
716 F.Supp. 543 (1988)
UNION PACIFIC RAILROAD COMPANY, a Utah corporation, and the Denver & Rio Grande Western Railroad Company, a Delaware corporation, Plaintiffs,
v.
STATE TAX COMMISSION OF UTAH and State of Utah, Defendants,
and
Salt Lake County, et al., Defendants in Intervention.
SOUTHERN PACIFIC TRANSPORTATION COMPANY, Plaintiff,
v.
STATE OF UTAH, et al., Defendants,
and
Salt Lake County, et al., Defendants in Intervention.
Nos. C-84-0839J, C-84-0840J and 82-C-0998J.
United States District Court, D. Utah, C.D.
December 19, 1988.
*544 Leonard J. Lewis, Robert A. Peterson and Eric C. Olson, VanCott, Bagley, Cornwall & McCarthy, Salt Lake City, Utah, for Union Pacific R. Co.
L. Ridd Larson and William A. Marshal, Salt Lake City, Utah, and Wm. E. Saul, San Francisco, Cal., for Southern Pacific Transp.
Stephen G. Schwendiman and Maxwell A. Miller, Asst. Attys. Gen., Bill Thomas Peters and Gary Thorup, Sp. Asst. Atty. Gen., Prince Yeates & Geldzahler, Salt Lake City, Utah, for defendants.

MEMORANDUM OPINION AND ORDER
JENKINS, Chief Judge.
The plaintiff railroads  Union Pacific (UP), the Denver & Rio Grande Western (D *545 & RG) and Southern Pacific (SP)  brought these consolidated actions to challenge their ad valorem property tax assessments for 1984 and 1985 on the grounds that the assessments discriminated against them in violation of section 306 of the Railroad Revitalization and Regulatory Reform Act of 1976 (the 4R Act), Pub.L. No. 94-210, § 306, 90 Stat. 31, 54 (1976). The cases were tried to the court beginning on February 9, 1988, and ending on March 17, 1988, with some brief respites in between. The court heard closing arguments on March 30, 1988. Robert A. Peterson and Eric C. Olson represented the plaintiffs UP and D & RG. L. Ridd Larson and William A. Marshall represented plaintiff SP. Rex E. Madsen, Reed L. Martineau and Maxwell A. Miller represented the defendants, and Bill Thomas Peters represented the defendants in intervention, some twenty Utah counties.[1] There were 788 exhibits, some of great complexity. After digesting the evidence and the arguments of counsel, the court now enters this memorandum opinion and order, which, under Federal Rule of Civil Procedure 52(a), shall constitute the court's findings of fact and conclusions of law.

I.

THE STATUTE
In 1976, in part to "restore the financial stability of the railway system of the United States," Pub.L. No. 94-210, § 101(a), 90 Stat. 31, 33 (1976), Congress passed the 4R Act. Section 306 of the act, codified at 49 U.S.C. § 11503, prohibits states and local taxing authorities from discriminating against railroad property. That section makes it unlawful for a state to assess railroad
transportation property at a value which bears a higher ratio to the true market value of such transportation property than the ratio which the assessed value of all other commercial and industrial property in the same assessment jurisdiction bears to the true market value of all such other commercial and industrial property.
Id. § 306(1)(a), 90 Stat. at 54.[2] A railroad that thinks it has been treated unfairly may bring an action in federal district court for injunctive and declaratory relief. Id. § 306(2). The court is then required to compare two ratios: the ratio of the assessed value of rail transportation property to its true market value, and the ratio of the assessed value of all other commercial and industrial property in the same assessment jurisdiction to its true market value. The court may grant relief to the railroad only if the ratio of assessed value to true market value for rail transportation property "exceeds by at least 5 per centum the ratio of assessed value to true market value, with respect to all other commercial and industrial property in the same assessment jurisdiction" (in this case, the state of Utah). Id. § 306(2)(c).[3]
*546 The plaintiff railroads claimed that Utah had discriminated against them in two ways: by overvaluing their property and by denying them a twenty-percent discount in their assessed value that was available to locally assessed commercial and industrial real property under Utah law, Utah Code Ann. § 59-5-4.5 (Supp.1986). Plaintiff SP settled its valuation claim with the state before trial. At the trial, the parties presented the court with a stipulation setting forth two alternatives for the ratio of assessed value to true market value for all other commercial and industrial property in Utah  one ratio if the court upholds the twenty-percent discount statute and another if the court strikes down the twenty-percent discount statute.[4] Because the railroads' assessed value is given, see infra note 48 and accompanying text, the only issues for the court to decide are the true market value of the UP and D & RG as of the assessment dates (January 1, 1984, and January 1, 1985) and the allegedly discriminatory effect of the twenty-percent discount statute. The court will consider these issues in order.

II.

THE PLAINTIFFS' VALUATION CLAIMS
Plaintiffs UP and D & RG claim that Utah has discriminated against them by overvaluing their rail transportation property for the assessment years 1984 and 1985.[5] To determine whether that is so, the court must determine the plaintiffs' true market value and then compare that figure to the state's assessed value, which was based on the state's determination of the plaintiffs' true market value.[6] Under Utah law, the plaintiffs' assessed value for assessment years 1984 and 1985 should be .20 of their true market value. See supra note 3. If it is greater, then the state has overvalued the railroads, regardless of any equalization claim they may have.
The court's task is complicated by the fact that the defendants concede that the plaintiffs' initial assessed values for 1984 and 1985 were not based on their true market value. In May 1984 the state assessed UP based on a true market value of $3,875,000,000. On June 4, 1984, the state issued a revised assessment for UP based on a true market value of $3,600,000,000. The state has since become convinced that the methods it used to arrive at those figures were wrong and has abandoned those appraisals. See Transcript [hereinafter Tr.] at 341, 345-46, 350-51. For trial the state relies on a new appraisal for UP based on a different approach, which places *547 the value of UP for assessment year 1984 at $3,700,000,000. The state followed a similar approach for UP for assessment year 1985 and for the D & RG for 1984 and 1985, with similar results.[7] Thus, the defendants concede that the plaintiffs were assessed at rates that were not based on their true market value for assessment years 1984 and 1985. To determine how much the plaintiffs' newly determined values differ from their "true market value," if at all, the court must still determine their true market value as of January 1, 1984, and January 1, 1985.
In deciding the valuation question, the court has the advantage of expert help. The plaintiffs have presented the appraisals of their expert witness, Dr. Arthur Schoenwald, a financial consultant specializing in railroad and utility ratemaking and valuation. See common exhibits 30 & 33, 36 & 39. The defendants rely on the newly prepared appraisals of Mr. Ekhardt Prawitt, the utility and railroad valuation manager for the Property Tax Division of the Utah State Tax Commission. See common exhibits 32, 35, 38 & 41. However, to bolster Mr. Prawitt's appraisals, the defendants also offered appraisals prepared jointly by Mr. Michael Goodwin, an independent appraiser specializing in the valuation of public utilities, railroads and other multistate corporations, and Dr. James Ifflander, an assistant professor of finance at Arizona State University. See common exhibits 31, 34, 37 & 40. The plaintiffs and intervenors also offered the testimony of various experts retained to critique or comment on the competing appraisals.
Unfortunately, all these expert opinions may only verify George Bernard Shaw's observation that, "[i]f all economists were laid end to end, they would not reach a conclusion." The operative word here is "a"; for, after listening to seventeen full days of expert testimony spread over six weeks, the court suffers from no lack of conclusions. The problem is that the proffered expert conclusions differ from one another by over a billion dollars in the case of UP and by a like order of magnitude in the case of the D & RG.[8] Fortunately, the parties do agree on some things. To that extent, the court can begin on common ground.
The parties agree, for example, that the proper approach for valuing a railroad for taxation purposes is the so-called unitary approach. Under that approach, the state determines the value of the entire railroad as a unit, even though its assets may be located in several states, and then allocates a portion of that total value to the taxing state (in this case, Utah) based on such factors as the percentage of the railroad's total trackage that runs through the taxing state. The parties also agree on the percentage of the total value of each railroad's property that should be allocated to Utah. See infra note 47 and accompanying text; Tr. at 13-14. Finally, the parties agree in principle on the three standard methods for valuing a railroad: the cost approach, the income approach and the stock and debt approach. It is in applying the three standard approaches to reach a conclusion as to true market value that the parties part ways.

A. Overview of Valuation Approaches
At the risk of oversimplification,[9] the court can summarize the three basic approaches as follows.
*548 The Cost Approach. The cost approach values a railroad based on historical costs  that is, how much it actually cost to produce the assets initially. From historical cost is deducted accumulated depreciation to get net book value. Then, from net book value an amount is deducted to reflect obsolescence. The final figure is the cost indicator of value. All the parties agree that the cost indicator is the least accurate indicator of true market value.[10]
The Stock and Debt Approach. The stock and debt approach is a substitute market approach. Because of the infrequent sales of railroad properties, the absence of an organized market for such properties and the lack of accurate, current information about sales of railroad properties as such, appraisers must look to a substitute source for accurate information. There is an organized market for the purchase and sale of fractional ownership interests in railroad properties; shares or ownership interests in debt, bonds and such are bought and sold with some regularity. A specialist in dealing with such shares on an organized exchange "makes a market" for them. He offers to buy. He offers to sell. He can thus respond to offers to buy and sell. An appraiser uses such market information as some indication of value.
Those who use such data assume that the "market" has depth as of a particular moment in time and that multiplying the market value of the fractional share by the number of outstanding shares will produce a figure equal to the whole market value, which, when added to outstanding debt, will produce an approximation of true market value of company assets subject to ad valorem taxation. The argument is that the whole is equal to the sum of its parts, a conservative position, one could argue, in today's era of leveraged buyouts. It does not factor in the element of control or the break-up value frequently perceived by some to be hidden in the assets of a target company.
Often the outstanding shares of a railroad are held in their entirety by a holding company. The organized market to which an appraiser looks for data is in the shares of the holding company  not in the shares of the railroad. Thus, the data to which the appraiser looks for an indication of value is two steps removed from the actual assets appraised. The appraiser must determine in some appropriate fashion what fraction of the market value attributed to the shares of the holding company is represented by the holding company's ownership, through its railroad subsidiary, of railroad assets.
In applying the stock-and-debt approach, there is relatively little disagreement among the parties as to the value of the plaintiff companies' debt. See, e.g., Tr. at 1243. The main disagreement is over the companies' equity value and specifically over how to determine what portion of the holding company's gross equity is attributable to railroad property.
The state of Utah uses basically two approaches for attributing a portion of the holding company's equity to the railroad. Both use various multipliers. In the first approach, the state compares the subject railroad to other railroads in the industry. It calculates an industry multiplier based on the ratio of various railroads' stock prices to their cash flows and earnings. It then applies those price/cash flow and price/earnings ratios or multipliers to the subject railroad's cash flow and earnings to get estimates of the value of the railroad's stock. In its second approach, the state compares the subject railroad to its holding company. The state calculates multipliers based on the ratio of the railroad's net profit, revenues, income and assets to the holding company's net profit, revenues, income and assets and applies the multipliers to the company's total equity value to determine the equity value of the railroad. See, e.g., common ex. 32 at S/2.
On the other hand, Dr. Schoenwald, the railroads' expert, calculates the equity value *549 of each of the nonrail assets of the holding company and deducts those values from the holding company's total equity value. What's left over, he concludes, is the equity value of the railroad.
The Income Approach. The theory behind the income approach is that anyone who buys a railroad buys it only for the income the railroad will generate. The basic principle is that the present value of a company is equal to the value of all future benefits to be derived from ownership of the company, discounted to their present value (expressed in dollars). Since the future benefits to be derived from ownership of a company are simply the income one can expect to receive from the company, the income approach tries to project the income from the railroad's operations over a period of time and then places a present value on that income.[11] The present value of future income is expressed by the following formula:
        I1         I2                In
V0 = ________ + ________ + . . . + _______
     (1 + i)1   (1 + i)2           (1 + i)n
where V0 is the value at time zero, I1 is the income for year 1, and i is an interest rate or discount rate.
Obviously, this basic valuation formula is almost impossible to apply accurately because one can't know precisely the value of all the variables. It is impossible to predict accurately the income for each future year for the life of the railroad, to know how long the railroad will continue to produce income and to predict the appropriate interest rate for future years. Thus, each of the appraisers in this case simplifies the basic formula based on certain assumptions.
All the experts essentially agree on at least one simplification of the basic formula, namely,
                      CF1
                 V0 = ___
                      k-g '
where CF1 represents the net cash flow in period 1, k represents the cost of capital, and g represents the growth rate. See pltffs' ex. 358 (Dr. Schoenwald); Tr. at 1088 (Dr. Ifflander) & 1455 (Dr. Pettit).[12]
This approach to income valuation, which tries to estimate future cash flows over a period of time and discount them to their present value, is called yield capitalization or a "discounted cash flow" (DCF) model and is widely used (in one form or another) by appraisers and financial analysts to value income-producing property. See, e.g., Tr. at 1348-49 (testimony of Dr. Ifflander), 1491 (testimony of Dr. Pettit), 1728 (testimony of Mr. Van Drimmelen, a real estate appraiser), 2077 (testimony of Mr. Fitzgerald).[13]
*550 The standard simplifications of the basic formula used in a yield capitalization model assume that k, g and b (the retention rate, see supra note 12) are constant and are all equally influenced by inflation. They also assume that the growth rate, g, is equal to b times r, the marginal rate of return on new investment. See Tr. at 1455.
The plaintiffs' appraiser, Dr. Schoenwald, on the other hand, starts from the basic formula but makes a different assumption, namely, that r (the rate of return on new investment) equals k (the cost of capital). Using this assumption, he simplifies the basic formula to
                 NCF1
            V0 = ____
                  k
where NCF1 is the net cash flow for year 1.[14] In essence, he has eliminated growth from the equation. He is able to do this because, given his assumption that r equals k, any growth in the company's future earnings is merely expansion growth and not real growth; thus, according to the witness, it does not add anything to present value.[15] Hence, Dr. Ifflander has called Dr. Schoenwald's income valuation model an expansion model, a term the court will use at times to distinguish it from the standard yield capitalization model. Although Dr. Schoenwald's model is in theory a yield capitalization model, it proceeds from a very different assumption than the standard yield capitalization models described by the other experts.[16]
The state uses another method to value the railroads based on their projected income, called direct capitalization. In the direct capitalization method, the appraiser determines a company's value by multiplying its accounting earnings by a price/earnings ratio or by dividing the earnings by the earnings/price ratio. The ratios are derived from stock market data for comparable companies.
Under the state's direct capitalization method, value at time zero (V0) is equal to earnings for time 1 (E1) divided by the earnings-price ratio (E/P), or, expressing the relationship algebraically,
                 E1
            V0 = ___
                 E/P .
Although not directly derived from the basic valuation formula,[17] the direct capitalization method proceeds from the assumption that the price of a company's stock will represent the consensus of investors' opinions about a company's future cash flows, cost of capital and growth prospects. In other words, it uses the stock market as the best evidence of willing buyers' and sellers' opinions of value, which presumably *551 are based on their own yield capitalization analyses.
For its earnings figure, the state uses a five-year weighted average of the railroad's net operating income, adjusted for inflation, in which income for more recent years is weighted more heavily than income for earlier years.
Obviously, the two basic questions in applying the income approach are, How do you define the income stream to be capitalized? and What capitalization rate do you use? Although the parties disagree somewhat about what constitutes the proper income stream to capitalize, their most fundamental disagreement is over the capitalization rate. As one can see from the basic valuation formulae, since the capitalization rate is a fraction that appears in the denominator, a small change in the capitalization rate can produce a big difference in computed value.[18]
The plaintiffs argue that the state's capitalization rates, which vary from 8.28 to 11.98 percent, see appendix A, are clearly wrong since all the experts agreed that the driving force behind the capitalization rate, however expressed, namely, the cost of capital (debt and equity), was no less than 13 percent and closer to 15 percent during the relevant periods. See, e.g., intervenors' exs. 1a through 1d at 2. However, that argument overlooks the fundamental differences between yield capitalization and direct capitalization. The capitalization rate for yield capitalization is based directly on k, the cost of capital, and therefore should be on the order of 15 percent. The capitalization rate for direct capitalization, on the other hand, is based on price-earnings ratios taken from stock market data. It is not based directly on the cost of capital. Because there is no direct relationship between the cost of capital and P/E or E/P ratios, the fact that a direct cap rate or E/P ratio may be less than the cost of capital (k) is of no moment. Although there was wide disagreement among the experts about the price-earnings ratios to be used and their importance in the process, the evidence suggested that the state values were well within the very broad range of possible ratios. Thus, the plaintiffs' argument has merit only if the state was required to use a yield capitalization method as opposed to a direct capitalization method in arriving at an approximation of value.

B. Choice of Method
The parties do not disagree so much over the proper application of each other's methodology as they do over the choice of method in the first place.
Technically, methodology is not the issue in this case  discrimination is. But discrimination under the 4R Act must be measured in terms of "true market value"  the congressionally mandated measure  and one's conclusion as to true market value depends on the path one takes to reach the conclusion.
One problem with subjecting complex issues like valuation to judicial determination is that the court generally must choose among the competing claims of experts. Unless the court performs its own appraisala task it is not inclined to undertake[19]  the court must hold either for the plaintiff or the defendant, when often the truth  or at least a more exact picture of reality  lies somewhere in between. The court, of course, may adjust an expert's appraisal up or down based on other experts' critiques of the appraisal,[20] but the starting point for judicial determination is *552 always one appraisal or another, and each appraisal is based on a particular methodology that, to a large extent, predetermines the result. Thus, implicit in the court's holding is a decision as to method.
For example, if the court were to hold for the plaintiff and accept Dr. Schoenwald's valuations, it would in effect be saying that Dr. Schoenwald's methodology produces the correct result, and any methodology that produces a different result must be wrong. Given that hypothetical premise, it naturally follows that, if the state must tax the plaintiffs in proportion to their true market value, which it must under the 4R Act, then the state should apply Dr. Schoenwald's methodology in valuing the railroads, since that is the only methodology that will consistently produce the right result.[21]
Thus, although the plaintiffs argue that the court need not dictate to the state a particular methodology, some choice of methodology is inescapable. The court's decision on valuation must recognize (at least implicitly) one valuation method at the expense of other methods. That in no sense determines that one is right and the others are wrong.
The defendants suggest that the court should simply defer to their current choice of methodology. However, the plaintiffs were initially assessed based on a methodology that even the state now concedes was flawed. The question, then, is whether the state's new appraisals, based on a new methodology, are entitled to the same deference.
The plaintiffs argue that they are not.[22] They argue that the court should determine the valuation question based on which method it finds the most reasonable. They further contend that Dr. Schoenwald's valuation method is more reasonable than the state's, best reflects reality and leads to the actual or correct true market value.
The evidence suggested that yield capitalization is generally preferred to direct capitalization because it is directly derived from basic value theory, is more sophisticated than direct capitalization and generally produces a better result. However, the evidence also showed that both approaches were widely used to value railroads and other properties. The question, then, is whether the state is free to choose among accepted valuation methods or whether the 4R Act compels the use of one particular method.
In the Burlington Northern case the Supreme Court expressly left open the question "whether a railroad may, in an action under [the 4R Act], challenge in the district court the appropriateness of the accounting methods by which the State determined the railroad's value, or is instead restricted to challenging the factual determinations to which the State's preferred accounting methods were applied." Burlington N. R.R. Co. v. Oklahoma Tax Comm'n, 481 U.S. 454, 107 S.Ct. 1855, 1861 n. 5, 95 L.Ed.2d 404 (1987). Although the question may be an open one, this court has found nothing in the 4R Act itself or in its legislative history that requires this court to make the state apply a particular valuation methodology.
Indeed, the legislative history of the 4R Act suggests just the opposite. The committee report on Senate Bill 927, one of several precursors to the 4R Act,[23] stated that the bill
does not suggest or require a State to change its assessment standards, assessment practices, or the assessments themselves. *553 It merely provides a single standard against which all affected assessments must be measured in order to determine their relationship to each other. It is not a standard for determining value; it is a standard to which values that have already been determined must be compared.
S.Rep. No. 1483, 90th Cong., 2d Sess. app. B (1968), quoted in Burlington Northern Railroad Company v. Lennen, 573 F.Supp. 1155, 1161 (D.Kan.1982) (emphasis omitted), aff'd, 715 F.2d 494 (10th Cir.1983), cert. denied, 467 U.S. 1230-31, 104 S.Ct. 2690, 81 L.Ed.2d 884 (1984).[24]
In subsequent legislative proposals Congress reaffirmed its position that it did not intend to dictate state valuation methods. See Lennen, 573 F.Supp. at 1163-64. For example, in hearings on House Bill 16245, another forerunner of the 4R Act, Philip M. Lanier, a railroad representative, testified that the bill "would not deal with valuation being standard. The standards and methods of valuation that any State wishes to use would be totally unaffected by this legislation." Hearing Before the Subcommittee on Transportation and Aeronautics of the Committee on Interstate and Foreign Commerce on H.R. 16245, 91st Cong., 1st Sess. 138 (1970), quoted in 573 F.Supp. at 1163 (emphasis omitted). Thus, the legislative history suggests that the statute was not meant to dictate a state's choice of methodology, at least as long as the methodology chosen had a rational basis and was not chosen for a discriminatory purpose.[25]
The plaintiffs argue, however, that the statute itself requires this court to choose the correct valuation method from among the competing methods. They argue that the statute requires the court to determine their "true market value" and that the only way the court can do that is by determining which method gives the "true" true market value. That method is the one that is most reasonable and most accurate and hence arrives at the most correct result. They further argue that Dr. Schoenwald's methodology and data are the most reasonable and most accurate and can be applied most consistently and hence give the best indication of true market value. See Tr. at 1151-52.
The court declines the plaintiffs' invitation to adopt Dr. Schoenwald's methodology as the only correct methodology for determining true market value.
Each expert asserts that his methodology results in a value that most closely corresponds to reality. However, absent a willing buyer and a willing seller, there is no absolute way to test the assertions of competing valuations or competing claims of correspondence to "true market value," if such a thing exists in the order of things.
From the beginning of this case, the court was willing to assume that there was such a thing as "true market value" that could be determined objectively from evidence much the same way a court can *554 determine a wrongfully discharged employee's back wages from evidence. See Union Pac. R.R. Co. v. State Tax Comm'n, 635 F.Supp. 1060, 1067 at n. 10 (D.Utah 1986). Indeed, the approach of the 4R Act presupposes that, like Plato's ideal, there is in fact a "true market value," that it exists, that it can be pointed to, pictured, recognized and can be used as the standard against which valuation figures may be compared. Success in valuation would be indicated by the correspondence of the valuation figures with the ideal.
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 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.
The appraisals in this case generally contain two or three estimates of value, which, within the same appraisal, may vary by as much as 100 percent or more. See, e.g., common ex. 30 & 34 at 75 & 83; see also appendix A. Thus, the same appraiser may come to vastly different conclusions as to the value of the same railroad for the same assessment date, depending on the method he uses. Moreover, each method requires various estimates and calculations, small variations in any of which may lead to large differences in value. See, e.g., supra note 18. Absent evidence of an actual sale, the term "true market value" is at best a rational fiction. Conclusions as to true market value are based on each appraiser's best judgment, and each appraiser approaches the task of valuation a little differently, with his own assumptions and theories as to what mythical buyers and sellers consider (or should consider) in arriving at an agreed-on price. Perhaps Clifford Fitzgerald, a corporate finance expert who testified on behalf of the plaintiffs, said it best: "There is not one universal concept of value." Tr. at 2096. Nor is there "any one perfectly correct method." Id. at 2110-11. See also id. at 1718 (testimony of Mr. Voytko that there is no standard approach to value).
Mr. Goodwin described Dr. Schoenwald's methodology as "assumption driven." The epithet was apparently meant disparagingly and was contrasted with his own methods, which, he claimed, were "market driven." In truth, however, each appraiser's methodology is assumption driven.[26] The assumption may be r equals k or that growth is constant, or the assumption may be that the price of a company's stock is the best indicator of the value of its assets. (Presumably that is what Mr. Goodwin meant when he said his model was "market driven.") The latter assumption, of course, may oversimplify matters by not accounting for the effect of other variables on the stock marketeconomic and otherwise (perhaps even including the conference of the Super Bowl winner). See, e.g., Tr. at 1337-39, 1421 (testimony of Dr. Ifflander that stock market prices do not always accurately reflect value); id. at 1507-10 (Dr. Pettit's attempt to explain the stock market crash of 1987 based on various factors unrelated to a company's true market value).[27]
*555 From all the evidence presented it is clear that there is more than one way to value a railroad. See, e.g., Tr. at 1718, 2110-11. Each method may represent what some buyers and sellers actually do.[28] All the methods may be equally rational given their underlying assumptions. And they are all irrational if pressed to extremes. For example, using the income approach, one would be forced to conclude that a company with a net loss for the year or over a period of years actually had a negative value  a skewed and discordant picture of reality. See, e.g., Tr. at 2201-03. Or, using the stock and debt approach, one might be forced to conclude that over 20 percent of the value of a company evaporated in the few short hours between the opening and closing of the New York Stock Exchange on October 19, 1987, despite the fact that the company's functioning assets remained virtually unchanged over that period. Each method or theory depends on certain assumptions that cannot ultimately be proved or disproved by reason alone nor replicated in experience. Thus, this court cannot say that any one method is necessarily more rational than any other. Nor can the court say that one method alone arrives at the railroad's "true market value." Rather, the evidence suggests that the term "true market value" "is a judgment not subject to mathematical precision that is based on a wide variety of factors" and "is at best an approximation." Rio Algom Corp. v. San Juan County, 681 P.2d 184, 192 (Utah 1984). From all the evidence in this case, the court cannot say that the state's judgment as to the plaintiffs' true market value is wrong.[29]
The state suggests that its methods have the advantage that they are used consistently to value all centrally assessed property, so if the method produces any error in valuations, the effect is not to discriminate against the railroad. Presumably, if application of the same method overvalues or undervalues all commercial and industrial property in the state equally, there is no discrimination against railroads. However, the state concedes that it did not treat all centrally assessed property equally for the assessment years in question. For 1984 and 1985 it assessed all centrally assessed property using its discarded methodology. If one of the 350 centrally assessed property owners appealed, the state prepared a new assessment based on its new methodology, as it did in this case. Thus, the state did not treat all centrally assessed property equally in 1984 and 1985.
Moreover, even if the state did treat all centrally assessed property equally (as it claims to do now), it may still have violated the 4R Act if its uniform method has the effect of overvaluing railroads. It is no defense under the 4R Act "to say that the state may also be discriminating against ... other companies." Louisville & Nashville R.R. Co. v. Louisiana Tax Comm'n, 498 F.Supp. 418, 422 (M.D.La.1980).[30]
*556 Nevertheless, the state's argument may have some force. If the court were to require the state to use Dr. Schoenwald's valuation methods, the state would have to apply the methods to all centrally assessed property so that the discriminatory effect of the state's valuations could be properly measured. The court has found no evidence that Congress intended the 4R Act to dictate how a state must value non railroad property. If, as it appears from the record, all centrally assessed properties are now appraised using the methods the state used in its current appraisals of the plaintiff railroads, that may be reason to give those appraisals greater weight.
But the court believes that it should not disturb the state's choice of methodology for other reasons as well. From the testimony of the state's witnesses, the court concludes that the state's appraisers sincerely seek to arrive at what they consider to be the railroads' true market value and that, to that end, they constantly reevaluate their methods and change them when they become convinced that they are wrong.[31] The state's witnesses also testified that appraisal methods and philosophy are continually changing, presumably for the better, and that they try to keep current on new developments in the field without regard for the source, that is, whether the developments be from other state appraisers or from industry experts. Were this court to conclude that the 4R Act codified the Schoenwald method of valuation, it would prevent states from critically examining their appraisal methods and would discourage them from adopting new and better methods as they become accepted by the appraisal profession.
For all of these reasons, the court concludes that the 4R Act no more enacts the Schoenwald method of valuation than the fourteenth amendment enacts Herbert Spencer's "Social Statics." Cf. Lochner v. New York, 198 U.S. 45, 75, 25 S.Ct. 539, 546, 49 L.Ed. 937 (1905) (Holmes, J., dissenting).
All parties must remember that the purpose of producing a figure as to value, whether we label it "fair cash value" or "true market value," is to provide a figure against which one may then apply the tax percentage to arrive at what is due and owing by the taxpayer to the taxing unit. If one has a choice of methods and chooses a method with a rational footing and is *557 consistent and evenhanded in applying the method to all comparable properties, then conceptually the end result should be payment by taxpayers of a tax bill that is not disproportionate to the like payments of all other comparable taxpayers. The court holds that, as long as the state's methodology has a rational basis and was not chosen for a discriminatory purpose, the court will not disturb that choice. The court concludes from all the evidence that the state's methodology has a rational basis and was not chosen with the intent of overvaluing railroads. Thus, it will not second-guess the state's choice of method.
Even if the court were forced to choose among the competing methodologies, the court believes that the state's methodology has much to commend it. Not only does the state consistently use essentially the same approach for all centrally assessed property, but also its approach is based on historical data and market data readily available both to investors and to the state.[32] Moreover, it is easy to apply  an important consideration given the state's limited resources and the tremendous time pressures under which the state's appraisals must be prepared. See, e.g., Tr. at 339 & 402. For example, although a yield capitalization model is more elegant and might be preferred to a direct capitalization model, Mr. Fitzgerald, one of the plaintiffs' experts, testified that it took him two and one-half years, working full time, to value seven railroads, an average of over four months for each. See id. at 2068. The state simply does not have that luxury. Given its time constraints, it may legitimately choose an approach that is easier to apply than a more precise but more complex model.
In many respects, the state's methodology is closer to Dr. Schoenwald's than is Messieurs Goodwin and Ifflander's. For example, both the state and Dr. Schoenwald use a five-year average of NROI as the basis for their income calculations, whereas Mr. Goodwin and Dr. Ifflander use projections based on strategic plans known more for their inspirational value than for their prediction value and on a form of regression analysis discredited by the plaintiffs' statistical expert. Both the state and Dr. Schoenwald use the full debt rate in determining the cost of debt, whereas Mr. Goodwin and Dr. Ifflander use what they call current yield. Both the state and Dr. Schoenwald treat current assets and current liabilities in their stock-and-debt approach; Messieurs Goodwin and Ifflander do not. Both the state and Dr. Schoenwald allocate both debt and equity to the railroad. Mr. Goodwin and Dr. Ifflander allocate only equity. And in the cost approach both the state and Dr. Schoenwald purport to measure obsolescence based on the entire railroad industry; the other appraisers do not. See generally id. at 1898-1913 (Dr. Schoenwald's summary of the basic differences among the three approaches).
Even if the court were inclined to require the state to apply yield capitalization rather than direct capitalization, however, the court would not require it to apply the Schoenwald method of yield capitalization (that is, the expansion model). The Schoenwald method is based on a critical assumption, namely, that r equals k. The assumption is problematic at best. It was debated at length during the course of the trial. Needless to say, there was no consensus among the experts (who included several Ph.Ds in finance) about the reasonableness of the assumption. The experts vigorously disputed the issue, predictably aligning themselves according to the party on whose behalf they were called to testify.[33]*558 Without deciding the reasonableness of the assumption, the court can at least say that the assumption would appear to be less than self-evident and not whole-heartedly accepted in the finance community, judging from the expert testimony.
Dr. Schoenwald attempted to prove the validity of his assumption by showing that historically the railroads have failed to earn a return commensurate with the cost of capital. See pltffs' ex. 95(a). (Said exhibit is annexed to this opinion as appendix B). In exhibit 95(a) Dr. Schoenwald calculated a value for UP using his expansion model based on UP's average NROI for the period 1950-54. Using his expansion model, he valued the railroad at $581,514,000. He then did a more traditional yield capitalization analysis for the period 1955-84, discounting the actual net cash flows for those years based on the actual discount rates and adding a terminal value based on the average NROI for the period 1980-84, and concluded that the actual total market value of the railroad's net cash flows from 1955 into perpetuity was only $247,504,000. Thus, he concluded, his model actually overvalued UP by more than double, showing the r did not even equal k for UP over the last thirty years.
Mister Goodwin and Doctors Ifflander and Pettit criticized Dr. Schoenwald for using actual, historical figures. They argued that the value of the railroad as of January 1, 1955, depended on what investors would have been willing to pay for it, which in turn would have depended on their expectations. They further argue that no one could have accurately predicted the actual numbers, which Dr. Schoenwald uses. Implicit in their argument is that investors are overly optimistic and would have projected much higher cash flows and lower discount rates than actually occurred. All Dr. Schoenwald tried to show was that, had the investors had perfect foresight and applied his model, they still would have overvalued the railroad. From this he concludes that his assumption that r equals k is a generous assumption.
Nevertheless, it appears to the court's untrained eye that exhibit 95(a) is flawed. It suffers from one of those classic "mismatches" that Dr. Schoenwald is fond of talking about. Dr. Schoenwald's expansion value is based on a discounted average NROI, yet the yield capitalization approach he compares it to is based on discounted net cash flows. It is apparent from exhibit 95(a) that NROI is substantially higher than net cash flows, especially for the early years of the study. For example, for the period 1955-59, the first five-year period for which complete data are available, the average NROI is over four times greater than the average net cash flow. Of course, under Dr. Schoenwald's expansion model, a *559 higher NROI translates into a proportionately higher final value. Thus, by using NROI for the period 1950-54 to value the railroad, Dr. Schoenwald arrives at a higher value than he would have reached had he used net cash flows for the same period. In other words, Dr. Schoenwald concludes that his model overvalues the railroad based on a comparison of an expansion value derived from high NROIs to a yield capitalization value derived from relatively low net cash flows.
Had Dr. Schoenwald compared values that were both based on net cash flows or both based on NROI, he may have reached very different results. For example, if one were to estimate the average net cash flow for the period 1950-54 by dividing NROI (Dr. Schoenwald's capitalized income stream) by four, it would reduce his expansion value accordingly and might turn out that his model actually under valued the railroad significantly. Unfortunately, exhibit 95(a) omits all the data the court needs to make the proper comparison. At best, however, the court concludes that exhibit 95(a) only supports Dr. Schoenwald's second assumption  that NROI is a generous estimate of net cash flow[34]  and not his primary assumption, namely that r is no greater than k.
Dr. Schoenwald also tried to prove his assumption that r is no greater than k by calculating expected growth rates and comparing them to the expected growth that the investment publication Value Line, the defendants' Bible, projected for the same time period. Using the basic formula that growth (g) equals retained earnings (b) times the rate of return (r) and using the ICC's cost of capital for the rate of return (based on his assumption that r equals k), Dr. Schoenwald concluded that not even Value Line expected the railroads to grow at even an expansionary growth rate. See Tr. at 2059-64; 2117-19; pltffs' exs. 464 & 465. However, Dr. Ifflander testified that the calculated growth rate (b × r) showed growth in earnings, and if one used return on equity (ROE) for r and compared the calculated growth rate with Value Line's projected growth rate for earnings, the railroads as a whole were projected to grow at a rate faster than Dr. Schoenwald's expansionary model allows for.[35]See Tr. at 2230-32; defs' ex. 236.
Rather than assuming that r equals k, the state lets the market decide the values of r and k. Implicit in the market price of a security are the market participants' determinations of the alphabet soup of economic variables for the company  r, k, g and b. It appears that at least some investors believed that r would be greater than k for the plaintiff railroads during the assessment years. See, e.g., Tr. at 1504-06; intervenors' ex. 8. Philip Anschutz bought the D & RG (or, more precisely, its holding company, Rio Grande Industries) in 1984, one of the assessment years, and in fact paid a premium for the company's stock,[36] suggesting that he viewed the railroad as a good investment that could return a rate greater than the cost of capital.[37]
*560 Assuming for the moment that Dr. Schoenwald's conclusion as to historical facts is correct, that does not necessarily mean that his model correctly values the railroad. Looking at history, the willing seller may conclude that r is no greater than k. Indeed, that may be why he wants to sell  because he cannot earn even his cost of capital. Nevertheless, regardless of past performance, it seems somewhat counterintuitive to suggest that in valuing a prospective investment willing buyers assume that they will not be able to earn a return at least equal to their cost of capital. Otherwise, one would think that they would look elsewhere to invest their money. Since the elusive true market value depends on both a willing buyer and a willing seller, the assumption that r is no greater than k may at best be half true, and, as Justice Frankfurter used to observe, a half-truth is often a whole lie. See P. Elman, Response, 100 Harv.L.Rev. 1949, 1952 (1987).
The court does not have to decide the reasonableness of the assumption, however, because the Schoenwald valuation method suffers from a more serious defect. There is no evidence that those in the business of valuing railroads for buyers and sellers actually use Dr. Schoenwald's expansion model.[38] For example, when the board of directors of Rio Grande Industries (the holding company for D & RG) was deciding whether to accept Mr. Anschutz's offer to buy the company, it did not ask Dr. Schoenwald to value the railroad. Rather, it commissioned a study by the investment firm of Morgan Stanley, and Morgan Stanley did not value the railroad using Dr. Schoenwald's expansion model. See Tr. at 1241; defs' ex. 155. Its study used a discounted cash flow model similar to the method Messieurs Goodwin and Ifflander used in the 1984 appraisal of UP and also, as a check, applied various price multiples in a fashion similar to the state's appraisal and, incidentally, with results closer to the state's appraisal than to Dr. Schoenwald's.[39]
On the other hand, it is undisputed that the state's methods are used by other professional appraisers and by market analysts. See, e.g., Tr. at 1682 (testimony of Mr. Voytko that P/E ratios are widely used by security analysts). Dr. Schoenwald himself used price-earnings multiples to value the nonrailroad subsidiaries of the railroad holding companies in his stock-and-debt approach.[40] The state's direct capitalization approach may not be the preferred approach of the more sophisticated analysts, but at least analysts generally use price-earnings multiples as a check on their yield capitalization results. Moreover, the ICC used a direct capitalization method in analyzing the offers of competing railroads' to buy the core lines of the Milwaukee Railroad and concluded that, of the three methods it used to evaluate the offers, "the price-to-earnings (P/E) ratio is a more reliable basis to make an evaluation, since it is less susceptible to outside influences or to speculative considerations." Defs' ex. 17 *561 at 54; see also Tr. at 560-63. The ICC also used a direct capitalization approach when it decided the question of compensation for the trackage rights the D & RG was awarded as a result of the Union Pacific  Missouri Pacific merger. See defs' ex. 18 at 4. Perhaps most telling, the D & RG itself argued that the interest rental portion of the compensation should be calculated using a price-earnings multiple, id. at 7, and UP agreed, id. at 8. Thus, the plaintiffs themselves have used a form of direct capitalization to determine value.
The plaintiffs argue that the state's appraisals are flawed because the state looks to the stock market for both its income and its stock and debt approaches. Because both approaches depend on the same source, they argue, they cannot produce independent and hence accurate results. Dr. Schoenwald's income approach has an advantage over the state's, they suggest, in that it does not depend on market data for its conclusions. Thus, it provides an independent indicator to compare to the stock-and-debt indicator of value and is therefore the better method.
Of course, nothing in the 4R Act requires a state to use three separate and independent indicators of value. Dr. Schoenwald himself uses at most only two indicators of value. See supra note 10.[41] The fact that the state looks to the stock market for the data for two of its approaches does not mean that its appraisals are flawed. Rather, it merely reflects the state's underlying assumption, namely, that the stock market is the best indicator of a company's value. Given all the evidence, the court cannot say that that assumption is any less reasonable than Dr. Schoenwald's  namely, that r equals k.[42] Consequently, the court believes that the state's income indicator of value is a proper estimate of true market value.
While the choice between the parties' income approaches may present a choice between equally reasonable alternatives, the court believes that the defendants' stock-and-debt approach is more reasonable than Dr. Schoenwald's and arrives at a more accurate indicator of value. Dr. Schoenwald assumes that the value of the railroad is whatever is left over after valuing the other components of the holding company. While that assumption is theoretically sound, as the state's experts pointed out, it makes the railroad bear the burden of any measurement errors. A number of small errors valuing the other properties would create a large error in the value of the railroad. For example, Dr. Ifflander suggested that Dr. Schoenwald may have overvalued Champlin Petroleum, a subsidiary of Union Pacific Corporation, the holding company, by as much as a billion dollars. Using the Schoenwald method, that error alone would translate into a billion dollar error in the railroad's value. The plaintiffs' own witness, Mr. Fitzgerald, called Dr. Schoenwald's stock-and-debt method "a discredited activity which I place very little judgment on," Tr. at 2104, one which could result in "a cascade of capricious error" in the railroad's value, id. at 2106. The court believes that the state's allocation method arrives at a more accurate figure by allocating not only the stock price but also the risk of error.
In short, the court concludes that the plaintiffs have not shown that Dr. Schoenwald's methodology produces a better result. There is thus no reason to disturb the state's choice of method.

C. The State's Valuation
Ordinarily, the court's conclusion in part I-B that the state's valuation methods are reasonable and acceptable would end the dispute. The railroads could appeal any alleged error in applying the state's methods to the state tax commission. Once the tax commission (and the state courts if necessary) had corrected any errors in applying the method, this court could then simply plug the state's final valuation figure into the equation and determine *562 whether the 4R Act had been violated. However, because the state in this case relies on appraisals that were newly prepared for this proceeding, the plaintiffs have not had a chance to challenge the application of the state's chosen methods before the tax commission. Therefore, the court will consider the plaintiffs' major claims of error in the state's application of its methods.
The plaintiffs first claim the state erred in applying its direct capitalization method under its income approach. The state's direct capitalization rates or earnings-price ratios are not simply the E/Ps for the subject companies but are composites for the railroad industry derived from comparing the E/Ps and other financial data of a number of railroads. Everyone agrees that, to be useful, the companies compared must in fact be comparable to the subject railroad. The parties dispute which other railroads are truly comparable to UP and D & RG. The plaintiffs claim that there are no true comparables. That is just another way of arguing that the state should not have used a direct capitalization approach in valuing the railroads. For the reasons discussed in part I-B, the court concludes that the state's approach is acceptable. There may be no perfect comparable, but the evidence suggests that that fact does not prevent appraisers and other analysts from comparing railroads and valuing them based on their comparisons. The state's approach has an advantage over Mr. Goodwin's and Dr. Ifflander's in that it at least tries to select the most comparable companies and eliminates the so-called outliers. The state has offered plausible reasons for its choice of comparables. Moreover, at least in the case of the UP for assessment year 1984, the state's choice coincides with those companies Mr. Voytko, the plaintiffs' witness, said he considered the most comparable. Compare Tr. at 1655-61 (Mr. Voytko's testimony), with common ex. 32 at S/2. In the ultimate analysis, the choice of comparables is a judgment call by the particular appraiser. This court cannot say that the railroads the state chose are not comparable or even that they are not the most comparable. It therefore declines to disturb the state's choices.
The plaintiffs next argue that the state erred by applying its E/P ratios to the wrong earnings figure. It claims that the state has created a mismatch by using a current E/P and applying it to projected earnings. The court concludes that the mismatch, if any, is insignificant.
The state bases its E/Ps on Value Line's so-called trailing P/Es, which in turn relate a current price to the last twelve months' earnings. See Tr. at 956; defs' ex. 28 at B/2. Thus, trailing P/Es are based on historical data.[43] The state applies this trailing ratio to an earnings figure that, although a projection, is also based on historical data.[44] Although the *563 two historical periods do not correspond completely, because the state weights the earnings figures to arrive at its five-year average, the earnings for the last twelve months receive the greatest weight. Because those earnings relate directly to the trailing ratio, there is a match, though perhaps an imperfect match. The price is at least roughly matched to the earnings that produced it.
The state's approach tries to establish a relationship between price and earnings based on so-called normalized data, that is, data that reflects historical trends, at the same time minimizing the effect of anomalous data. It does this by a five-year weighted average of earnings and by using an E/P derived from the industry and not merely from the subject railroad. It is, in effect, not the E/P for any one railroad but for a hypothetical, composite railroad. The court does not believe that Dr. Schoenwald's proposed alternatives would necessarily produce a better result. For example, to increase the E/P, as Dr. Schoenwald does, see, e.g., pltffs' ex. 475, based on a projected "increase" in earnings (which is really just a normalized earning figure) in effect begs the question by assuming what effect such an increase in earnings will have on price (namely, none). Similarly, to apply the trailing E/P to actual earnings for the year, as Dr. Schoenwald also does, see, e.g., pltffs' ex. 476, does not establish the relationship between price and projected income and may produce a skewed result if the earnings for that particular year were atypical for any reason, for example, because of unusual capital expenditures undertaken during the year.[45]
The plaintiffs next argue that the state appraisals err in their treatment of intra-company debt in the stock-and-debt approach because the stock market does not look at intracompany debt in valuing a company. However, Mr. Prawitt testified that he prepared his stock-and-debt analysis based on the railroad's balance sheet and that debts among the railroad and affiliated entities in effect offset each other on the balance sheet. The court believes there was nothing improper about the state's treatment of intracompany debt.
The court has considered the plaintiffs' other criticisms of the state appraisals and has rejected them.[46] In short, the court accepts the state appraisals prepared by Mr. Prawitt as the best evidence of the plaintiffs' true market value as of the assessment dates.

D. Conclusions
The court holds that, for purposes of applying the 4R Act to the state's assessments of the plaintiff railroads, the true market value of the plaintiffs for the assessment years in question was as follows:


          1984                1985
UP        $3.7 billion        $3.4 billion
D & RG    $320 million        $320 million

The court finds that the portion of the railroads' true market value that should be allocated to Utah for the assessment years is as follows:[47]


          1984                1985
UP        4.99%               4.97%
D & RG    28.39%              26.81%

Thus, the true market value of the railroads' rail transportation property in Utah for the assessment years was:


          1984                1985
UP        $184,630,000        $168,980,000
D & RG    $90,848,000         $85,760,000

*564 The assessed value of the plaintiffs' rail transportation property in Utah was as follows:[48]


          1984                1985
UP        $35,928,000         $39,760,000
D & RG    $19,305,200         $20,048,565

Thus, the ratio of assessed value to true market value was as follows:


          1984                1985
UP        19.46%              23.53%
D & RG    21.25%              23.38%


III.

THE PLAINTIFFS' EQUALIZATION CLAIMS
The court's conclusions in part II-D of this opinion give the left half of the equation required by the 4R Act, namely, the ratio of assessed value to true market value of rail transportation property within the state. See supra note 3. The parties have stipulated to the right half of the equation, namely, the ratio of assessed value to true market value for all other commercial and industrial property in the state. The stipulation presents the court with two scenarios, depending on whether or not the court upholds a state statutory scheme that discounts the assessed value of real property in the state an additional twenty percent.[49]
Section 59-5-4.5 of the Utah Code stated:
When the county asses[s]or uses the comparable sales or cost appraisal method in valuing taxable property for assessment purposes, the assessor is required to recognize that various fees, services, closing costs, and other expenses related to the transaction lessen the actual amount that may be received in the transaction. The county assessor shall, therefore, take 80% of the value based on comparable sales or cost appraisal of the property as its reasonable fair cash value for purposes of assessment.
Utah Code Ann. § 59-5-4.5(1) (Supp. 1986).[50]
Two county assessors testified that local assessments of commercial and industrial real property are generally based on the cost appraisal method. See Tr. at 2344, 2351, 2374.[51] The defendants therefore argue *565 that, for purposes of the 4R Act, the true market value of locally assessed commercial and industrial property should be 80 percent of the appraised value, as required by the statute.
The state's intent in passing the discount statute appears to have been to tax real property owners only on what they might expect to receive from a sale of their property and not on a hypothetical gross sales price.[52] That intent may be admirable. Moreover, the statute may pass constitutional muster.[53] Nevertheless, the court concludes that applying the statute to determine assessment ratios under the 4R Act discriminates against the railroads by artificially increasing the ratio for other commercial and industrial property.
The 4R Act requires a comparison between two ratios, and, as all the experts in this case agreed, for comparisons to be valid the items compared must be comparable. That which is compared under the 4R Act is "true market value." Although the statute does not define "true market value," the experts all basically agreed that true market value (or its various synonyms) is the price that a willing and knowledgeable seller and a willing and knowledgeable buyer would agree on in an arm's length transaction. See, e.g., Tr. at 12 (Dr. Schoenwald's definition of fair market value). The fact that the seller might not net the sale price does not mean that that price is not true market value.[54]
The evidence in this case was that the figures arrived at using the comparable sales and cost appraisal methods of valuation  before applying any discount  are considered true market value. See, e.g., Tr. at 2302 (testimony of Max Arnold), 2361-62 (testimony of Steven C. Bexell); common ex. 11 (Utah State Tax Commission Assessment Sales Ratio Study for 1984) at 2 (referring to the undiscounted values as "fair market value").[55] In arriving at the railroads' true market value, the state relies in part on a cost appraisal method, yet it does not reduce its final cost indicator of value by 20 percent. Similarly, its stock-and-debt approach is a form of comparable sales appraisal method, yet the state does not reduce its stock-and-debt indicator of value by 20 percent, nor does it deduct so-called transaction costs, such as brokerage commissions, in arriving at its final stock-and-debt indicator of value. Thus, if the court is to compare true market value to true market value, it should compare values before any adjustments for transaction costs or other so-called intangibles are made.
*566 In short, the court concludes that, for purposes of the 4R Act, the true market value of "all other commercial and industrial property" in the state of Utah must be determined before the 20 percent discount statute is applied. Cf. Louisville & Nashville R.R. Co. v. Department of Revenue, 736 F.2d 1495 (11th Cir.1984) (an across-the-board reduction in assessed values of commercial and industrial properties under a state statute authorizing reductions in values to reflect costs of sale constituted discrimination in violation of the 4R Act because it "hand[ed] non-selling local property owners a windfall ... that was not bestowed on railroads").[56] This does not mean that the state cannot continue to give the 20 percent discount to locally assessed real property. It simply means that, in determining whether the state's assessments of railroads discriminates against the railroads in violation of the 4R Act, the court must consider the value of locally assessed real property before the statutory discount is applied. The state may still be free to choose to tax real property on the basis of the net amount the property owner could expect to receive from a sale of his property. But that net amount is not "true market value" as that term is used by appraisers and in the 4R Act.
Based on the stipulation of the parties, the court finds that the ratio of assessed value to true market value for all other commercial and industrial property within the state for assessment year 1984 was 15.4 percent and for assessment year 1985 was 16.13 percent.

IV.

CONCLUSION
Based on the court's conclusions in part II-D and part III of this opinion, it is clear that the state of Utah has discriminated against the plaintiff railroads in its tax assessments of the plaintiffs for the years 1984 and 1985 in that it has assessed them at a higher rate than it assessed all other commercial and industrial property within the state for the same period. However, the 4R Act only authorizes relief if the ratio of assessed value to true market value for rail transportation property exceeds the ratio for all other commercial and industrial property "by at least 5 per centum." Pub.L. No. 94-210 § 306(2)(c), 90 Stat. at 54. The court must therefore compare the various assessment ratios for each of the plaintiffs and for "all other commercial and industrial property" in the state for each assessment year to determine whether the plaintiffs are entitled to relief. The percentage by which UP and the D & RG were overvalued for each of the assessment years is as follows:


          1984            1985
UP        26%             46%
D & RG    38%             45%

Thus, the plaintiffs are entitled to relief under the 4R Act.[57]
The defendants are hereby ORDERED to assess the plaintiffs as follows: For assessment year 1984, the defendants are ORDERED to assess the plaintiffs based on an assessed value that is 15.4 percent of their true market value as determined by the court or stipulated to by the parties. For assessment year 1985, the defendants are ORDERED to assess the plaintiffs based on an assessed value that is 16.13 percent of their true market value as determined by the court or stipulated to by the parties. The defendants are hereby ENJOINED from collecting property taxes from the plaintiffs for assessment years 1984 and 1985 based on assessed values that bear a greater ratio to true market value than 15.4 percent and 16.13 percent respectively.
IT IS SO ORDERED.


*567 APPENDIX A


                                 Comparison of Appraisals[1]
-------------------------------------------------------------------------------------------------
                                         UNION PACIFIC
                                              1984
-------------------------------------------------------------------------------------------------
                                                                                     Goodwin &
                                                 Schoenwald           State          Ifflander
                                                 (ex. C-30)         (ex. C-32)       (ex. C-31)
Cost Approach
Net book value                                    5,555,803          6,205,607        6,200,299
Obsolescence                                     (2,815,681)        (1,828,350)      (1,942,554)
                                                 ___________        ___________      ___________
Cost indicator                                    2,740,122          4,377,259        4,257,746
Income Approach
Income estimate                                                        320,000          356,910
Capitalization rate (direct cap)                                         9.77%            8.90%
                                                                    ___________      ___________
Capitalized value of income                                          3,275,333        4,010,229
Construction in progress                                                81,972
Capitalized value, operating leases                                     92,118
                                                                    ___________      ___________
Income indicator (direct cap)                                        3,449,423        4,010,229
Income estimate (NROI + net lease rentals)          338,643                            N/A
Capitalization rate (yield cap)                      15.40%                              15.11%
                                                   _________                         ___________
Income indicator (yield cap)                      2,198,981                           4,577,513
Stock and Debt Approach
Market value, R.R. stock                                             3,074,843        3,000,000
R.R. long-term debt                                                  1,491,073        1,414,415
R.R. net current assets & liabilities                                 (115,622)
                                                                    ___________      ___________
R.R. value                                                           4,450,294        4,414,415
Allocation factor (applied only to stock value
  by G & I)                                                             83.98%           89.39%
                                                                    ___________      ___________
Market value, R.R. operating property                                3,737,350        4,096,115
Leased equipment                                                       106,017           34,246
                                                                    ___________      ___________
Stock and debt indicator                                             3,843,367        4,130,361
Total value, parent's stock & debt               10,549,892
Total value, non-railroad & non-operating
  property                                       (7,531,760)
                                                 ___________
Stock and debt indicator                          3,018,132
Correlated Values
Cost indicator                                    2,740,122          4,377,259        4,257,746
Income indicator (direct cap)                                        3,449,423        4,010,229
Income indicator (yield cap)                      2,198,981                           4,577,513
Stock and debt indicator                          3,018,132          3,843,367        4,130,361
                                                 __________         __________       ___________
Correlated market value                           2,608,557          3,700,000        4,100,000



*568
-------------------------------------------------------------------------------------------------
                                         UNION PACIFIC
                                              1985
-------------------------------------------------------------------------------------------------
                                                                                     Goodwin &
                                                 Schoenwald           State          Ifflander
                                                 (ex. C-33)         (ex. C-35)       (ex. C-34)
Cost Approach
Net book value                                    5,671,608          6,475,611        6,467,163
Obsolescence                                     (3,187,444)        (2,076,376)      (2,661,884)
                                                 ___________       ____________      ___________
Cost indicator                                    2,484,164          4,399,234        3,805,279
Income Approach
Income estimate                                                        310,000          366,887
Capitalization rate (direct cap)                                        11.98%           10.30%
                                                                   _____________     ___________
Capitalized value of income                                          2,587,646        3,562,010
Construction in progress                                                85,752
Capitalized value, operating leases                                     87,113
                                                                   _____________     ___________
Income indicator (direct cap)                                        2,760,511        3,562,010
Income estimate (NROI + net lease rentals)          310,815
Capitalization rate (yield cap)                      16.00%
                                                  __________
Income indicator (yield cap)                      1,942,594
Stock and Debt Approach
Market value, R.R. stock                                             2,674,843        2,600,000
R.R. long-term debt                                                  1,427,374        1,322,267
R.R. net current assets & liabilities                                   32,454
                                                                   ____________      ___________
R.R. value                                                           4,134,671        3,922,267
Allocation factor (applied only to stock value
  by G & I)                                                             81,77%           86.69%
                                                                   ____________      ___________
Market value, R.R. operating property                                3,380,866        3,567,207
Leased equipment                                                        93,256           28,640
                                                                   ____________      ___________
Stock and debt indicator                                             3,474,122        3,604,847
Total value, parent's stock & debt                8,881,003
Total value, non-railroad & non-operating
  property                                       (6,290,824)
                                                 ___________
Stock and debt indicator                          2,590,179
Correlated Values
Cost indicator                                    2,484,164          4,399,234        3,805,279
Income indicator (direct cap)                                        2,760,511        3,562,011
Income indicator (yield cap)                      1,942,594
Stock and debt indicator                          2,590,179          3,474,122        3,604,847
                                                 ___________       ____________      ___________
Correlated market value                           2,266,387          3,400,000        3,600,000
-------------------------------------------------------------------------------------------------
                                      DENVER & RIO GRANDE
                                              1984
-------------------------------------------------------------------------------------------------
                                                                                     Goodwin &
                                                 Schoenwald           State          Ifflander
                                                 (ex. C-36)         (ex. C-38)       (ex. C-37)
Cost Approach
Net book value                                      467,739            541,000          537,697
Obsolescence                                       (286,022)          (197,962)        (207,282)
                                                 ___________       ____________      ___________
Cost indicator                                      181,717            343,039          330,415
Income Approach
Income estimate                                                         23,000           25,851
Capitalization rate (direct cap)                                         8.28%            8.30%
                                                                   ____________      ___________
Capitalized value of income                                            277,778          311,453



*569
                                                                                     Goodwin &
                                                 Schoenwald           State          Ifflander
                                                 (ex. C-36)         (ex. C-38)       (ex. C-37)
Construction in progress                                                 8,163
Capitalized value, operating leases                                      5,954
                                                                    ___________      ___________
Income indicator (direct cap)                                          291,894          311,453
Income estimate (NROI + net lease rentals)            25,183
Capitalization rate (yield cap)                       15.40%
                                                 ___________
Income indicator (yield cap)                         163,526
Stock and Debt Approach
Market value, R.R. stock                                               350,000          300,000
R.R. long-term debt                                                     87,657           75,757
R.R. net current assets & liabilities                                   (5,025)
                                                                    ___________      ___________
R.R. value                                                             432,632          375,757
Allocation factor (applied only to stock value
  by G & I)                                                             81.87%           89.43%
                                                                    ___________      ___________
Market value, R.R. operating property                                  354,187          344,047
Leased equipment                                                         8,946            6,771
                                                                    ___________      ___________
Stock and debt indicator                                               363,133          350,817
Total value, parent's stock & debt                   677,366
Total value, non-railroad & non-operating
  property                                          (331,531)
                                                 ___________
Stock and debt indicator                             345,835
Correlated Values
Cost indicator                                       181,717           343,039          330,415
Income indicator (direct cap)                                          291,894          311,453
Income indicator (yield cap)                         163,526
Stock and debt indicator                             345,835           363,133          350,817
                                                 ___________        ___________      ___________
Correlated market value                              254,681           320,000          330,000
-------------------------------------------------------------------------------------------------
                                      DENVER & RIO GRANDE
                                              1985
-------------------------------------------------------------------------------------------------
                                                                                     Goodwin &
                                                 Schoenwald           State          Ifflander
                                                 (ex. C-39)         (ex. C-41)       (ex. C-40)
Cost Approach
Net book value                                                         598,509          585,883
Obsolescence                                                          (159,082)        (198,380)
                                                                    ___________      ___________
Cost indicator                                                         439,428          387,503
Income Approach
Income estimate                                                         27,000           30,727
Capitalization rate (direct cap)                                        11.00%           10.10%
                                                                    ___________      ___________
Capitalized value of income                                            245,455          304,232
Construction in progress                                                 1,582
Capitalized value, operating leases                                      5,038
                                                                    ___________      ___________
Income indicator (direct cap)                                          252,075          304,232
Income estimate (NROI + net lease rentals)
Capitalization rate (yield cap)
Income indicator (yield cap)
Stock and Debt Approach
Market value, R.R. stock                                               350,000          275,000
R.R. long-term debt                                                     79,394           82,405



*570
                                                                                     Goodwin &
                                                 Schoenwald           State          Ifflander
                                                 (ex. C-39)         (ex. C-41)       (ex. C-40)
R.R. net current assets & liabilities                                   13,999
                                                                    ___________      ___________
R.R. value                                                             443,393          357,405
Allocation factor (applied only to stock value
  by G & I)                                                             87.67%           93.22%
                                                                    ___________      ___________
Market value R.R. operating property                                   388,729          338,760
Leased equipment                                                         6,181            8,132
                                                                    ___________      ___________
Stock and debt indicator                                               394,910          346,892
Total value, parent's stock & debt                  491,129
Total value, non-railroad & non-operating
  property                                         (212,393)
                                                 ___________
Stock and debt indicator                            278,736
Correlated Values
Cost indicator                                                         439,428          387,503
Income indicator (direct cap)                                          252,075          304,232
Income indicator (yield cap)
Stock and debt indicator                            278,736            394,910          346,892
                                                 ___________        ___________      ___________
Correlated market value                             278,736[2]      320,000          325,000


APPENDIX B


                                            1955-1984
                       SCHOENWALD'S 5 YEAR VALUE FROM 1950-1954 FOR 1955 AY
                                     (ADJUSTED DISCOUNT RATE)
                                              (000)
                          1950-1954 5 YR NROI AVG. =            $34,193
                          DISCOUNT RATE                           5.88%
                          PRESENT VALUE                        $581,514
                                                                                PV
                                                          NET                DISCOUNT
                DEPRECIATION   DEFERRED     CAPITAL       CASH    DISCOUNT     RATE        PRESENT
YEAR    NROI  +   EXPENSE    +  TAXES  - EXPENDITURES  =  FLOW      RATE      FACTOR        VALUE
                                                                                    1
1955   43,739      25,007           0        61,914        6,832     5.88%     0.9445        6,453
1956   42,137      25,888           0        47,812       20,213     5.91%     0.8918       18,026
1957   38,818      26,847           0        60,239        5,426     6.20%     0.8397        4,556
1958   43,461      28,423           0        54,310       17,574     6.91%     0.7854       13,803
1959   36,957      32,746           0        70,093         (390)    6.68%     0.7362         (287)
1960   32,835      35,536           0        56,329       12,042     7.25%     0.6864        8,266
1961   31,814      38,032           0        49,898       19,948     7.40%     0.6391       12,749
1962   46,775      39,103           0        64,404       21,474     7.34%     0.5954       12,786
1963   51,112      41,428           0        75,803       16,737     7.35%     0.5546        9,282
1964   53,468      42,938           0       107,876      (11,470)    7.16%     0.5175       (5,936)
1965   66,944      45,942           0       121,323       (8,437)    7.20%     0.4827       (4,073)
1966   86,256      50,806           0       207,929      (70,867)    7.40%     0.4494      (31,848)
1967   81,458      54,572           0       147,546      (11,516)    7.99%     0.4161       (4,792)
1968   80,239      54,962           0        82,087       53,114     8.45%     0.3837       20,380
1969   81,553      55,828           0       144,169       (6,788)    9.17%     0.3515       (2,386)
1970  114,416      59,506           0       163,697       10,225    10.01%     0.3195        3,267
1971  108,234      61,301           0       147,239       22,296    12.57%     0.2838        6,328
1972  132,085      63,280           0       116,463       78,902    11.61%     0.2543       20,065
1973  151,342      65,833           0       137,610       79,565    10.95%     0.2292       18,236
1974  123,691      68,379      30,143       197,844       24,369    11.55%     0.2055        5,008
1975  112,872      73,838      31,758       205,527       12,941    12.98%     0.1819        2,354
1976  135,790      78,039      15,739       179,948       49,620    12.57%     0.1616        8,019



*571
                                                                                PV
                                                          NET                DISCOUNT
                DEPRECIATION   DEFERRED      CAPITAL       CASH    DISCOUNT     RATE        PRESENT
YEAR    NROI  +   EXPENSE    +  TAXES  - EXPENDITURES  =  FLOW      RATE      FACTOR        VALUE
1977  149,754      82,891      39,697       203,837       68,505    11.90%     0.1444        9,892
1978  179,842      86,441      16,315       250,076       32,522    11.63%     0.1294        4,208
1979  190,818      93,698      42,860       308,504       18,872    12.59%     0.1149        2,168
1980  214,351     105,279      44,920       379,586      (15,036)   15.11%     0.0998       (1,501)
1981  214,407     109,989     118,790       136,779      306,407    17.50%     0.0849       26,014
1982  127,733     110,143       9,513       102,861      144,528    18.25%     0.0718       10,377
1983  131,956     109,343      68,538        61,118      248,719    16.50%     0.0616       15,321
1984  113,168     104,724      30,128       112,038      135,982    15.40%     0.0534        7,261
1985                                                                16.00%
                                                                                          ________
                                                                                          $193,996
5 YEAR NROI AVERAGE 1980-1984 =   $160,323  DIVIDED BY   16.00% = $1,002,019   0.0534       53,508
                                                                                          ________
TOTAL MARKET VALUE OF NET CASH FLOW FROM 1955-1984 PLUS OUT YEAR INTO PERPETUITY          $247,504
                                                                                          ========
SCHOENWALD 5 YR NROI AVG 1950-1954 =   $34,193  DIVIDED BY  5.88% = $581,514        1     $581,514
SCHOENWALD OVER VALUATION (UNDER VALUATION)                                               $334,010

NOTES
[1]  The intervening counties are Box Elder, Cache, Carbon, Davis, Emery, Grand, Iron, Juab, Millard, Morgan, Piute, Salt Lake, Sanpete, Sevier, Summit, Tooele, Utah, Wasatch, Washington and Weber.
[2]  The wording and structure of section 306 were changed when the section was recodified as part of the revised Interstate Commerce Act. See Act of Oct. 17, 1978, Pub.L. No. 95-473, § 11503, 92 Stat. 1337, 1445-46. Because the recodification was not meant to change the substantive law, see id. § 3(a), 92 Stat. at 1466, this court will use the original language of section 306 for convenience and clarity.
[3]  The court's analysis can be expressed by a simple equation:
      Assessed value of rail transportation          Assessed value of all other commercial
      property                                       and industrial property
                                                 ?
      ----------------------------------------       ----------------------------------------   × 1.05
                                                 >
      True market value of rail transportation       True market value of all other commercial
      property                                       and industrial property

At the time of the assessments at issue in this case, Utah law required that all taxable property in the state not specifically exempt from taxation be assessed "at 20% of its reasonable fair cash value." See Utah Code Ann. § 59-5-1 (Supp.1985); see also infra note 6 ("reasonable fair cash value" is synonymous with "true market value"). Thus, the ratio for both rail transportation property and all other commercial and industrial property for the years in question should be .20.
In 1985 the statute was amended to make the assessed value the same as "reasonable fair cash value." However, the statute did not take effect until January 1, 1986. See 1985 Utah Laws ch. 165, § 64.
[4]  In other words, the parties have stipulated to the right half of the equation set forth in footnote 3, supra. Which stipulated value the court will ultimately apply depends on the court's holding on the plaintiffs' claim of de jure discrimination under the equalization aspect of this case. See infra part III.
[5]  Originally UP took the position that it was foreclosed from challenging the state's valuation of its property by the Tenth Circuit's decision in Burlington Northern Railroad Company v. Lennen, 715 F.2d 494 (10th Cir.1983), cert. denied, 467 U.S. 1230, 104 S.Ct. 2690, 81 L.Ed.2d 884 (1984). See Union Pac. R. Co. v. State Tax Comm'n, 635 F.Supp. 1060, 1063 (D.Utah 1986). However, the Supreme Court opened the door for UP to assert its valuation claims in this case by its decision in Burlington Northern Railroad Company v. Oklahoma Tax Commission, 481 U.S. 454, 107 S.Ct. 1855, 95 L.Ed.2d 404 (1987). Ironically, SP, which had asserted that Lennen did not preclude it from challenging the state's valuation, see 635 F.Supp. at 1065-66, is no longer asserting a valuation claim, it having settled its valuation dispute with the state.
[6]  Utah law requires that taxable property within the state be assessed on the basis of its "reasonable fair cash value." See Utah Code Ann. § 59-5-1; see also supra note 3. "Reasonable fair cash value" is equivalent to "market value." Kennecott Copper Corp. v. Salt Lake County, 122 Utah 431, 250 P.2d 938, 939-40 (1952). For simplicity, unless otherwise indicated the court shall use the terms "value" and "true market value" to refer to both "reasonable fair cash value" and "true market value."
[7]  The state's original assessment for UP for assessment year 1985 was based on a true market value of $4 billion. In this proceeding, the state relies on a new appraisal, which places the value of UP for 1985 at $3.4 billion.

The state initially valued the D & RG based on a true market value of $370 million for assessment year 1984. In June 1984 it revised its valuation based on a value of $340 million. In this proceeding it relies on a new appraisal placing the true market value of the D & RG at $320 million. Similarly, it initially valued the D & RG for 1985 at $375 million and now relies on a new appraisal placing the true market value at $320 million.
[8]  The results of the various appraisals are summarized in appendix A.
[9]  Cf. Louis L. Jaffe, Was Brandeis an Activist? The Search for Intermediate Premises, 80 Harv. L.Rev. 986, 991 (1967) ("It is, of course, one of the risks of subjecting complex controversies to judicial determination that the rules evolved compel arbitrary simplification").
[10]  Although he calculates a cost indicator of value, Dr. Schoenwald gives it no weight in determining the final value of the railroads. The other appraisers give it some weight but less than they give the other indicators of value.
[11]  The court uses the term "income" loosely. More precisely, what the appraiser tries to value is net cash flow, which Dr. Schoenwald defined as net operating income plus depreciation and deferred income taxes (where applicable) less capital expenditures. See pltffs' ex. 73. Because capital expenditures for railroads in recent years have generally exceeded depreciation and deferred taxes, Dr. Schoenwald has used net railroad operating income (NROI)  which he characterizes as a "generous" measure of net cash flows  as his income stream to capitalize.
[12]  All of the experts also basically agree on another variation of the basic model, the dividend model. See, e.g., pltffs' ex. 54; Tr. at 1088-89. The dividend model uses dividends paid out in year 1 as the income to be capitalized and is expressed by the following equation:
                      D1
                 V0 = ___
                      k-g

where D1 is the dividends at year 1 and g is the growth rate.
The basic formula was also sometimes recast to include another variable, b, which represents the percentage of the firm's earnings that it retains to reinvest:
                      E1(1-b)
                 V0 = _______
                        k-g
where E1 is the earnings in period 1. See Tr. at 1455; intervenors' ex. 6.
[13]  Mr. Goodwin and Dr. Ifflander used (or misused, from the plaintiffs' perspective) a standard yield capitalization or DCF model for their appraisal of UP for 1984, in which they projected the railroad's cash flows for the next five years, discounted them to present value and added a terminal value, representing the present value of all the cash flows after the five-year period. See common ex. 31 at 76-102. For all of the years in question, they also use a direct capitalization method, similar to the state's. See infra p. 550.
[14]  Dr. Schoenwald further assumes that net railroad operating income (NROI) is a generous estimate of net cash flow, see supra note 11, so he substitutes NROI for NCF in the equation. For his projected net railroad operating income for year 1 he uses an average of the railroad's NROI for the five previous years.
[15]  According to Dr. Schoenwald, a company may grow through new, additional investment, but if the returns on new investment are not greater than the cost of capital  that is, if the cost of the growth offsets any gain from the new investment  then there is no actual or net growth. Net growth occurs when the company earns more than the cost of its additional capital, and only net growth  as opposed to gross or expansion growth  increases net present value. A company that only earns its cost of capital may grow, and that growth may make the company worth more five years down the road, but that future growth adds nothing to the company's value today because it will cost the company as much as it will add to its value in the future. See Tr. at 33-39; pltffs' ex. 54.
[16]  The court has spared the reader the mathematical manipulations by which one gets from one formula to another. Suffice it to say that the various formulae appear to be mathematically correct and internally consistent if one accepts the underlying assumptions. It is a simple matter of applying mathematical principles to the basic formula. In making that application, however, one should bear in mind Robert Heilbroner's observation that "[m]athematics has given economics rigor; but alas, also mortis." The simplified formulae are no better than the basic formula and the experts' assumptions.
[17]  While recognizing that direct capitalization is not merely a variation of the yield capitalization model, by making certain assumptions, Dr. Ifflander showed how one might conclude that Dr. Schoenwald's expansion model also uses an earnings/price ratio for its capitalization rate (k). See Tr. at 1107-09.
[18]  For example, Dr. Schoenwald calculated an income indicator of value for UP for 1984 of $2,198,981,000, based on earnings of $338,643,000 and a capitalization rate of 15.4%. See common ex. 30 & 33 at 89. Lowering the capitalization rate just 1%, to 14.4%, increases the value of UP by almost 7%, to $2,351,687,500.
[19]  Were the court to undertake its own, independent appraisal, its choice of methods would enjoy undue sanction, and the application of its methods would be subject to many of the same types of criticisms that the parties' appraisals are subject to but without the same opportunity the parties have had to critique each other's appraisals.
[20]  The court's task is complicated by the fact that often, as here, the experts themselves cannot always agree whether the appraisals were properly performed or not.
[21]  None of the experts in this case suggest that all roads lead to Rome. Rather, the testimony was that two different methods will produce the same result only by coincidence. As one can see from appendix A, the varying methods the three sets of appraisers used produced widely varying results.
[22]  The plaintiffs suggest that, if anything, the state should have the burden of proving the validity of its new appraisals. See infra note 29.
[23]  It is well settled that the legislative history of precursors to a statute are relevant in construing the statute. See Burlington Northern Railroad Company v. Lennen, 573 F.Supp. 1155, 1160 n. 5 (D.Kan.1982), aff'd, 715 F.2d 494, 497 (10th Cir.1983), cert. denied, 467 U.S. 1230-31, 104 S.Ct. 2690, 81 L.Ed.2d 884 (1984), and cases cited therein.
[24]  The quoted passage from appendix B to Senate Report 1483 appears to have been taken from the testimony of James N. Ogden, Vice-President and General Counsel of the Gulf Mobile and Ohio Railroad Company, during hearings on Senate Bill 927. See Burlington Northern, 573 F.Supp. at 1161-62.
[25]  To the extent Lennen concluded from the legislative history that the whole valuation question was essentially off limits to federal courts, see 573 F.Supp. at 1164 ("the issue of the appropriate `true market value' of a railroad is generally not to be an issue in a Section 306 case"), it has since been overruled. See Burlington N. R.R. Co. v. Oklahoma Tax Comm'n, 481 U.S. 454, 107 S.Ct. 1855, 95 L.Ed.2d 404 (1987). However, this court agrees with Judge Rogers's conclusion that Congress did not intend "for the federal courts to become involved in establishing ... procedures for the states in the valuing of railroads." 573 F.Supp. at 1164. It is one thing to say that the 4R Act allows federal courts to review railroads' claims of overvaluation. It is quite another to say that the Act dictates a state's choice of valuation methods. The 4R Act may provide relief if a state overvalues a railroad by misapplying its chosen methodology or by using a methodology that has no rational basis or is chosen for the purpose of overvaluing railroads. See, e.g., Burlington N., 107 S.Ct. at 1859 (the railroad's only claim of discriminatory taxation was that the state had misapplied its own valuation methodology). But, this court believes, the Act does not necessarily provide relief just because the state's chosen methodology results in higher values than some other method the state could have chosen.
[26]  The court is reminded of the old story of the economist marooned with a companion on a desert island. A can of food washed up on the beach. The economist's starving companion asked him how they could open the can, to which the economist blithely replied, "Assume a can opener."
[27]  The vagaries of the stock market once prompted a member of the Council of Economic Advisors to suggest that market behavior could be explained not so much by market analysis but by psychoanalysis.
[28]  Indeed, perhaps the best evidence of the railroads' true market value is not any single appraisal but, assuming that each appraiser has performed his work accurately and in good faith, the average of all the appraisers' judgments concerning true market value.
[29]  In a 4R Act case "the burden of proof with respect to the determination of assessed value and true market value shall be that declared by the applicable State law." Pub.L. No. 94-210, § 306(2)(d), 90 Stat. at 55 (1976). The plaintiffs argue that the burden of proof should be on the state to prove its assessment is correct. They cite the court to no authority for this proposition. Rather, they argue that, under Utah law, once it is shown that a state's assessment is wrong, the burden shifts to the state to prove that its new assessment is correct, and, they note, the state has already admitted its original assessments were wrong. But see Utah Power & Light Co. v. Utah State Tax Comm'n, 590 P.2d 332, 335 (Utah 1979) (if the taxpayer claims error in a proceeding before the tax commission, "it has an obligation, not only to show substantial error or impropriety in the assessment, but also to provide a sound evidentiary basis upon which the Commission could adopt a lower valuation") (citations omitted). Even assuming that the plaintiffs' argument is correct, given the court's decision that the state was free to adopt the method of its choice, the court concludes that the state has met the burden of proving the correctness of its new assessments by a preponderance of the evidence.
[30]  Although it may not be a defense to say that all centrally assessed properties are overvalued as a result of the state's choice of methodology, if in fact they are it is likely that together all the owners of centrally assessed property will have sufficient political power to force the state to change its valuation methods. After all, it is not every property owner that can achieve beneficial legislation such as the 4R Act. As Auberon Herbert once observed: "It is the small owner who offers the only really profitable and reliable material for taxation.... He is made for taxation.... [H]e has less skill, and ingenuity as regards escape; and he still has a large supply of `ignorant patience of taxation.'" Quoted in F. Coffield, A Popular History of Taxation, quoted in A Dictionary of Legal Quotations 165 (S. James & C. Stebbings comp. 1987). The court, however, does not base its conclusions as to discrimination on the state's relative treatment of centrally assessed properties but on its conclusion as to the railroads' true market value.
[31]  Indeed, of all the appraisers in this case, the court was most impressed with the credibility of the state appraiser, Mr. Prawitt, and of his supervisor, Mr. Monson. Of all the appraisers, Mr. Prawitt seemed the only one who was not out to achieve a particular, predetermined result. Indeed, he testified that he prepared his appraisals without even looking at the state's earlier appraisals so that the earlier appraisals would not affect his conclusions. The other experts all had a theory to defend, which colored their choice of data and methods. Each appraisal required the appraisers to make numerous judgments, but the other appraisers often seemed to base their judgments on the end result, using a technique or methodology if it tended to support the desired result and changing it when convenient. For example, the plaintiffs criticized the state's witnesses for using average P/Es, arguing that a mechanical computation of averages ignored the factors that went into an informed judgment. See, e.g., Tr. at 1661-63. Yet they then turned around and argued that their true market value should be determined by mechanically computing the average of Dr. Schoenwald's income and stock and debt indicators of value (ignoring the cost indicator altogether), when the disparity between Dr. Schoenwald's income and stock-and-debt indicators was so great as to make one or the other suspect without even comparing Dr. Schoenwald's figures with the other appraisers'. See, e.g., Tr. at 1511. None of the appraisers may have been perfectly consistent, but Mr. Prawitt seemed most concerned with discovering an objective value and least committed to a particular theory or methodology.
[32]  For example, unlike Messieurs Goodwin and Ifflander, who place much weight  possibly too much  on the company's projections for the coming year, gleaned in part from internal company documents not available to the public generally, the state uses the weighted average of the five previous years' income to determine the railroad's projected income in its income approach.
[33]  The opinions of some of the experts as to whether or not r is greater than k appeared to depend to some extent on their opinion about the prospects of the railroad industry. At times it seemed the experts were testifying about two different industries. In Dr. Schoenwald's view, the railroads have been in decline since at least the 1920s and can never expect to earn a rate of return even equal to the cost of capital. In fact, it is a wonder that they are still in business. On the other hand, in the opinion of Messieurs Goodwin and Ifflander the Staggers Act, which was passed in 1980, ushered in a new Golden Age of railroading.

Perhaps there is more than one railroad industry. At least the railroad industry of the late 1800s was a far different industry from the railroad industry of the mid-1900s. Thus, Chesterton could write:
[W]hen I was a boy, which was just before the motor-car burst upon the world, I never dreamed of doubting that the railway-train dominated the whole future of the world. It was the latest great locomotive that man had invented.... To talk, as some people are now talking, of whether railways will become obsolete, or whether steam can be superseded, of whether railway stock will always be as safe as it was  all this would have been to me a prophecy as unintelligible as some of those Old Testament visions that seem a medley of wheels and wings and clouds. Railways had been firmly established before I was born; I never dreamed of doubting that they would remain exactly the same after I died.
G.K. Chesterton, Come to Think of It ... 16-17 (1931). Yet the railroads did change. Chesterton lived to see their economic power decline. Messieurs Goodwin and Ifflander would have the court believe that if Chesterton had lived another fifty years he would have seen the rebirth of the railroad industry. The railroads' experts, on the other hand, talk as though the railroads will never recover. But if they've changed once, they may change again.
There was testimony that the railroad industry is a cyclical industry. According to Messieurs Goodwin and Ifflander, the industry has come full circle. Perhaps only time will tell whether or not they are right. In any event, the court does not have to choose between the competing prognostications. The market makes its own choice. And the state's valuation methods, based on the market as they are, should reflect the market's outlook.
[34]  In fact, exhibit 95(a) casts doubt on Dr. Schoenwald's second assumption as well. Dr. Schoenwald justified his use of NROI as opposed to net cash flow on the grounds that NROI is a "generous" estimate of net cash flow. However, at least for the years from 1980 to 1984, the years that Dr. Schoenwald averaged for his 1985 income estimate, net cash flow was greater than NROI for UP, despite a negative net cash flow for 1980.
[35]  Even Dr. Ifflander conceded that, no matter how one compares projections with implied growth rates, the D & RG was not expected to achieve even expansionary growth for 1984. So the assumption that r is no greater than k may have been true for the D & RG for 1984.
[36]  The plaintiffs suggest that the stock market may not be the best indicator of a railroad's value. Given that Dr. Schoenwald's stock-and-debt approach consistently valued the plaintiffs higher than his income approach and that Mr. Anschutz was willing to pay a premium over the company's stock market price, the plaintiffs may be right. The stock market may undervalue railroads.
[37]  The plaintiffs point out that both Union Pacific and Southern Pacific also had the opportunity to buy the D & RG but turned it down. Of course, the fact that some investors or potential buyers may see the value of a company differently than others does not necessarily mean that there is no market for the company or that it is overvalued. In fact, differences of opinion as to value are what make for a market in the first place.
[38]  Mr. Fitzgerald of First Boston Corporation testified that in his yield capitalization method he uses a method similar to Dr. Schoenwald's to arrive at a terminal value, that is, a value for the cash flows after the last year of his analysis. However, his basic analysis is the traditional yield capitalization approach, similar to Messieurs Goodwin and Ifflander's, by which he forecasts future cash flows for a period of time  in his case, over a ten-year period. The terminal value in such an approach is only a small fraction of the total value.
[39]  Morgan Stanley concluded that the railroad's equity value was roughly $280 million. See defs' ex. 155 at ex. 1, p. 1. When the debt value is added to the equity value, the value becomes approximately $360 million, see Tr. at 1176, compared to the state's estimated value of about $389 million for the railroad's stock and debt. See common ex. 41 at S-1. To the stock and debt value must be added another $6 million or so for operating leases to arrive at a total stock and debt indicator of value. In comparison, Dr. Schoenwald's total value for the railroad for the same assessment year was less than $280 million.
[40]  If the use of price-earnings multiples in fact overvalues properties, as Dr. Schoenwald suggested in critiquing the appraisals of Messieurs Goodwin, Ifflander and Prawitt, then Dr. Schoenwald overvalued the holding companies' nonrailroad subsidiaries, and, under his stock-and-debt methodology, any overvaluation of the nonrailroad subsidiaries attributable to Dr. Schoenwald's use of price-earnings ratios would produce a commensurate undervaluation of the railroad. See infra p. 561.
[41]  In fact, for his 1985 appraisal of D & RG, Dr. Schoenwald used only one indicator. See appendix A, p. 67 n. 2.
[42]  The state's assumption was even supported by one of the plaintiffs' own witnesses. See Tr. at 1717 (testimony of James Voytko).
[43]  Messieurs Goodwin and Ifflander, on the other hand, use Value Line's "straddle" P/Es. The straddle P/E is based on the last one or two quarters' actual earnings and two or three quarters of projected earnings. The court believes that the use of trailing ratios produces a more objective and hence better result.
[44]  The state's projections, like Dr. Schoenwald's, are backwards looking in that they project future income based on past performance. The primary difference between the two is that the state weights previous years' NROI so as to put greater emphasis on more recent history.

The state also adjusts previous years' figures for inflation so that all the figures are in current dollars. The plaintiffs argue that such an adjustment is improper absent any evidence that inflation actually benefits rail assets, and, they claim, it does not. However, the state's inflation adjustment is not meant to indicate the effect of inflation on the assets but merely to enable the appraiser to look at history in terms of constant dollars. It may be, as Dr. Schoenwald suggests, that any adjustment for inflation is improper since the question is not buying power but actual, normalized earnings. The court cannot say from the evidence, however, that inflation has no positive effect on rail transportation property, and any error in the state's adjustment is partially offset by its weighting process, in which revenues from the oldest years (those most influenced by inflation) receive the least weight. Had the state based its projections on a straight five-year average, as Dr. Schoenwald did, instead of a weighted five-year average adjusted for inflation, its income figures would have been higher, resulting in higher overall values. Thus, any error in the state's use of an inflation factor is more than offset by its allegedly improper use of a weighted average.
[45]  The plaintiffs might argue that if the earnings for the year were atypical, the price-earnings ratio should also be atypical and applying the actual P/E to the actual earnings will still produce a correct result. However, the E/P that the state applies is not the E/P for any particular company but supposedly an E/P for the industry. An atypical year for one railroad may not have much effect on the industry E/P, and applying that E/P to abnormal earnings may produce an abnormal result.
[46]  The court's conclusion is not meant in any way to preclude the plaintiffs from challenging the state's application of its chosen methodology for other assessment years, through the appropriate state procedures.
[47]  The parties basically agree on these percentages. The figures are conveniently summarized in Plaintiffs' Supplemented and Amended Proposed Findings of Fact and Conclusions of Law at ¶¶ 13, 15, 19 (UP for 1984); 20, 22, 25 (UP for 1985); 27, 29, 32 (D & RG for 1984); 33, 35, 38 (D & RG for 1985).
[48]  See pltffs' exs. 391 at 4; 392 at 2; 394 at 2; and 396 at 2.
[49]  The stipulation also resolves by agreement the question of what constitutes "all other commercial and industrial property" in Utah for purposes of the 4R Act. The stipulation specifies four categories of other commercial and industrial properties  certain mining and oil and gas properties, utilities, locally assessed personal property and locally assessed real property. The parties have agreed on the true market value and assessment rates for three of the four categories. See pltffs' exs. 496 & 497. The only dispute is over the true market value and assessment rate for locally assessed real property, and the only disagreement between the parties there is whether or not the court should apply the 20 percent discount statute in determining true market value.
[50]  A revised version of the statute was enacted in 1987 and is codified at section 59-2-304 of the Utah Code.

The statute further required the State Tax Commission to "develop and implement comparable sales or cost appraisal methods in valuing taxable property" that exclude "the various fees, services, closing costs, and other expenses related to the sales transaction and other intangible values." Utah Code Ann. § 59-54.5(2) (Supp. 1986). The timetable for the State Tax Commission to develop and implement such methods has been pushed back to January 1, 1990. See id. § 59-2-304(2) (Supp.1988). County assessors are required to use the methods the State Tax Commission develops for assessments beginning January 1, 1990. Id.
[51]  The assessors also testified that, of the three approaches commonly used, namely, the cost, income and market comparable approaches to value, the cost approach generally results in the highest values. See Tr. at 2343-44, 2374. The intervenors suggest that the discount statute simply brings the assessed values of locally assessed real property more in line with the values of state assessed properties, which give more weight to the income approach  in other words, that one should discount cost indicators of value by 20 percent to get a value that is comparable to values based on an income indicator. A similar argument was rejected in Louisville & Nashville Railroad Company v. Louisiana Tax Commission, 498 F.Supp. 418, 421 (M.D.La.1980). This court similarly finds the argument unpersuasive. It also ignores the evidence. The evidence showed that Mr. Prawitt gives some weight to the cost indicator of value for the railroads. Moreover, Mr. Bexell, the Weber County Assessor, testified that the cost approach for real property results in values about 20 percent less than those determined under sales assessment ratio studies, the statutorily authorized method of valuing other commercial and industrial property under the 4R Act. See Pub.L. No. 94-210 § 306(2)(e), 90 Stat. at 55. Yet the state still reduces the values determined under the cost approach by 20 percent.
[52]  The legislative history of the statute suggests that the act may also have been meant to reduce the relative burden on locally assessed taxpayers that "arose out of [a] statewide reappraisal program, which had the effect of immediately injecting a high degree of inflation into residential values." Rio Algom Corp. v. San Juan County, 681 P.2d 184, 193 (Utah 1984). The legislature apparently felt that the reappraisal program placed an unfair burden on locally assessed properties because "the formulae used to assess state-assessed properties did not tend to factor the effects of inflation into the state-assessed properties, or if they did, they did so at a much more modest and less abrupt pace." Id. The evidence in this case makes the legislature's assumptions suspect. Dr. Schoenwald testified that the state's appraisal methods do factor in the effects of inflation, and, if they do so at a much more modest pace, it may be because inflation affects the value of rail assets less dramatically than it affects the value of real property. In trying to adjust taxpayers' relative burdens, the legislature would do well to bear in mind Sir Hermann Black's warning: "Oh what a tangled web we weave when [first] we practice to relieve." "Sayings of the Week," Sydney Morning Herald, July 6, 1985, quoted in A Dictionary of Legal Quotations 163 (S. James & C. Stebbings comp. 1987).
[53]  In the Rio Algom case, 681 P.2d 184 (Utah 1984), the Utah Supreme Court held that section 59-5-4.5 did not violate article XIII of the Utah Constitution or the equal protection provisions of either the state or federal constitutions. See 681 P.2d at 194.
[54]  Indeed, the parties would generally consider the transaction costs associated with the sale in arriving at true market value.
[55]  The parties' stipulation itself indicates that the "true market value" of locally assessed real property is the value determined by the assessment sales ratio study before the 20 percent reduction is applied. See Settlement Stipulation, § D(3)(b)(v).
[56]  The Eleventh Circuit left open the question of whether the state would violate the 4R Act if, in determining the just value of commercial and industrial property it deducted the actual costs of sale for those properties that actually sold during the year.
[57]  The state concedes that, if UP and D & RG are entitled to equalization relief under the 4R Act, SP is entitled to relief as well.
[1]  All dollars are expressed in thousands. Final indicators may vary slightly from column totals due to rounding.
[2]  Dr. Schoenwald's appraisal of D & RG for assessment year 1985 is based solely on his analysis of the purchase of Rio Grande Industries, Inc., by the Anschutz Corporation in the fall of 1984.
