MEMORANDUM OPINION AND ORDER

JENKINS, Chief Judge.

The plaintiff railroads — Union Pacific (UP), the Denver Rio Grande Western (D 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. 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.

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. 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. 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. 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 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. 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. 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, the court can summarize the three basic approaches as follows. 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. 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 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. 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).

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).

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. 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. 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.

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, 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 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.

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 — 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, but the starting point for judicial determination is 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.

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. 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, stated that the bill

does not suggest or require a State to change its assessment standards, assessment practices, or the assessments themselves. 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).

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.

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 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. 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).

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. 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.

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).

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. 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 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. 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. 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 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 — 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 X 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. 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, suggesting that he viewed the railroad as a good investment that could return a rate greater than the cost of capital.

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. 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.

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. 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 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. 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. 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 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. The state applies this trailing ratio to an earnings figure that, although a projection, is also based on historical data. Although the 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.

The plaintiffs next argue that the state appraisals err in their treatment of intracompany 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. 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:

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

The assessed value of the plaintiffs' rail transportation property in Utah was as follows:

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.

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).

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. The defendants therefore argue 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. That intent may be admirable. Moreover, the statute may pass constitutional muster. 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.

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"). 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.

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"). 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.

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.

APPENDIX A