
801 F.Supp. 37 (1992)
SOUTHERN RAILWAY COMPANY, et al., Plaintiffs,
v.
Patsy STAIR, et al., Defendants.
Civ. A. Nos. 90-1029, 90-1210, 91-1004 and 92-1042.
United States District Court, W.D. Tennessee, E.D.
May 15, 1992.
Order Denying Motion for a New Trial July 15, 1992.
Order on Motion to Amend Judgment August 21, 1992.
*38 Everett B. Gibson, Memphis, Tenn., for plaintiffs.
Jimmy G. Creecy, Chief Special Counsel, and Daryl Brand, Asst. Atty. Gen., Nashville, Tenn., for defendants.

FINDINGS OF FACT AND CONCLUSIONS OF LAW
TODD, District Judge.
Plaintiffs in these consolidated cases are five interstate rail carriers that own rail transportation property in Tennessee. Each plaintiff is a part of the Norfolk Southern Corporation rail system. Defendants are the Tennessee State Board of Equalization ("State Board") and the county and city officials of those jurisdictions in Tennessee in which plaintiffs have taxable property and who have the responsibility to collect property taxes in their respective jurisdictions.
The plaintiffs seek injunctive and declaratory relief pursuant to 49 U.S.C. § 11503 (Section 306 of the Railroad Revitalization and Regulatory Reform Act of 1976) ("4-R Act"), Pub.L. No. 94-210, 90 Stat. 54 (1976).[1] Plaintiffs ask this court to issue a permanent injunction directing defendants to reduce ad valorem property taxes upon plaintiffs' rail transportation property for the 1989, 1990, and 1991 tax years to the same ratio of appraised value to true market value as that at which commercial and industrial property was taxed in Tennessee for those tax years. Additionally, plaintiffs ask for a declaratory judgment pursuant to 28 U.S.C. § 2201 that the assessment of plaintiffs' rail transportation property at a higher ratio of appraised value to true market value than the ratio of appraised value to true market value at which commercial and industrial property was assessed in Tennessee for the 1989, 1990, and 1991 tax years violates Section 306.
This court has jurisdiction pursuant to 28 U.S.C. §§ 1331 and 1337 as well as 49 U.S.C. § 11503(c). Upon application of the plaintiffs, the court previously granted preliminary injunctive relief, enjoining the defendants from collecting 1989, 1990, and *39 1991 ad valorem taxes at a level in excess of 65.4% of the taxes which plaintiffs would have otherwise paid.
Plaintiffs seek relief under 49 U.S.C. § 11503 by contending that commercial and industrial property in Tennessee is appraised for property tax purposes, on average, at approximately 60% of true market value, whereas plaintiffs' rail transportation property for the tax years 1989, 1990, and 1991 has been appraised for property tax purposes at 100% of true market value.
Under Tennessee law, T.C.A. § 67-5-1301, the property of railroads and utilities is appraised annually for assessment purposes by the Tennessee Public Service Commission ("Commission"). The Commission appraises a railroad operating system as a single unit. The unit value is first apportioned to the State of Tennessee and then distributed to counties and cities in Tennessee by use of a statutory apportionment formula. See T.C.A. §§ 67-5-1302(a)(2), 67-5-1323 to -1325. The entire assessment apportioned to local governmental units is determined by the Commission.
Real and tangible personal property is assessed for ad valorem taxation at varying percentages of true market value. Pursuant to T.C.A. §§ 67-5-801(a) and 67-5-901(a), real property and personal property in Tennessee are assessed at different assessment ratios. In accordance with these sections, railroad real and personal property would have been assessed at 55% of its market value; however, as a result of the ruling of the United States District Court for the Middle District of Tennessee in Tennessee v. Louisville & Nashville R.R. Co., 478 F.Supp. 199 (M.D.Tenn.1979), aff'd w/o opinion, 652 F.2d 59 (6th Cir.), cert. denied, 454 U.S. 834, 102 S.Ct. 135, 70 L.Ed.2d 114 (1981), the Commission now assesses railroad real property at the same statutory level of assessment as commercial and industrial real property (40%) and assesses railroad personal property at the same level of assessment as commercial and industrial personal property (30%).
Railroad property tax values must be submitted by the Commission to the State Board annually under T.C.A. § 67-5-1327(c). The State Board may then increase or decrease the values or do nothing. The State Board then certifies the final values back to the Commission under T.C.A. § 67-5-1329 and the Commission certifies the proportionate assessed values to county trustees and city recorders pursuant to T.C.A. § 67-5-1331(a) for collection. County and municipal officials then apply the tax levy and collect ad valorem taxes on distributable railroad operating property as assessed, apportioned, and distributed by the Commission and certified by the State Board.
All commercial and industrial property in Tennessee, other than railroad and utility property, is assessed locally by the county tax assessors under T.C.A. § 67-5-502. For assessment purposes, commercial and industrial real property is appraised for tax purposes infrequently, and no more than once every six years. T.C.A. § 67-5-1601(a)(2).[2] The State Board, by statute and practice, has recognized that local real property appraisals for assessment purposes may sometimes be less than true market value. Using ratio studies conducted every two years by the Tennessee Division of Property Assessment ("Division") under T.C.A. §§ 67-5-1604 and 1605, the State Board will direct the Commission to reduce the assessments of centrally assessed taxpayers, including railroads, in each county found by the State Board to appraise real property, on average, below true market value. The State Board makes no effort to equalize centrally assessed taxpayers on the basis of personal property appraisal levels in Tennessee counties.
Plaintiffs allege several causes of discrimination against rail transportation property. First, plaintiffs contend that the annual appraisal of railroad property and the infrequent appraisal of commercial and *40 industrial real property other than utility and railroad property results in a situation where commercial and industrial real property is appraised for assessment purposes at substantially below true market value. Plaintiffs contend that inflation alone causes commercial and industrial real property appraisals to be substantially below true market value before application of the constitutional and statutory assessment percentage of 40%.
Second, plaintiffs complain of the practices for assessment of commercial and industrial personal property. County tax assessors traditionally rely upon the individual taxpayer to report tax values of commercial and industrial personal property for assessment purposes. Although the Tennessee State Board of Equalization recently promulgated rules designed to improve personal property assessment practices, those rules were enacted for the first time in 1989. Consequently, plaintiffs contend that appraisals of commercial and industrial personal property are still far below true market value before application of the constitutional and statutory assessment percentage of 30%.
Plaintiffs contend that they are entitled to injunctive relief enjoining defendants from collecting taxes assessed on plaintiffs' property to the extent that the plaintiffs' appraised values exceed the appraised values of all other commercial and industrial taxpayers on average.
Defendants contend that Tennessee's system of ad valorem property taxation does not discriminate against rail transportation real or personal property or otherwise violate 49 U.S.C. § 11503. Pursuant to 49 U.S.C. § 11503(c), the plaintiffs are entitled to relief only if the ratio of assessed value to true market value of rail transportation property exceeds by at least 5 percent the ratio of assessed value to true market value of other commercial and industrial property in the same assessment jurisdiction. Defendants contend that any disparity that existed in Tennessee for tax years 1989, 1990, and 1991 between the ratio of appraised value to true market value of rail transportation property and the ratio of appraised value to true market value of other commercial and industrial property, was less than 5 percent, and, therefore, the plaintiffs have no basis for relief. Defendants contend that a separate analysis must be made of real property and of personal property with the burden being upon the plaintiffs to prove that taxation of their real property and of their personal property discriminatory in violation of 49 U.S.C. § 11503.
Defendants maintain that the levels of appraisal and assessment of commercial and industrial property, both real and personal, by Tennessee taxing jurisdictions are much higher than asserted by the plaintiffs, and fall within the range permitted by 49 U.S.C. § 11503. Defendants contend that computations by the plaintiffs' witnesses purporting to show lower levels of appraisal and assessment are inaccurate and misleading due to deficiencies in methodology and data bases, and due to the erroneous inclusion of classes of property which should not be considered part of the comparison class of commercial and industrial property.
Also, defendants contend that plaintiffs have failed to recognize that equalization factors, determined for each county taxing jurisdiction by the ratio of appraised value to market value of real property in each such taxing jurisdiction, are developed at least every two years, as required by T.C.A. § 67-5-1605(b), and not once every six years.
As to personal property, defendants contend that the State of Tennessee initiated a valuation and equalization program for each county in the State, which has improved assessment practices and raised the level of appraisal of commercial and industrial personal property. As a result, defendants contend that the taxation of railroad personal property for tax years 1989, 1990, and 1991 is not discriminatory under 49 U.S.C. § 11503.
Finally, defendants contend that, for purposes of 49 U.S.C. § 11503 (and Section 306), the level of assessment of railroad property should be compared not with the average level of assessment of commercial *41 and industrial property statewide, but rather comparison should be made with the median levels of assessment of commercial and industrial property in each of the affected taxing jurisdictions, i.e., the counties in which the plaintiff railroads have property.
This action was tried to the court on July 8, 9, and 10, 1991. The court has considered all the evidence admitted at trial, as well as the arguments, pleadings, and legal briefs of the parties. This order constitutes the court's findings of fact and conclusions of law pursuant to Rule 52(a) of the Federal Rules of Civil Procedure.
The issues presented in this case are as follows:
1) What is the appropriate assessment jurisdiction within the meaning of Section 306, the state as a whole or the individual counties?
2) How should the ratio of assessed value to true market value be calculated, by use of the ratio of aggregates or by use of the median?
3) Have the plaintiffs carried their burden of proof in presenting evidence of the ratio of assessed value to true market value of commercial and industrial personal property?

DISCUSSION
In 1976, after 15 years of congressional study, the Railroad Revitalization and Regulatory Reform Act, Pub.L. 94-210, 90 Stat. 31 (the "4-R Act"), was enacted. Its purpose, as stated, was to "provide the means to rehabilitate and maintain the physical facilities, improve the operations and structure, and restore the financial stability of the railway system of the United States." § 101(a). Among the means chosen by Congress to fulfill these objectives, particularly the goal of furthering railroad financial stability, was a prohibition on discriminatory state taxation of railroad property. The solution to discriminatory state taxation of railroads was embodied in § 306 of the Act, codified at 49 U.S.C. § 11503.
Section 11503 prohibits a state from imposing a discriminatory tax upon rail transportation property and defines discriminatory taxation, in part, by reference to a specific comparison between railroad transportation property and other commercial and industrial property. 49 U.S.C. § 11503(a)(4) and (b). Under the statute, relief can only be granted if there is at least a 5% discrepancy in the assessed value of rail property and commercial industrial property. 49 U.S.C. § 11503(c).

ASSESSMENT AND VALUATION METHODS
In Tennessee most commercial, industrial, residential and farm property is locally valued by county assessors. T.C.A. §§ 67-5-102, -103. Assessments of real property are made in periodic revaluations by the assessor. Assessments of personal property are made annually primarily on the basis of information supplied by the property owner in a schedule filed with the county assessor.
Assessments of public utility and common carrier property, including the plaintiffs' property, are made annually by the Assessment Division of the Tennessee Public Service Commission, primarily upon the basis of information supplied by the property owner in a schedule filed with the Assessment Division. T.C.A. § 67-5-1301. The assessments are reviewed by the State Board of Equalization and equalized on the basis of median appraisal ratios determined by the Board for each county taxing jurisdiction. T.C.A. § 67-5-1328.
In valuing the plaintiffs' operating property for ad valorem tax purposes the Assessment Division employs a mass appraisal method commonly referred to as the "unit method" of property tax valuation. T.C.A. § 67-5-1302. The "unit value" for all operating property in the plaintiffs' entire multi-state system is first determined. An allocation factor is then applied to apportion a part of the system value to Tennessee. T.C.A. § 67-5-1322 to -1323. The State Board of Equalization has the duty under T.C.A. § 67-5-1328 to examine and review the assessments of utilities and carriers *42 made by the Public Service Commission. Once this is done by the Board, the valuation fixed upon each property is certified back to the Public Service Commission, T.C.A. § 67-5-1329, which in turn certifies to each county and municipality its portion of the total assessment. T.C.A. § 67-5-1331. The assessment ratio of 40% of value for commercial and industrial real property and 30% of value for commercial and industrial personal property, set by Article II, Section 28 of the Tennessee State Constitution, is also applied to rail transportation real and personal property.[3]
Tennessee state law has established an elaborate statutory process to ensure that centrally valued railroads are assessed at the same level as locally valued properties. T.C.A. § 67-5-1605(b)(1). Railroads and other public utilities are valued annually by the Public Service Commission at 100% of true cash value. The Board of Equalization then certifies to the Public Service Commission the ratio appraisal levels for each county which are applied to the railroad and public utility assessments, thereby reducing their assessed values. T.C.A. § 67-5-1606(c). This statutory process, which is called "equalization," ensures that railroads and other public utility property which is centrally valued by the Public Service Commission is assessed the same as locally assessed properties.
Property taxes are collected by county trustees and by city recorders and treasurers after adoption of a tax rate determined by the governing body of the taxing jurisdiction.
The total appraised unit value placed upon the plaintiffs' property, real and personal, by the Tennessee Public Commission for 1989 was $3.9 billion and for 1990 was $4.2 billion. Of the total unit value, 7.38%, or $287,820,000, was allocated to Tennessee for 1989, and 7.38%, or $309,960,000, was allocated to Tennessee for 1990. After applying the appropriate assessment factors (40% for real property; 30% for personal property), the assessed value of the plaintiffs' property totalled $108,400,000 for 1989, and $116,600,000 for 1990. After applying equalization factors, the taxable value of the plaintiffs' property was $100,153,907 for 1989, and $107,654,242 for 1990.

ISSUE 1

What is the appropriate assessment jurisdiction within the meaning of 49 U.S.C. § 11503, the state as a whole or the individual counties?
Plaintiffs contend that the average level of appraisal of commercial and industrial property for tax equalization purposes should be the average obtained from using the state as a whole. The State Board contends that separate averages should be used for each county in which plaintiffs own property.
49 U.S.C. § 11503 requires that rail transportation property be assessed at the same level of assessment of all other commercial and industrial property "in the same assessment jurisdiction." 49 U.S.C. § 11503(a)(2) defines "assessment jurisdiction" as follows:
[A] geographical area in a State used in determining the assessed value of property for ad valorem taxation.
Plaintiffs contend that the assessment jurisdiction in this case should be the state as a whole because plaintiffs are centrally assessed by the State. Defendants contend that comparison should be made on a county-by-county basis.
In Arizona v. Atchison, Topeka & Santa Fe R.R. Co., 656 F.2d 398, 405 (9th Cir.1981), the United States Court of Appeals for the Ninth Circuit relied on the legislative history of the 4-R Act to determine that the entire State of Arizona *43 should be used for ratio comparison purposes rather than a county-by-county comparison in each county in which plaintiffs operated their railroads. In reaching its decision, the court reasoned that Arizona's taxing scheme applied statewide and not according to county vagaries.
The United States District Court for the Western District of Wisconsin followed the holding of the Ninth Circuit in Burlington N.R.R. Co. v. Department of Revenue, 604 F.Supp. 1575 (W.D.Wis.1985). In reaching its decision that the entire state was the most appropriate assessment jurisdiction, the court stated:
[L]ocal jurisdictions have not been treated in actuality as assessment jurisdictions under the 4-R Act; parties have not sought examination of the comparative rate situation in individual local jurisdictions. Given the statewide perspective on taxing rail transportation property adhered to by all parties, I now hold that in applying 4-R the state is the appropriate assessment jurisdiction. See, Atchison, Topeka and Santa Fe Ry. Co. v. Lennen, 552 F.Supp. 1031, 1035 n. 7 (D.Kan.1982).
Id.
As the foregoing quotation suggests, the district court in Kansas expressly held that the state is the assessment jurisdiction for 4-R Act litigation purposes. Lennen, supra, rev'd on other grounds, 732 F.2d 1495 (10th Cir.1984). The United States District Courts for the Northern District of California and the Northern District of Georgia also have held that the state, not the individual counties, is the appropriate assessment jurisdiction under the 4-R Act. Southern Ry. Co. v. State Bd. of Equalization, 712 F.Supp. 1557, 1564 (N.D.Ga. 1988); Southern Pac. Transp. Co. v. California, No. C-81-4848-SW, slip op. at 13 (N.D.Cal. Apr. 4, 1984). Thus, in every jurisdiction in which the question has been raised in 4-R Act litigation, the courts have unanimously held that the state is the assessment jurisdiction.
The reason that the courts have held that the entire state is the assessment jurisdiction is because in Arizona, California, Georgia, Kansas and Wisconsin, an agency of the state appraises rail transportation property for tax assessment purposes, not the counties. The counties collect the taxes, but the state is the assessor. In that respect Tennessee is identical to Arizona, California, Georgia, Kansas and Wisconsin. In Tennessee, a branch of the state, the Public Service Commission, appraises and assesses rail transportation property for property tax purposes, subject to the concurrence of the State Board, which is also a state agency.
The State Board has cited a 4-R Act case originating in North Carolina as precedent for using individual counties as the assessment jurisdictions. Clinchfield R.R. Co. v. Lynch, 527 F.Supp. 784 (E.D.N.C.1981), aff'd, 700 F.2d 126 (4th Cir.1983). That case was also cited to the Georgia district court on this issue. The Georgia district court observed:
They are correct in stating that individual counties were used as assessment jurisdictions in those two cases. The cases do not serve as useful precedent, however. It does not appear that the question of whether the state or the counties should be the assessment jurisdiction was ever raised in those cases. Also, it appears that neither the district court nor the court of appeals in either Clinchfield I or Clinchfield II [Clinchfield R.R. Co. v. Lynch, 605 F.Supp. 1005 (E.D.N.C.1985)] even considered whether the state or the county should be treated as the assessment jurisdiction for the purpose of measuring relief from discrimination.
Southern Ry. Co., 712 F.Supp. at 1565.
The only other 4-R Act case on this issue relied upon by the State Board is Burlington N.R.R. Co. v. Department of Revenue, 570 F.Supp. 585 (W.D.Wis.1983). That case serves as no useful precedent, however, because the same court in the same case reversed itself in a later ruling and held that the state was the appropriate assessment jurisdiction. Burlington N.R.R. Co. v. Department of Revenue, 604 F.Supp. 1575, 1583 (W.D.Wis.1985).
*44 This court joins the other courts where this issue has actually been contested. The court concludes that, because railroads in Tennessee are centrally assessed by a state agency, the state as a whole is the assessment jurisdiction within the meaning of the 4-R Act.

ISSUE 2

How should the ratio of assessed value to true market value be calculated, by use of the ratio of aggregates or by use of the median?
The ratio of aggregates represents the total appraised value of all commercial and industrial property divided by the total estimated market values of all commercial and industrial property. The ratio of aggregates is the mean of the appraisal ratios weighted by the dollar value of each appraisal and the dollar value of each selling price. The median, on the other hand, is the middle appraisal ratio, with half of the appraisal ratios above the median and half of the appraisal ratios below the median.
Plaintiffs offered evidence of the ratio of appraised value to true market value of commercial and industrial property using the ratio of aggregates. Plaintiffs combined the total appraised values of all types of commercial and industrial property, real, personal and non-railroad utility, into a single numerator, and combined the market values of the same types of property into a single denominator, which produced a combined appraisal ratio of 60.2%.
Defendants argued that the court should reject the ratio of aggregates as the method to be used and should adopt the median as the appropriate measure.
The court decisions on this issue are in conflict. The first court deciding this issue ruled in favor of the median as the average to be used for equalization purposes. Clinchfield R.R. Co. v. Lynch, 527 F.Supp. 784 (E.D.N.C.1981), aff'd, 700 F.2d 126 (4th Cir.1983) ("Clinchfield I"). The defendant county in Clinchfield I offered evidence aggregating real property data with non-railroad utility property data. No evidence was offered on the actual level of assessment of personal property.
The United States District Court for the District of Kansas followed Clinchfield I and also ruled in favor of the median. Atchison, Topeka & Santa Fe Ry. Co. v. Lennen, 552 F.Supp. 1031, 1044 (D.Kan. 1982). The district court was reversed on this issue by the Tenth Circuit, 732 F.2d 1495 (10th Cir.1984), because, in the Kansas case, the parties did offer evidence on the personal property assessment ratio. The Tenth Circuit held as follows:
A median has no significance if the items on the continuum are not alike in some relevant way. See International Association of Assessing Officers Assessment Standards Committee, Standard on Assessment Ratio Studies, § 3.10.3 (1980). "Parcel" as plaintiffs use it in this case is not a unit measurement. In plaintiffs' calculations a small farm and an entire public utility each are one "parcel." The median "parcel" seems an even more inappropriate measure in a case such as this where all "parcels" of personal property would also have to be included in the assessment ratio for "all other commercial and industrial property." When, as here, categories of property that are subject to different methods of appraisal must be factored together to produce the assessment ratio for "all other commercial and industrial property," each category should be factored in proportion to its share of the total true market value of all such property.
732 F.2d at 1504-05.
The ratio of aggregates has the advantage of permitting different types of commercial and industrial property to be combined into a single appraisal ratio. According to the evidence in this case, different types of commercial and industrial property can only be combined using the ratio of aggregates, because personal property assessment data is only available on an aggregate basis. Moreover, the courts have consistently held throughout the history of the 4-R Act that if evidence of the appraisal level of commercial and industrial personal property exists, district courts must consider such evidence of personal property appraisal levels in fashioning relief *45 under the Act. Lennen, 732 F.2d at 1503; Clinchfield R.R. Co. v. Lynch, 700 F.2d 126, 133 (4th Cir.1983). Likewise, the courts have consistently held that appraisal levels of utility property must be accounted for because utility property is included within the definition of "commercial and industrial property" contained in the 4-R Act. Clinchfield, 700 F.2d at 130 n. 5; Ogilvie v. State Bd. of Equalization, 657 F.2d 204, 209 (8th Cir.1981).
Statistically, neither method is without its shortcomings. The ratio of aggregates is disproportionately affected by extreme values. The median does not reflect differences in value between valuations near the median and those far from it.
However, plaintiffs' expert witness in statistics, Dr. Frederick A. Ekeblad, testified that the ratio of aggregates should be used as the average in this case. Dr. Ekeblad prefers the ratio of aggregates for use in this case because personal property assessment data is only available in aggregate data and can therefore only be combined with real property assessment data using the ratio of aggregates. The court agrees.
Because the plaintiffs have offered evidence of assessment data of personal property and because the 4-R Act appears to describe the ratio of aggregates, the court concludes that the ratio of aggregates should be used as the average to determine the average level of assessment of commercial and industrial property in Tennessee in 4-R Act litigation.

ISSUE 3

Have the plaintiffs carried their burden of proof in presenting evidence of the ratio of assessed value to true market value of commercial and industrial personal property?
49 U.S.C. § 11503(b)(1) provides, in pertinent part:
(b) The following acts unreasonably burden and discriminate against interstate commerce, and a State, subdivision of a State, or authority acting for a State or subdivision of a State may not do any of them:
(1) assess rail transportation property at a value that has a higher ratio to the true market value of the rail transportation property than the ratio that the assessed value of other commercial and industrial property in the same assessment jurisdiction has to the true market value of the other commercial and industrial property.
49 U.S.C. § 11503(c) provides, inter alia, that "[t]he burden of proof in determining assessed value and true market value is governed by State law." 49 U.S.C. § 11503 is designed to grant rail carriers a federal forum to address their claims of discrimination. The federal statute recognizes that railroads should be compared to similarly situated commercial and industrial taxpayers within each state.
Under Tennessee case law, the burden of proof is upon the taxpayer to show that tax assessments are invalid or that discrimination exists with respect to the property tax imposed. Southland Mall, Inc. v. Garner, 455 F.2d 887 (6th Cir.1972); Cox v. Bristol, 183 Tenn. 82, 191 S.W.2d 160 (1945); Williams v. Williams, 25 Tenn. App. 290, 156 S.W.2d 363 (1941).
Under § 11503, in order to succeed on the merits, a plaintiff railroad must prove the discriminatory effects of the tax by a preponderance of the evidence. Burlington N.R.R. Co. v. James, 911 F.2d 1297, 1300 (8th Cir.1990); Burlington N.R.R. Co. v. Bair, 766 F.2d 1222, 1226 (8th Cir.1985).
The appraisal of property for tax purposes is not an exact science but involves a considerable amount of judgment and discretion in which able practitioners may vary. As noted by the United States District Court for the District of Utah:
From the six weeks of testimony in this case, however, certain things became apparent. First, valuation is an art, not a science. It is a function of judgment, not of natural law. Try as it might, even Congress is incapable of enacting either a natural law of the market or Plato's ideal. "True market value," then, must needs mean something else. Absent a *46 miracle of time, place and circumstance  willing buyer, willing seller, high noon, January 1, 1984, for example  true market value for purposes of ad valorem taxation is always an estimate, always an expression of judgment, always a result built on a foundation of suppositions about knowledgeable and willing buyers and sellers endowed with money and desire, whose desires are said to converge in a dollar description of the asset. All of this is simply a sophisticated effort at "let's pretend" or "modeling," in modern jargon, and all of it involves judgment. Not natural law, not science  judgment.
Union Pac. R.R. Co. v. State Tax Comm'n, 716 F.Supp. 543, 554 (D.Utah 1988).[4]
The plaintiffs' allegations that for tax years 1989, 1990, and 1991 commercial and industrial personal property was appraised poorly by local tax assessors, and substantially below true market value, is not borne out by the evidence. The testimony of the local tax assessors, Mr. Strader, Mr. Elrod, Ms. Camille-Hubbard, and Mr. Bayne by deposition, all support the finding that they are valuing all local personal property substantially at or very near market value.
All of the local tax officials based their personal property valuations and assessments upon rules promulgated by the Tennessee State Board of Equalization and a filing form developed therefrom. These rules were effective for the tax years 1989, 1990, and 1991, and were adopted after a two to three year period of hearings receiving input from private and public parties and recommendations from staff members. Under the rules personal property is valued upon an original acquisition cost less straight line depreciation with a minimum basis of valuation being 25 percent of the original acquisition cost. The rules contain various categories of property and a standard of depreciation lives for each category. Inventories of raw materials and supplies are reported at cost basis upon a firstin, first-out method of valuation. A provision for a nonstandard value is available if the standard approach does not give fair market value. The Division of Property Assessments of the Tennessee Comptroller's Office monitors assessment summaries of each county to ensure that a county is properly applying the rules and picking up personal property accounts. The rules also provide that audits of the personal property accounts may be performed if and as deemed necessary by the county assessors.
While the plaintiff offered the opinion of Mr. Melvin Fineberg, an appraiser of machinery and equipment, that the depreciation methods used in the State Board rules were inadequate, Mr. Fineberg conceded that the use of straight-line depreciation yields a higher taxable basis than his modified double-declining balance method. Mr. Fineberg further admitted that there were problems with his method, particularly when applied to machinery and equipment purchased used. In applying his approach to railroad property, Mr. Fineberg concluded that the state had understated the value of railroad machinery and equipment while overstating the value of machinery and equipment in other industries. Since the court finds and the parties concede the railroad real and personal property is accurately valued in Tennessee for the tax years in question, Mr. Fineberg's testimony does not disprove the accuracy or the propriety of the State Board rules for the valuation of personal property.
The testimony of Lyman Martin, chief personal property appraiser for Hall County, Georgia, was offered to show that there are workable procedures available for personal property appraisers and assessors to achieve true market value of property. This testimony was admitted subject to the court's ruling on defendants' objection that the testimony was not relevant. The court concludes that Mr. Martin's testimony is relevant and it is therefore admitted. However, the court notes that Mr. Martin *47 knows little about the laws and regulations pertaining to personal property in Tennessee and he has never examined any of the assessment practices in Tennessee. Although relevant, Mr. Martin's testimony sheds little light upon the issues before the court.
Contrary to the allegations of the plaintiffs that commercial and industrial personal property is appraised poorly by local tax assessors, the evidence and testimony show that local assessors are doing an adequate job in the discovery and valuation of personal property within their jurisdictions. The testimony of several of these officials shows that reviews and desk audits are performed on all filed personal property tax returns as well as follow up correspondence, inspection, and review of records if discrepancies are noted. An effort is made to discover unreporting taxpayers by inspections of phonebooks, city directories, business license records and visual inspections. All of the local assessment officials testified that they felt that commercial and industrial personal property was being accurately assessed in their jurisdictions for 1989 and 1990,[5] and they did not know of any property which was underassessed or omitted. While an audit performed for Shelby County of thirty large personal property taxpayers revealed a substantial additional tax assessment, eleven of those taxpayers had actually overpaid and most of the remainder have appealed the additional assessment to the local board of equalization. Thus, the results of that audit are inconclusive and do not lead to the conclusion that there is a systematic undervaluation and underreporting of personal property in the State of Tennessee.
The proof shows that a statutorily mandated biannual appraisal ratio study is performed by the Division of Property Assessments to determine the overall level of appraisal in each county. Ratios derived from that study are used to equalize railroad property assessments with locally assessed property. These equalization ratios were developed for each county to alleviate any distinctions between local assessments and centrally assessed property such as the railroad plaintiffs. All of the plaintiffs' property, both real and personal, is adjusted by these equalization ratios before allocation of their value to the individual counties. The testimony shows that in many of these counties, while a reduction in assessment due to application of the equalization ratios is given railroad personal property, local commercial and industrial personal property is not afforded this reduction unless formal petition is made. Realistically very few local taxpayers make such a formal petition. Plaintiffs have failed to show by a preponderance of evidence that for the tax years 1989, 1990, and 1991 commercial and industrial property is being appraised poorly by local tax assessors substantially below market value.
Additionally, plaintiffs presented the testimony of two expert witnesses, Dr. Dick Netzer and Dr. Frederick Ekeblad. Dr. Netzer, an economist, used economic statistics on the value of certain assets to develop an estimate of total market value of commercial and industrial personal property in Tennessee. He has done similar estimates in 4-R Act litigation since 1983 in at least 15 other states. Dr. Netzer used data from the U.S. Department of Commerce  Bureau of Economic Analysis including the Fixed Tangible Reproducible Wealth in the United States, the Census of Manufacturers, the Census of Retail Trade, the Census of Wholesale Trade, the Census of Agriculture, the Census of Construction Industries, the Census of Mineral Industries, as well as County Business Patterns, 1988: United States, and County Business Patterns, 1988: Tennessee.
Dr. Netzer used an employment allocator to convert a national estimate of value for non-farm machinery and equipment into an estimate of the market value of commercial and industrial personal property in Tennessee as of December 31, 1988. One of Dr. Netzer's assumptions is that the economic characteristics of firms in a given type of *48 business tend to be the same in different parts of the country. The witness computed a total estimated market value for commercial and industrial personal property in Tennessee in an amount in excess of $37 billion.
On cross-examination the witness stated that he was not an appraiser and had not examined or contacted any business in Tennessee in regard to their machinery and equipment personal property. Dr. Netzer also stated that there had been no independent verification of his results and that no one else had used his particular methodology to estimate property values in a state other than for use in 4-R Act litigation. To Dr. Netzer's knowledge, no tax administrators or professional appraisers use his methodology. Much of Dr. Netzer's national economic data is self-reporting and no audit is made to verify its accuracy. It was admitted that his national figures had improperly included items classified as personalty which were in fact items of fixtures, and that he had made no attempt to exclude them in deriving his Tennessee estimate of personal property. One of Dr. Netzer's basic premises was that the ratio of the number of employees per equipment would be the same in any part of the country as in Tennessee. Dr. Netzer included agricultural machinery and equipment and livestock in his estimate even though such property is exempt by statute.
Dr. Frederick A. Ekeblad testified as an expert witness in the area of applied economics and statistics and had previously testified on behalf of the railroads in 4-R Act litigation in twenty other states. He calculated a composite ratio of total appraisal value to estimated market value of real and personal property in Tennessee and arrived at an appraisal ratio of 60.2%. The figure that he used for commercial and industrial personal property in the amount of $37 billion was determined by Dr. Netzer. Dr. Ekeblad conceded that his ratio of 60.2% was based on Dr. Netzer's figures and that, if Dr. Netzer's figures were changed, then his computations would change.
Dr. William Fox, a professor of economics at the University of Tennessee and research director at the Center for Business and Economic Research at the University, disagreed with Dr. Netzer's approach. Dr. Fox contested Dr. Netzer's central assumption that the amount of equipment or capital plus the amount of inventories per worker is the same in Tennessee as in the rest of the nation. Dr. Fox concluded that Dr. Netzer's methodology and assumptions were faulty in several respects: (1) different prices for wages, land and other expenses will cause firms to use different amounts of equipment per employee, (2) firms are producing different kinds of products, (3) firms use different technologies, and (4) the location of the employment and equipment measures are not done for tax purposes but are substantially under the discretion of the firm. He further noted that the very assumptions that underlie the analysis are incorrect, the data was not developed for use at the state level, and the data was never intended to be used in the kind of allocator system used by Dr. Netzer. The particular technique of using national data and allocating it to the State of Tennessee, according to Dr. Fox, is unacceptable as a measure of the value of commercial and industrial personal property in Tennessee.
Dr. Harry A. Green, Executive Director of the Tennessee Advisory Commission on Intergovernmental Relations, also testified as an expert in the field of economics and public finance. Green stated that, in his opinion, Dr. Netzer's methodology was inaccurate and inappropriate for estimating personal property for taxation purposes in Tennessee. Among the flaws noted in Dr. Netzer's methodology was that the data relied upon by Dr. Netzer included a census of large firms but only a survey of small firms, thus incorporating potentially significant errors in the reporting process. Dr. Green further noted that the Standard Industrial Classifications used by Dr. Netzer included 125 three and four digit categories of industries found in the United States as a whole but not in Tennessee. Use of such overinclusive industrial categories by Dr. *49 Netzer tended to overvalue personal property in Tennessee.
Dr. Green then used the Netzer approach to value railroad personal property in Tennessee. The Netzer approach yielded a value of railroad personal property in Tennessee in the amount of $771 million while the Public Service Commission had placed a value of $181 million on the same property. A similar comparison was made for the specific plaintiff railroad, Norfolk Southern. Utilizing the Netzer approach, the plaintiffs' railroad value of personal property was $338 million while the Public Service Commission had placed a value of $79.5 million on plaintiff's same personal property. The Netzer approach yielded a value four times the actual value placed on the personal property by the Public Service Commission. The parties have stipulated and agreed that the Public Service Commission has accurately valued the plaintiffs railroad property at 100% market value for the 1989 and 1990 tax years. Dr. Green concluded that if the Netzer approach overvalues railroad property by this magnitude then it must also significantly overvalue the estimate of all personal property in the State of Tennessee.
Mr. Robert Gloudemans also testified as an expert in the field of ratio studies and real property appraisal. In his opinion, Dr. Netzer's approach is not valid for estimating the total market value of property in Tennessee. Mr. Gloudemans noted numerous flaws in Dr. Netzer's approach and in the underlying data, and made an independent analysis in regard to perceived data classification problems of real property versus personal property. Dr. Netzer's exact approach was applied using national data as to improvements on realty rather than machinery and equipment. Government sources give both data for personal property and the value of structures. This approach yielded a value for improvements to realty in Tennessee as of December 31, 1988, in the amount of $18,707,000,000. The actual value reported by the Division of Property Assessments was $35,860,000,000 for improvements. In addition to the inaccuracy of the approach, this confirmed Mr. Gloudemans' observation that, in the reporting method used in the federal data, some improvements or realty were actually reported as personalty. Thus, the data used by Dr. Netzer incorrectly overstated the amount of personal property in Tennessee.
Mr. Barry Murphy, a Certified Assessment Evaluator, Director of Assessments for the Public Service Commission, also testified that Dr. Netzer's approach to valuing personal property in Tennessee is not a recognized appraisal methodology and would not be used by him in valuing railroads for property taxation purposes.
The burden is upon the plaintiff, as the party attacking the accuracy of the State Board's values and sales ratios, to show by a preponderance of the evidence what the accurate values are. Burlington N.R.R. Co. v. Bair, 766 F.2d at 1226. "In evaluating the evidence the District Court should give due deference to the [State Board's] expertise in valuation." Id.
Based upon the significant flaws in the methodology used by Dr. Netzer as noted by defendants' expert witnesses, and the clearly erroneous results such an approach renders if applied to the railroads, this court must conclude that plaintiffs have failed by a preponderance of evidence to show that the approach used by Dr. Netzer produces an accurate estimate of the market value of commercial and industrial property in Tennessee. Accordingly, the use of Dr. Netzer's results by Dr. Ekeblad must also fail.

CONCLUSION
Based upon the foregoing, the court concludes that for purposes of 49 U.S.C. § 11503 in this case, the ratios of assessment to true market value of railroad property and the ratios as to other commercial and industrial property may be compared on a statewide basis, rather than on a county-by-county basis; and that the appropriate statistical measure upon which to base such comparisons is the weighted mean or ratio of the aggregates, rather than the median ratio of appraised value to true market value. Finally, the court finds that *50 the plaintiffs have failed to carry their burden of showing by a preponderance of the evidence that the levels of assessment of their real or personal property in Tennessee for tax years 1989, 1990, and 1991 are unlawfully discriminatory under 49 U.S.C. § 11503.
Therefore, the court finds that the plaintiffs have failed to establish their entitlement to relief in these cases, and accordingly judgment will be entered for defendants. The preliminary injunctions previously entered in these actions are dissolved.
IT IS SO ORDERED.

ORDER DENYING MOTION FOR A NEW TRIAL
Plaintiffs have moved pursuant to Fed. R.Civ.P. 59 for a new trial and, impliedly, for an amendment of the findings of fact and conclusions of law entered on May 15, 1992, and entry of a new judgment thereon. Defendants, engaging plaintiffs in a flurry of replies, responses, counter-replies, and counter-responses, oppose the motion for new trial and amendment of the judgment.
In their motion for new trial, plaintiffs contend that, under the Findings of Fact and Conclusions of Law entered by the court, plaintiffs are entitled to have their assessments reduced from 92.39% of fair market value for the 1989 tax year and 92.33% of fair market value for the 1990 tax year to 86% of fair market value. As a basis for the motion, plaintiffs contend that, based upon Dr. Ekeblad's analysis of the statewide assessment ratio and the conclusion of the court that commercial and industrial personal property in Tennessee is appraised at or near fair market value, the equalization relief accorded plaintiffs for 1989 and 1990 fell substantially below equalization based upon the 86% assessment level calculated by Dr. Ekeblad. Consequently, the railroads contend that they are entitled to additional equalization relief, or a reduction to 86% for the 1989 and 1990 tax years. Plaintiffs make no claim for additional equalization relief for 1991 because plaintiffs failed in that year to meet the 5% jurisdictional threshold required by the 4-R Act.
Defendants responded to plaintiffs' motion for new trial by contending that the 92.3% and 92.33% aggregate equalization ratios for plaintiffs' railroad property for 1989 and 1990, respectively, were computed only for the counties in which the plaintiff railroads do business. Defendants contend that the statewide median for commercial and industrial property of 88.79% in 1989 should be used for comparison purposes. Defendants contend that the 5% differential threshold required by Section 306(2)(c) of the 4-R Act has not been met by comparing plaintiffs' computed figure of 86% to the 88.79% statewide median.
Plaintiffs countered that the 5% threshold must be determined by taking 5% of the estimated value and not by comparing the two appraisals to see if they are numerically within five percentage points of each other. See Southern Railway Co. v. State Board of Equalization, 712 F.Supp. 1557, 1565 (N.D.Ga.1988). Plaintiffs then pointed out that there is a 6.07% difference between the railroad assessment level and the assessment level of other commercial and industrial property. Plaintiffs also point out that defendants incorrectly used the median assessment level rather than the ratio of aggregates.
Defendants next contend that plaintiffs have incorrectly relied upon the computations of Drs. Netzer and Ekeblad, which computations have been rejected by the court. Plaintiffs then respond that defendants have incorrectly used the median in calculating the estimated market value of real property in Tennessee for 1989.
Although almost obscured by the replies and responses of the parties, the issue before the court is whether plaintiffs have correctly calculated the total estimated market value of property in Tennessee for 1989 which calculation demonstrates unlawful discrimination against the railroad because the ratio of assessed value to true market value with respect to railroad property exceeds by at least 5% the ratio of assessed value to true market value of all other commercial and industrial property in *51 Tennessee. Because the court has previously rejected the methodology used by Drs. Netzer and Ekeblad upon the basis that it did not produce an accurate estimate of the market value of commercial and industrial property in Tennessee, the court concludes that plaintiffs have failed to show by a preponderance of the evidence that the ratio of assessed value to true market value of railroad property exceeds by at least 5% the ratio of assessed value to true market value of all other commercial and industrial property in Tennessee. Therefore, plaintiffs' motion for new trial, and impliedly for amendment of the judgment, is denied.
IT IS SO ORDERED.

ORDER ON MOTION TO AMEND JUDGMENT
Plaintiffs have moved the court pursuant to Fed.R.Civ.P. 60(a) for an order amending the judgment previously entered in this action to prohibit defendants from collecting penalties and attorney's fees upon taxes paid after their due date. Plaintiffs contend that the preliminary injunctions against collection of the taxes for 1989, 1990, and 1991 make it inequitable for defendants to collect penalties and attorney's fees. After the court issued its opinion denying plaintiffs the relief they sought, plaintiffs paid the past-due taxes (or tendered payment to those jurisdictions that would not accept payment of taxes without the penalty), plus statutory interest which had accrued on the taxes. Apparently several defendant taxing jurisdictions have notified plaintiffs that they plan to seek penalties for the past-due taxes and at least one jurisdiction has filed suit and apparently seeks attorney's fees as well.
Defendants contend that the penalty provided by T.C.A. § 67-5-2010 is mandatory and the statute does not permit waiver or abatement of the penalty.
Plaintiffs rely upon language from the Tenth Circuit Court of Appeals in Burlington Northern Railroad Co. v. Lennen, 715 F.2d 494, 498 (1983):
Because we stayed the payment of the portion of taxes at issue here pending decision of this appeal, no penalty shall be assessed against the railroads if they pay the taxes that they have withheld because of our grant of a temporary injunction within seven days after the issuance of the mandate in this case.
Although the Tenth Circuit did prohibit the collection of a penalty when the railroad did not pay the tax when it became due, the court offered no citation of authority for its ruling nor any reasoning for its holding. The court has been unable to find any other authority for that holding.
The Tennessee Supreme Court, however, has addressed this issue squarely. In Illinois Central R.R. Co. v. Garner, 193 Tenn. 91, 101, 241 S.W.2d 926 (1951), the Supreme Court held:
If he [the taxpayer] elects to litigate with the State and thus postpone the payment of the tax he does so at the peril of paying interest and penalties. "Even if the taxpayer is successful to the extent of having a portion of the tax invalidated by the courts, he is nevertheless liable for the penalty for failure to pay the portion of the tax sustained." [Citation omitted].
This court adopts the reasoning of the Tennessee Supreme Court insofar as the penalty is concerned. Because the penalty is an incentive to pay the tax before it becomes delinquent, and because a taxpayer has the right to pay the tax and then litigate its propriety later, there is no reason to prohibit the collection of the penalty even when the tax was not paid pursuant to an injunction. Plaintiffs' motion to amend the judgment to prohibit the payment of a penalty for delinquent taxes is denied.
The issue of attorney's fees is another matter. Attorney's fees are allowed only when the delinquent tax attorney has filed suit against the taxpayer to enforce a tax lien pursuant to T.C.A. § 67-5-2410. Any suit to enforce a tax lien against plaintiffs in this case was a violation of the court's injunction against such efforts to collect the taxes. Therefore, the suit filed in the Chancery Court for Jefferson County *52 by the Jefferson County Trustee on March 30, 1990, was filed in violation of this court's injunction of March 2, 1990. The Jefferson County Trustee is not entitled to collect attorney's fees for action taken in violation of this court's order. The Trustee of Jefferson County is ordered to cause the dismissal of that action at no cost to plaintiffs. In the event plaintiffs have not paid all delinquent taxes and penalty within thirty (30) days of the date of this order, the Trustee of Jefferson County may reinstitute the suit.
Because the court presumes that all other plaintiffs obeyed the court's injunction against suits to enforce the delinquent taxes, it is not necessary to amend the judgment to prohibit such suits. However, any suit against plaintiffs in violation of the injunctions will be dealt with on a case by case basis. Therefore, for the foregoing reasons, plaintiffs' motion to amend judgment is denied.
IT IS SO ORDERED.
NOTES
[1]  Section 306, originally codified at 49 U.S.C. § 26c, was recodified in 1978 at 49 U.S.C. § 11503. The language of 49 U.S.C. § 11503 differs from the language of Section 306 as enacted. The codification of 49 U.S.C. § 11503 cannot be construed as making any substantive changes to the meaning of Section 306. See, Burlington N.R.R. v. Oklahoma Tax Comm'n, 481 U.S. 454, 457, n. 1, 107 S.Ct. 1855, 1858, n. 1, 95 L.Ed.2d 404 (1987). Therefore, the court will occasionally refer to 49 U.S.C. § 11503 as "Section 306." On occasion, § 11503 will be also referred to as the "4-R Act."
[2]  Under a recently enacted statute, currently being implemented, counties will periodically revise real property assessments between reappraisals by use of market derived indices. See T.C.A. § 67-5-1601(b).
[3]  While the Tennessee Constitution, Article II, Section 28, actually mandates a 55% assessment for real property and personal property of public utilities, the Railroad Revitalization and Regulatory Reform Act ("4-R Act"), 49 U.S.C. § 11503, requires that railroads be assessed the same as commercial and industrial classification property, i.e., 40% for real property and 30% for personal property. The constitutionality and application of this Act to Tennessee have been upheld. See, Tennessee v. Louisville & Nashville R.R. Co., 478 F.Supp. 199 (M.D.Tenn. 1979), aff'd without opinion, 652 F.2d 59 (6th Cir.1981), cert. denied, 454 U.S. 834, 102 S.Ct. 135, 70 L.Ed.2d 114 (1981).
[4]  Plaintiffs contend that this language has no application to this case because the Utah court was faced with an issue involving valuation of railroad property, not the right to equalization. However, the court's comments concerning the difficulties in valuation are applicable in either case.
[5]  Although 1991 taxes have become an issue in this action, they were not at issue at the time of trial. The action alleging discrimination in 1991 was filed after the trial but was consolidated with actions alleging discrimination in 1989 and 1990.
