad was internationally and arbitrarily overvalued by about 33 1/3%.
The company had 278.35 miles of main line track in Wyoming and that constituted 3.29% of the main line track included in its system extending into nine States. Neither it nor the board dealt with that in Wyoming as a separate line; both appraised it as a part of the system. They took the value of the whole, attributed to Wyoming a portion and divided it among the four counties. The only matter in controversy is the amount to be assigned to that State.
To ascertain system value, respondent made calculations based on a five year period ending with 1930. It found the average market value of its stocks and bonds. deducted non-operating property locally taxed, added the remainder ($385,800,085) to an amount produced by capitalizing at 6% average net operating income ($364,771,720). The sum divided by two produced $375,285,902 which the board accepted for the purposes of its calculation, though one of its members testified "there are certain flaws in it."
To ascertain the value to be taxed in Wyoming respondent found for each year and also the average for the five-year period the percentages that Wyoming traffic units (ton miles and passenger miles) bore to the system total, the corresponding relation of use of rolling stock (car miles and engine miles) and of gross operating revenues, *106 and by the calculations printed in the margin,[1] arrived at $5,849,570.
In pursuance of § 115-1803, respondent filed a return showing "grand total valuation $8,281,950." It attached a statement which includes the following:
"The valuations shown in this return are based upon the estimated cost of reproduction new of the physical properties . .. less depreciation, and without further *107 reference to the market value of such properties, or . . . of the stocks and bonds . . . or the present earnings . . . or the present or future earning capacity or possibilities of such properties. It is claimed that the valuations stated in this return do not represent the fair cash value of the property for purposes of taxation. The value as to the system . . . and as to the part in . . . Wyoming is clearly and fairly set [forth] by the figures contained in the exhibits attached to this return . .. and which . . . show that the total true value . . . in . . . Wyoming, or properly allocated to the State does not exceed $5,849,570."
After receiving the return, the board found cost of reproduction new less depreciation of respondent's railroad properties in Wyoming on the basis of an appraisal by the Interstate Commerce Commission as of 1917 plus later betterments to be $11,724,126, depreciated that at the annual rate of 2.5% for 13 years and so produced $8,436,076; ascertained the Wyoming 1930 net operating income to be 2.23% of the total for that year, applied that ratio to system value ($375,285,902) and produced $8,368,876. Each of the two last mentioned indications of value is substantially more than the reproduction cost less depreciation given by respondent in its return. The board, in order to equalize the valuation of respondent's property with other Wyoming railroad properties, made the assessment $7,989,587 which is 2.13% of system value. This is considerably less than the cost figures stated in the return. After notice of the assessment there was a hearing at which respondent presented the theory and bases of its appraisal. It appeals that upon further consideration the board took into account the facts that for the five-year period Wyoming net revenue was 2.114% of the system total; respondent's estimated cost of reproduction less depreciation of the Wyoming property was 2.21% of the system value, and that one-half the sum of these *108 percentages is 2.162%. Of the percentages used by the respondent, the board accepted those based on traffic units and use of rolling stock, rejected that based on gross operating revenues, substituted for it one-half of the sum of the gross operating revenue percentage plus the net operating revenue percentage, introduced the percentage that Wyoming mileage is of system mileage and divided the total by four, producing 2.1%. Its ascertainment of the ratio used follows:


Traffic Units .........................................  1.58%
Use of Rolling Stock ..................................  1.65%
Average between gross and net operating revenues ......  1.89%
Main track mileage ....................................  3.29%
                                                        _______
Divided by 4 ..........................................  8.41%
                                                        _______
Percentage to be allocated to Wyoming .................  2.10%

The board applied this percentage to system value and so established the final assessment, $7,881,003.94, which is less than the earlier one by more than $100,000. This is about 63% of the mileage proportion of agreed system value.
The district court rejected as without support respondent's use of the gross operating revenue percentage. It found that the board used the mileage basis, 3.29%, without taking into account the fact that respondent's property in Wyoming measured on a mileage basis, was greatly less in quantity, quality, cost and value than the portion of its operating system located outside that State. It was upon that ground that the court concluded that respondent's property "was substantially and arbitrarily overassessed." And it condemned as unreasonable and arbitrary the board's use of the mileage percentage. Then proceeding to correct what it held to be the error of the board, the court found one-third of the sum of the percentages based on Wyoming and system traffic units, rolling *109 stock and the average between gross and net operating revenue to be 1.673%.[2] It applied that ratio to the admitted system value and so produced $6,278,534.14  being a reduction of the assessment by $1,602,468.90  directed respondent to pay taxes on that basis and enjoined petitioners from collecting more.
The ascertainment of the value of a railway system is not a matter of arithmetical calculation and is not governed by any fixed and definite rule. Facts of great variety and number, estimates that are exact and those that are approximations, forecasts based on probabilities and contingencies have bearing and properly may be taken into account to guide judgment in determining what is the money equivalent  the actual value  of the property. Boom Co. v. Patterson, 98 U.S. 403, 407 et seq. Cleveland, C., C. & St. L. Ry. Co. v. Backus, 154 U.S. 439, 445. Adams Express Co. v. Ohio, 166 U.S. 185, 220. Brooklyn City R. Co. v. New York, 199 U.S. 48, 52. Omaha v. Omaha Water Co., 218 U.S. 180, 202-203. Minnesota Rate Cases, 230 U.S. 352, 434, 454. Branson v. Bush, 251 U.S. 182. 185-188. Southwestern Bell Tel. Co. v. Pub. Serv. Comm'n, 262 U.S. 276, 287. United States v. New River Collieries, 262 U.S. 341. Brooks-Scanlon Corp. v. United States, 265 U.S. 106, 123-126. Standard Oil Co. v. Southern Pacific Co., 268 U.S. 146, 155 et seq. McCardle v. Indianapolis Water Co., 272 U.S. 400, 410, 414. Olson v. United States, 292 U.S. 246, 255 et seq. The apportionment of system value between Wyoming and the rest of the system involves the finding of the value of the portion of the railroad that is located in that State. The problem is quite like the ascertainment of the value of the whole. The determination *110 is to be made in the exercise of a reasonable judgment based on facts so pertinent and significant as to be of controlling weight as indications of the value of the property.
Where, as in this case, the evidence requires a finding that the railroad in one of the States reached by the system is clearly shown to be worth much less than the average value per mile of the system, an apportionment on mileage necessarily assigns an excessive amount to that State, and the use of that basis as the sole measure for apportionment must be condemned as arbitrary. Fargo v. Hart, 193 U.S. 490, 500. Union Tank Line Co. v. Wright, 249 U.S. 275, 282-283. Wallace v. Hines, 253 U.S. 66, 69. Cf. Chicago & N.W. Ry. Co. v. Eveland, 13 F. (2d) 442, 447. In arriving at the relation between value in Wyoming and system value, the State board did not confine its calculation to relative mileage. That percentage combined with the other ratios used in the calculation produced 2.1% finally adopted. Nor did it limit its consideration of the problem to the elements employed to make that computation. Among other things it took into account the cost of reproduction less depreciation of the Wyoming property; the relations between that figure and the agreed system value, and between operating net revenues derived from the Wyoming property and those earned by the system for the five-year period and for 1930. Each of these is an indication that the value of the Wyoming property is substantially more than the assessment in question.
The record shows that the board considered respondent's calculation. Refusal to accept that formula as the measure was not arbitrary. Respondent's use of the average of three ratios indicates that it realized that there were substantial objections against each as the sole test. It is obvious, even when results of operation over a substantial *111 period are considered, that as a matter of fact the value of respondent's Wyoming line does not rise and fall with decline and increase of ton miles, passenger miles, car miles, engine miles or gross revenue in any other State or upon the balance of the system. Moreover, by the use of its formula respondent failed to take into account facts that justly may be considered to have significant hearing upon the relation between Wyoming value and system value. Such, for example, are the length of line to be assessed and the net operating revenues. The other factors that are shown to have been considered by the board give substantial support to the percentage finally adopted as the basis of the assessment.
There is nothing in this record to suggest any lack of good faith on the part of the board. Overvaluation resulting from error of judgment will not support a claim of discrimination. There must be something that amounts to an intention, or the equivalent of fraudulent purpose, to disregard the fundamental principle of uniformity. Sunday Lake Iron Co. v. Wakefield, 247 U.S. 350. Sioux City Bridge Co. v. Dakota County, 260 U.S. 441. Chicago G.W. Ry. Co. v. Kendall, 266 U.S. 94. Iowa-Des Moines Bank v. Bennett, 284 U.S. 239, 245. Cumberland Coal Co. v. Board, 284 U.S. 23, 28. There was no discrimination against respondent by undervaluation of the property of others. We find no substantial support in the findings of the district court or in the evidence for the conclusion that the use that the state board made of relative mileage to ascertain the value of respondent's Wyoming railroad property was arbitrary or unreasonable or indeed erroneous, or for its conclusion that the property was substantially or arbitrarily overvalued. Respondent was not entitled to an injunction.
The trial court was not called upon, and it was no part of the judicial function, to determine the base or amount *112 of the tax that in its view might legally be exacted as a result of the assessment in question. State Railroad Tax Cases, 92 U.S. 575, 614-615. Thompson v. Allen County, 115 U.S. 550. Cf. Central Kentucky Gas Co. v. Railroad Comm'n, 290 U.S. 264, 271, et seq. If that assessment were illegal, the State, notwithstanding any adjudication against its validity as repugnant to the Federal Constitution, should have been left free again to value the property. Norwood v. Baker, 172 U.S. 269, 293. And see French v. Barber Asphalt Paving Co., 181 U.S. 324, 344.
The district court may cause to be corrected the error in calculation referred to in marginal note 2.[*]
Decree reversed.
NOTES
[1]                 | Value of entire |
                |  line as        |
                | represented     |
    Year        | by market       |
                |  values of      |
                | stocks and      |
                |   bonds         |
----------------|-----------------|
1 1926 ________ |  $ 342,767,737  |
2 1927 ________ |    398,490,108  |
3 1928 ________ |    397,772,006  |
4 1929 ________ |    398,555,050  |
5 1930 ________ |    391,415,526  |
                |-----------------|
6 Aggregate ___ | $1,929,000,427  |
7 Aver. 5 Yrs _ | $  385,800,085  |
===================================



---------------------------------------------------------------------------
                |          Assigned to State of Wyoming on basis of
                |-----------------------------------------------------------
    Year        |             |             |                 |
                |  Traffic    |   Operating | Use of rolling  |  Average
                |  units      |   revenues  |   stock         | of 3 bases
                |             |             |                 |
                |             |             |                 |
                |    (2)      |    (3)      |     (4)         |  (5)
----------------|-------------|-------------|-----------------|-------------
1 1926 ________ | $ 5,827,052 | $ 5,038,686 | $ 5,038,686     | $ 5,598,540
2 1927 ________ |   7,212,671 |   6,057,050 |   7,372,067     |   6,880,596
3 1928 ________ |   6,085,912 |   5,847,248 |   6,284,798     |   6,072,653
4 1929 ________ |   5,699,337 |   5,579,771 |   6,018,181     |   5,765,763
5 1930 ________ |   5,558,100 |   5,714,667 |   6,027,799     |   5,706,855
                |-------------|-------------|-----------------|-------------
6 Aggregate ___ | $30,383,072 | $28,237,422 | $31,632,727     | $30,084,407
7 Aver. 5 Yrs _ | $ 6,076,614 | $ 5,647,484 | $ 6,326,545     | $ 6,016,881
===========================================================================
                  |                  |
                  | Value of entire  |
                  |   line as        |
                  | represented      |
   Year           |  by income       |
                  | capitalized at   |
                  |  0%              |
------------------|------------------|
8  1926 ________  |  $ 371,585,653   |
9  1927 ________  |    337,628,225   |
11 1929 ________  |    437,002,491   |
12 1930 ________  |    290,547,517   |
                  |------------------|
13 Aggregate ___  | $1,823,858,601   |
14 Aver. 5 Yrs _  | $  364,771,720   |
                  |------------------|
    Ratio used    |   Entire line    |
                  |------------------|
15 1926 ________  |    100.00%       |
16 1927 ________  |    100.00%       |
17 1928 ________  |    100.00%       |
18 1929 ________  |    100.00%       |
19 1930 ________  |    100.00%       |
                  |------------------|
                  |                  |
                  |                  |
                  |                  |
                  |------------------|
20 Average        |                  |
 for 1930 only _  | ________________ |
21 Average        |                  |
 for Five Years _ | ________________ |
                  |                  |
-------------------------------------



===========================================================================
                 |
                 |        Assigned to State of Wyoming on basis of
                 |----------------------------------------------------------
                 |             |             |                 |
   Year          |  Traffic    |  Operating  | Use of rolling  |  Average
                 |   units     |   revenues  |    stock        | of 3 bases
-----------------|-------------|-------------|-----------------|------------
8  1926 ________ | $ 6,316,956 | $ 5,462,309 | $ 6,428,432     | $ 6,069,232
9  1927 ________ |   6,111,071 |   5,131,949 |   6,246,122     |   5,829,714
10 1928 ________ |   5,922,549 |   5,690,293 |   6,116,096     |   5,009,646
11 1929 ________ |   6,249,136 |   6,118,035 |   6,598,738     |   6,321,970
12 1930 ________ |   4,125,775 |   4,241,994 |   4,474,432     |   4,280,734
                 |-------------|-------------|-----------------|------------
13 Aggregate ___ | $28,725,487 | $26,644,580 | $29,863,820     | $28,411,296
14 Aver. 5 Yrs _ | $ 5,745,097 | $ 5,328,916 | $ 5,972,764     | $ 5,682,259
                 |             |             |                 |
                 |---------------------------------------------|------------
    Ratio used   |           State of Wyoming                  |
                 |---------------------------------------------|------------
15 1926 ________ |    1.70%    |   1.47%     |    1.73%        |
16 1927 ________ |    1.81%    |   1.52%     |    1.85%        |
17 1928 ________ |    1.53%    |   1.47%     |    1.58%        |
18 1929 ________ |    1.43%    |   1.40%     |    1.51%        |
19 1930 ________ |    1.42%    |   1.46%     |    1.54%        |
                 |             |             |                 |
                 |-------------|-------------|-----------------|------------
                 |             |             |                 |
                 |             |  Miles of   |   Per mile      |
                 |             |   road      |   of road       |
                 |-------------|-------------|-----------------|------------
20 Average       |             |             |                 |
 for 1930 only _ | ___________ |   278,35    |   $18,085       |  $5,023,795
21 Average       |             |             |                 |
 for Five Years  | ___________ |   278,35    |   $21,015       |  $5,849,570
----------------------------------------------------------------------------

[2]  The court also corrected an admitted error of the board, by substituting 1.79% for 1.89%, average between gross and net operating revenues.
[*]  The final sentence was added by order of December 3, 1934.  REPORTER.
