This ad valorem tax case is before us on appeals by both the taxpayer Union Pacific Railroad (UP) and the Department of Revenue (the Department) from ajudgment of the Oregon Tax Court setting the value of UP’s Oregon property for the 1983 and 1984 tax years at $125,860,000 and $171,360,000, respectively. Union Pacific Railroad v. Dept. of Rev., 11 OTR 165 (1989). On de novo review,1 we modify the decision of the Tax Court in the particulars stated below.
UP is a rail transportation common carrier engaged in interstate commerce and regulated by the Interstate Commerce Commission (ICC). It is a Utah corporation wholly owned by Union Pacific Corporation (UPC),2 which has three other principal operating subsidiaries: Champlin Petroleum Company, a company primarily involved in exploration for and production of oil and natural gas; Rocky Mountain Energy, a company involved in exploration for and production of coal, soda ash, and uranium, primarily in the State of Wyoming; and Upland Industries, a company devoted primarily to developing commercial and industrial properties.
UP is a combination of what formerly were three independent rail systems: the Union Pacific Railroad System, which operated primarily in the western United States; the Missouri Pacific Railroad Company, which operated primarily in the midwest; and the Western Pacific Railroad Company, which operated primarily within the State of California. The merger of the three separate operating entities was effected on December 22, 1982. By the earliest assessment date involved in this case — January 1, 1983 — the three were operating as one integrated unit, and they have been assessed as such in this case.
The operating rail properties of UP consist of approximately 22,000 miles of road (because of parallel *14tracks, the actual trackage is even longer), 60,000 freight cars, and 3,200 locomotives. UP transports approximately 200 million tons of freight yearly. Company revenues yearly approximate $4 billion.
To value the railroad operating assets, both UP’s and the Department’s appraisers first valued the integrated unit of railroad operating properties and then allocated a portion of that value, by means of a formula, to UP’s operations in the State of Oregon. The parties dispute the allocation formula and each piece of the valuation puzzle that must be assembled before the formula can be applied.
Valuation of railroad properties for ad valorem tax purposes is governed by ORS 308.515, which provides:
“(1) The Department of Revenue shall make an annual assessment, upon an assessment roll to be prepared by the division of the department charged with property tax administration, of the following property having a situs in this state:
(a) * * * [A]ny property used or held for its own future use by any company in performing or maintaining any of the following businesses or services or in selling any of the following commodities, whether in domestic or interstate commerce or both, and whether mutually, or for hire, sale or consumption by other persons: Railroad transportation; railroad switching and terminal; electric rail and trackless trolley transportation; sleeping car; refrigerator car; private car; tank car; * * * air or railway express * * *.
“(b) Refrigeration, tank and private cars of all companies not included in paragraph (a) of this subsection, where such cars are rented, leased or used in railroad transportation for hire.”
“Value” is “true cash value,” i.e., the “market value of the property as of the assessment date.” ORS 308.205 (1989). In other words, it means what it usually means: the amount that a willing buyer would pay and that a willing seller would accept for UP’s assets and liabilities, where neither buyer nor seller is under compulsion to carry out the transaction.
In the ordinary course of valuation, the subject property would be compared with sales of other railroads, and *15then such adjustments would be made as might appear necessary to compensate for individual differences between it and the other railroads. But it is doubtful that there ever has been a comparable sale of a railroad of this size and complexity; certainly, none was identified with respect to this valuation. Thus, it is necessary to value the property by alternative approaches, each of which is intended to arrive at roughly the same result that would be obtained if a true willing seller/ willing buyer scenario were available.
In the absence of comparable sales, Oregon law provides for three alternative approaches to valuation, viz., the cost approach, the income approach, and the stock and debt approach. OAR 150-308.205(A). The parties (and we) agree that the cost approach to valuation does not produce useful results in the context of this case. The parties therefore valued UP by using the income approach and the stock and debt approach. Several issues arose between the parties with respect to certain aspects of each approach. Those issues comprised the bulk of the fight before the Tax Court, and they reappear here, as well.
Our analysis begins with a review of a. complaint from both parties about the decisional methodology of the Tax Court. We also will address a specific argument made by the Department alleging overarching legal error in the Tax Court’s entire approach to its decision. We then shall deal with an evidentiary argument advanced by UP concerning a pretrial order of the Tax Court requiring UP to produce for inspection certain internal planning documents that UP had prepared. We next examine the two valuation approaches used by the parties and consider the competing contentions that each party makes concerning each approach. Finally, we shall announce our conclusions concerning the value the of Oregon component of UP for the tax years in question.
CONCERNS ABOUT TAX COURT METHODOLOGY
Both parties complain that the Tax Court ambiguously, arbitrarily, and incorrectly compromised the parties’, opinions of value. UP’s complaint is representative:
“The nature of the Tax Court’s decision makes it difficult to * * * identify the errors with which Union Pacific is concerned in this appeal. The Tax Court did not wholly *16accept any valuation approach, did not set forth its own valuation model, and did not indicate how much weight it gave to any particular approach.”
The Department joins in criticizing what it characterizes as the Tax Court’s “failure to explain its value conclusions and [the Tax Court’s decision] to arbitrarily compromise the parties’ opinions of values.” We reject the parties’ claims that legal error has been committed in this regard.
It could be argued that, because our review is de novo, we need not address those contentions. However, we think it appropriate to note that the degree of detail furnished by the Tax Court in its decision must be viewed with due regard for the task that the Tax Court faced. We already have indicated the enormous length of these proceedings and the record that they produced.3 A detailed analysis of that record would run to hundreds of pages, as the length of the parties’ trial briefs demonstrates.4 The Tax Court issued a 41-page opinion — no small effort in resolving the parties’ dispute, particularly in the light of that court’s significant burden of other cases.
It is a good practice for the Tax Court (or any trial court) to explain itself as fully as circumstances will permit. See PP&L v. Dept. of Rev., 308 Or 49, 59-60, 775 P2d 303 (1989) (both reviewing court and the parties would be assisted in certain circumstances if the Tax Court would more fully explain its conclusions); United Telephone Co. v. Dept. of Rev., 307 Or 428, 441-42, 770 P2d 43 (1989) (reviewingcourt left to speculate as to precise analysis used by Tax Court). But the fact that the Tax Court could have provided many more pages of explanation of its view does not establish that the Tax Court committed legal error. The court explained, in its opinion, what it identified as the analytical weaknesses of the parties’ positions. That was very useful to us. Had the court *17chosen to go on from there and identify its own methodology and assumptions, its work would have been even more useful.
The Department also argues that, from the structure of the Tax Court’s opinion, it appears that the court did not, at all times and with respect to all issues before it, require that UP show by a preponderance of the evidence that UP’s arguments were correct. ORS 305.427 provides:
“In all proceedings before the tax court and upon appeal therefrom, a preponderance of the evidence shall suffice to sustain the burden of proof. The burden of proof shall fall upon the party seeking affirmative relief and the burden of going forward with the evidence shall shift as in other civil litigation.”
See also PP&L v. Dept. of Rev., supra, 308 Or at 54-55 (discussing role of burden of proof). There is room from some of the language of the Tax Court’s opinion to make the argument that the Department makes, but, when the entire opinion is read in context, we believe that it is clear that the Tax Court understood and applied the appropriate rules on burden of proof to the controversy before it.
With respect to the case as it is presented in this court, we note only that, as to the claims that UP makes that would require a modification of the decision of the Tax Court, UP has the burden of proof by a preponderance of the evidence. We have required UP to meet that burden throughout our review of its evidence. As to the matters concerning which the Department asks this court to change the decision of the Tax Court or as to which it cross-assigns error, it is the Department that shoulders the burden of proof. See PP&L v. Dept. of Rev., supra, 308 Or at 54-55 (discussing burden of proof).
The Department makes one final methodological argument. It asserts that the Tax Court erred in ignoring the legal requirement that the court find a ‘ ‘going-concern’ ’ value for UP’s unit of property. We find no such error, and, in any event, the decision that we make on de novo review includes a “going concern” value for UP. We turn next to UP’s evidenti-ary concern with respect to its annual strategic plans.
*18EVIDENTIARY ISSUE
UP asserts that the Tax Court erred in not granting to it a protective order concerning production of copies of its annual strategic plans. We disagree. A strategic plan, as the name implies, is a narrative containing assessments of the major issues and trends in the company’s business environment, of the company’s position in its markets and its relative strengths and weaknesses compared to its competition, of asset and financing requirements, and of a host of other questions. The purpose of such plans appears to be to give top management a yearly device with which to plan and from which to set or revise company goals. UP presented extensive testimony as to the nature of the strategic plans and the way in which they are prepared. UP attempted to demonstrate that the approach taken and the methods used in preparing the plans (to the extent that they can be identified) bear little or no resemblance to the questions that must be answered in valuing UP for ad valorem tax purposes. We accept much of this testimony and agree that the plans are not so reliable in their detail as to justify the uses made of them by the Department’s experts during the presentation of the Department’s case on the merits.
The foregoing does not mean that we believe that the strategic plans have no relevance, however. For example, one of the major issues in this case concerned “growth” — would or would not UP’s income stream experience “growth”? UP’s expert, Schoenwald, predicted that UP would not experience any true growth. But if UP’s own internal projections, as reflected in its annual strategic plans for 1983 and 1984, were to indicate that UP did anticipate growth, that fact would both impeach (to some degree) Schoenwald and bolster (to some degree) the Department’s experts. As it happens, UP’s strategic plans did anticipate growth. The plans were relevant for the purposes described, as the Tax Court was entitled to assume that they would be.
UP next argues that the strategic plans are irrelevant, because they are not publicly available and therefore would not be used by potential investors in deciding what value to place on a company. That argument covers only half of the equation. The issue is what a willing buyer would pay and what a willing seller would accept for the asset to be *19valued. Here, the strategic plans indicate that the owner of the asset — UP — believes that the asset’s income stream will grow. That could make the seller “willing” to part with the asset only at a higher price than that which otherwise might be acceptable. In attemptingto value the asset, therefore, this seems to us to be relevant information.
Finally, UP alleges that there will be significant harmful effects if the strategic plans (which are prepared for use by a relative handful of senior officials in the company) of companies such as UP should become public knowledge. Assuming that to be true, UP has not demonstrated that the means chosen by the Tax Court to protect the strategic plans from public knowledge were insufficient.
UP’s motion for a protective order was made pursuant to Tax Court Rule 36C, which provides:
“Upon motion by a party or by the person from whom discovery is sought, and for good cause shown, the court in which the action is pending may make any order which justice requires to protect a party or person from annoyance, embarrassment, oppression, or undue burden or expense, including one or more of the following: (1) that the discovery not be had; (2) that the discovery may be had only on specified terms and conditions, including a designation of the time or place; (3) that the discovery may be had only by a method of discovery other than that selected by the party seeking discovery; (4) that certain matters not be inquired into, or that the scope of the discovery be limited to certain matters; (5) that discovery be conducted with no one present except persons designated by the court; (6) that a deposition, after being sealed, be opened only by order of the court; (7) that a trade secret or other confidential research, development, or commercial information not be disclosed or be disclosed only in a designated way; (8) that the parties simultaneously file specified documents or information enclosed in sealed envelopes to be opened as directed by the court; or (9) that to prevent hardship the party requesting discovery pay to the other party reasonable expenses incurred in attending the deposition or otherwise responding to the request for discovery.
“If the motion for a protective order is denied in whole or in part, the court may, on such terms and conditions as are just, order that any party or person provide or permit discovery.”
*20In the present case, the Tax Court, while denying the requested order “that the discovery not be had” concerning UP’s strategic plans, did create a very strong protection for those plans, including severely limiting the plans’ distribution among employees of the Department and entirely forbidding the sharing of the plans with any other governmental entity, including the Multistate Tax Commission. We are satisfied that the Tax Court’s choice lay well within its discretion, given the protections that it provided for the strategic plans. Moreover, and assuming that our review as to this question should be de novo, we would agree with and adopt the measures taken by the Tax Court on this subject.
The Tax Court did not err in denying a more extensive protective order concerning the strategic plans. We turn now to consideration of the substantive issues of the valuation controversy.
THE INCOME METHOD OF VALUATION
The premise of the income method of valuation is that a potential investor will be willing to pay a price for an asset that reflects the present value of the future benefits (i. e., income) that the investor can obtain from the asset. There are two parts to developing the income approach: (1) forecasting the amount of future benefits (usually described as a stream of income in money derived from the business application of the asset), and (2) then discounting those benefits at a rate (called the “discount” or “capitalization” rate) to a figure that will reflect the future benefits’ present value to the investor. There are several different ways (called “approaches” by the parties’ experts) in which to identify the income stream and the discount rate.
1. Forecasting the Amount of Future Benefits — Income
UP’s expert was Dr. Arthur A. Schoenwald, a person with extensive credentials and long experience in the management and valuation of public utilities. The Tax Court was highly laudatory of the articulateness and sophistication of his presentation. Schoenwald presented an income approach to value commonly referred to as the “yield capitalization” approach.
*21Ideally, yield capitalization methodology would project net cash flows that could be expected from an asset for each future period (the usual period being a year, for tax purposes). Thereafter, as will be discussed more fully in a later section of this opinion, net cash flows would then be “discounted” in order to arrive at a present value, i.e., what one would be willing to pay at a particular moment for the right to receive the projected income stream at the time or times in the future when it would be earned. The discounting would be accomplished by dividing the projected cash flows by a figure known as the “discount rate,” a figure that reflects both the “time value” of money and the relative risk to a potential investor that may be associated with that particular asset.
Schoenwald’s approach was to evaluate the characteristics of the assets that he was appraising to determine a normalized net cash flow that could be projected into the future. Next, he evaluated whether those net cash flows could be expected to “grow” in the future, i.e., to go up in ways that would increase the present value of the assets. This is what Schoenwald meant by “growth,” and it is different from a mere increase in the amount of income. Schoenwald recognized that, given traditional inflationary pressures, UP’s prices might go up and, therefore, its gross receipts from its railroad activities might go up correspondingly. That would not, however, be “growth” in the sense that a potential investor would be looking for “growth,” because it would not necessarily represent an increase in the value of the underlying asset base that was producing the income stream.
The difference between “growth” and “no growth” is significant to the valuation process. In algebraic terms, “value” may be represented by “V,” net cash flows by “NCF,” and the discount rate by “k.” If no growth is expected, the discounted value of the assets when there are net cash flows can be expressed by the simple formula V_ NOE- 5, on the 0ther hand, growth is to be expected, the formula becomes much more complicated algebraically. The Department states the “growth” formula this way:
*22Present value = CF0x d+g 1) (l+fcx) , a+g2)2 a+k 2)2 +•••+ dd-gopioo (l+&oo)00
where k - discount rate,
g — growth rate in cash flows, and
CF = cash flows to capital investors.
Because of the significance of the presence or absence of growth, Schoenwald first focused on whether there would be “growth” in net cash flows.
a. Growth or No Growth — the UP Model
Evaluating potential growth in net cash flows involves two considerations: historical experience and future prospects. Examining history tells an evaluation expert what actually happened in the past. Future prospects are those that the expert believes are the ones most likely to occur in the particular business during the period to which the net cash flow forecast of the expert will apply. By comparing historical circumstances with anticipated ones, the expert can make an estimate as to what the future income experience of the business will be.
Growth in net cash flows will arise either because the present asset base generates additional income or because additions to the asset base produce income beyond the cost of the additions themselves, including the costs of operating them. The latter source of growth will be possible only if an investor is prepared to forego some immediate return on investment {i.e., an amount equal to the cost of the new income-producing assets) in order to experience more satisfactory returns in the long run. If the net cash flows generated by increases in the asset base do not exceed the cost of the additional asset base and the costs of their operation, then there has been no “growth” from an investor’s standpoint.
Schoenwald projected net cash flows in the year following the appraisal date by taking the average of the total Net Railway Operating Income (NROI) figures for the preceding five years for the three (then separate) railroad systems and projecting that average as the “NCF” for the next year, when the three railroads would be operating as an integrated *23unit.6 Schoenwald concluded, after examining available data, that this five-year average would not grow unless additional asset base were purchased. He further concluded that, even if additional asset base were purchased, the resulting net cash flows would not produce a return exceeding the cost of capital, i.e., the resulting net cash flows would not be increased by the purchase of additional asset base, either. Schoenwald thus projected “no growth.” Based on that evaluation, Schoen-wald concluded that the numerator in the formula V=NCF k should be the average of UP’s NROI7 for the preceding five years. This produces the derivative formula V=NRQ1 ( where NROI equals average composite NROI for the five years preceding the tax year in question.8
The Tax Court rejected Schoenwald’s approach for several reasons, all of which are asserted by the Department before this court: (1) use of NROI averaged over the last five years does not allow for market-expected growth; (2) use of NROI alone does not accurately portray NCF, because it omits income from a source known as “Account510” (miscellaneous rent); and (3) use of NROI alone does not include income from deferred income taxes (“DIT”), another source of cash flow. The questions of inclusion of DIT and Account 510 income in any analysis of the value of UP are issues that we shall discuss later in this opinion. We here consider only the issue of expected “growth.”
The Department argues9 that growth was expected (by the market, by UP’s own management, and by others) to *24come from one or more of the following factors: (1) the benefits (e.g., economies of scale) expected to flow from the merger of the three railroad systems; (2) the benefits expected to flow to railroads generally from the Staggers Rail Act of 1980, Pub L No 96-448, 94 Stat 1895 (codified as amended in scattered sections of 11,45 and 49 USC) (“the Staggers Act”); (3) UP’s increased share of the transportation market; (4) a general recovery from the recession of the early 1980s, i.e., increased sales or volume, and (5) increased utilization of or productivity in existing assets.
With respect to the benefits expected from the merger, UP’s own executives and internal forecasts projected growth from the merger of the three rail systems. Investors could have shared that optimistic view as to the effect of the merger. However, those projections, although they represented the best and most knowledgeable thinking on the subject at the time within the company, were available only to internal management (not to potential investors) and were, in any event, no guarantee of results. It had been the norm for internal forecasts to project growth for UP; it also had been the norm for those forecasts to be overly optimistic. We are not persuaded by this factor.
Neither are we persuaded that a knowledgeable investor would believe that congressional action was going to increase earnings. The Staggers Act, which was intended to level the competitive playing field between railroads and their principal competitor, the trucking industry, was followed closely by the Motor Carrier Act of 1980, Pub L No 96-296,94 Stat 793 (codified as amended in scattered sections of 18 and 49 USC), and the Surface Transportation Assistance Act of 1982, Pub L No 97-424,96 Stat 2097 (codified as amended in scattered sections of 15,16, 23, 26, 33, 46 and 49 USC), both of which enactments, witnesses insisted, created new advantages for the highway transportation industry over the railroad industry. Investors aware of the Staggers Act would *25likely have been aware of the pendency of the other legislation, tending to offset the expected benefits under the Staggers Act.
Respecting an anticipated increase in UP’s share of the market, it is true that UP’s own internal forecasts projected growth to flow from an increase in UP’s market share, with its services extending from the midwest to the far west. But we do not think that those forecasts took sufficient account of the new competitive atmosphere in which the deregulated railroad found itself. UP’s wider market was one in which it was now forced to compete vigorously with surrounding railroads and with the surface transportation industry. That increased competition likely would lead to lower prices for UP’s services, which could be expected to offset the gains that UP otherwise might experience. This factor does not persuade us that growth was likely.
It also is possible that appraisers and potential investors could have believed, as UP’s management apparently hoped, that the end of the recessionary period in the early 1980s would see growth in rail transportation. On the other hand, neither the competitive situation nor the railroad industry’s performance in the recent past supported such optimism. We think that a knowledgeable investor would not have expected this factor, to produce growth.
Finally, it may be true that UP had the management expertise to improve its utilization of its own assets. However, past experience had not demonstrated such improvement, so there was no reason to expect sudden success on that front at that particular time.
It follows that we disagree with the Tax Court’s conclusion that Schoenwald’s income forecast was wrong in failing to project growth for UP. Subject to additions that must be made for miscellaneous rental (“Account 510”) receipts and for deferred income taxes (“DIT”), both of which we discuss later, we agree with Schoenwald that the average NROI for the three combined railroads for the preceding five years could be used as the future income stream to be capitalized in this approach to valuation. Even the Department’s experts hedged their bets on this question. They stated, in their appraisal:
*26“The railroad industry is a mature industry, with little possibility of expansion in terms of miles of road. In fact, due to the changing nature of the competition railroads face, it is likely that miles of road actually will decline in the future. There is also evidence to suggest that total unit sales as measured by ton-miles, for example, may also experience little growth for the industry. This does not imply that the income of individual railroads will not increase over time. Revenues, earnings and cash flows for an individual railroad can grow due to increases in labor productivity, increased traffic, increased market share and general price inflation. Individual railroads may increase market share at the expense of competitors both within the industry and across industry lines. There may also be distinct regional differences which may show significant growth for some carriers when other railroads in certain regions may not grow at all.”
We find the presence in the industry of so many growth-defeating factors, as summarized by the Department’s own experts, to lend credence to Schoenwald’s “no growth” projections.
Our tentative agreement with Shoenwald’s “no growth” conclusion does not end our inquiry on this point, however. If one or more of the Department’s approaches to the income indicator of value were more persuasive than the one advanced by UP, we would adopt such approach or approaches. We therefore turn next to a consideration of the Department’s alternative proposals under this indicator.
b. The Department’s Alternative Income Approaches
The Department’s experts were Michael Goodwin and Dr. James Ifflander. Goodwin, a private consultant in the field of valuation, had worked for several years as a staff appraiser for the Kansas Department of Revenue. Ifflander, an assistant professor of finance at Arizona State University, had appeared as an expert witness in railroad utility valuation cases on other occasions.
The Department’s experts utilized two different income models, the discounted cash flow model and the direct capitalization model. We shall discuss each model briefly.
(1) The Department’s discounted cash flow (DCF) model. We previously have set out the algebraic formula for *27calculating income under the Department’s DCF model, which basically attempts to do the same thing that Schoen-wald attempted to do, but assumes that there is a growth component (the “g” in the equation) in the railroad’s future income stream that must be factored in. The parties argue at some length over whether the Tax Court did, in fact, give any weight to the Department’s DCF method of valuation. We need not resolve this controversy. It is enough for our purposes to state that, because we are not persuaded by the evidence in this record that the method was applied properly in valuing UP, we do not give the Department’s DCF method of valuation any weight.
There are several flaws identified in the testimony concerning the Department’s DCF model, not the least of which is the Department’s reliance (in part), during its preparation of its DCF valuation, on UP’s internal strategic plans. We do not find those plans to be sufficiently reliable to be used as source data for projections of the kind made from them in connection with the Department’s DCF model, especially when the plans are viewed in the light of the plans’ own historic record of unjustified optimism and in the light of all the evidence in the record concerning the state of the railroad industry.
Even if we were not dissuaded from using the Department’s DCF model by the Department’s choice of sources for its data, we would have a further difficulty with the model. The Department attempted to massage its income projection data through a computer program called ‘ ‘PRISM” in order to obtain its final income figure. The Tax Court was unimpressed by “PRISM,” and we share that court’s misgivings. In addition to the fact that a witness for UP raised serious questions concerning the efficacy of the program, neither of the Department’s principal witnesses, Ifflander and Goodwin, seemed sufficiently conversant with the program, its assumptions or its limitations, to persuade us, any more than either persuaded the Tax Court, that the simulation produced by the program can be relied on here. Without prejudice to the Department’s right to persuade us in some future case that we should accept conclusions based on *28“PRISM,”10 we decline to utilize the Department’s valuation approach that depended on that program here.
Defending its use of “PRISM,” the Department argues that “[UP’s] evidence criticizing [the Department’s] computer-generated DCF results does not meet its burden of proof.” There is a profound misunderstanding here on the part of the Department. It is the Department that is offering in evidence a particular approach for identifying the taxpayer’s cash flow. As to that particular approach, acceptance of which would change the Tax Court’s decision, it is the Department’s burden to persuade us that the approach correctly identifies the pertinent cash flow and that we therefore should utilize the approach.
(2) The Department’s direct capitalization (DCAP) model. With respect to the Department’s DCAP method, our problem is a more general one. We find the testimony about this method and the various arguments made for and against it by the parties (and by the Tax Court) confusing and, ultimately, unsatisfying. The model requires the use of P/E (price/earnings) ratios, i.e., mathematical ratios derived from comparing the price at which particular companies’ stock sold with the earnings of those companies. If an appraiser uses P/E ratios, it is vital that the ratios be for “comparable” companies, i.e., be derived from companies sufficiently similar to the company being evaluated to make use of the ratios analytically meaningful.
We find, as did the Tax Court, that some of the “comparable” railroads used by the Department to calculate its P/E ratios were not comparable. 11 Moreover, what the Tax Court characterized as “[t]he apparent lack of in-depth analysis by [the Department’s] appraisers before the trial,” a problem that the Tax Court said “raises concerns about the reliability of their conclusions,” troubles us as well. Too much went unexplained in the testimony and in the exhibits to *29permit us to believe that we can rely on the Department’s evidence under this method. Furthermore, and as the Department itself acknowledged in its post-trial brief, its DCAP method takes on many of the same characteristics as its separate, stock and debt approach to value. We will consider the Department’s stock and debt approach later.
Finally, the Department itself attempted in its post-trial brief to establish different assumptions for, and in effect to amend, its DCAP approach. (The Department’s amendments would increase the valuation of UP.) The problem here is that the Department attempts to accomplish these amendments by impeaching its own experts. The net effect of all this is thoroughly to defeat the court’s ability to rely on the Department’s trial evidence concerning the DCAP method. We do not accept or give any weight to the Department’s valuation achieved through that method.
(3) The Department’s alternative argument. The Department makes one other point concerning the income stream. It argues that, even if we disregard the Department’s income stream projections as unpersuasive, we must use some income stream, and that income stream has two parts — debt flow and equity cash flow. The Department argues that those flows, generated as they are by different market forces, should be discounted separately. The Tax Court disagreed, taking the view that what the Department was attempting to do, in essence, was to amalgamate the income approach and the stock and debt approach. “It would seem preferable,” the court stated, “to obtain an indication of value wholly by the income approach and an indication of value wholly by the stock and debt approach and then [to] correlate those two indications of value rather than [to] mix the methods and obtain a diluted result.” Union Pacific Railroad v. Dept. of Rev., supra, 11 OTR at 184. We agree.
c. Conclusion — Income Stream to he Capitalized
In summary, we accept as more persuasive for the purposes of this case the income streams projected by Schoenwald. We find Schoenwald’s model (as he explained it) to be persuasive in the light of the essentially unrebutted history of railroad productivity (or lack thereof) that was demonstrated by UP and in the light of the evidence of the competitive *30atmosphere in which railroads found themselves as of the assessment dates.
We turn next to a consideration of whether there should be added to Schoenwald’s projected income streams for the two tax years amounts for deferred income taxes (DIT) and for “Account 510” (miscellaneous rental income). As we shall explain, we conclude that amounts should be added for both.
2. Proposed Additions to the Projected Income Stream
a. Deferred Income Taxes (DIT)
Most railroad assets are long-lived. These assets are depreciated, for normal (straight-line) accounting purposes, over a 10-year period. Depreciation is an offset against income for income tax purposes. NROI, which Schoenwald used as his basis for projecting future income streams, is an after-tax figure, i.e., all taxes are deducted from gross operating revenues in order to determine NROI. But, during the years in question, special tax rules enabled UP (like many other businesses) to accelerate its depreciation deduction for income tax purposes so that a portion of UP’s operating income was offset (or “sheltered,” as the Tax Court put it), and NROI was reduced correspondingly for the years in question.
Accelerating depreciation means that, in later years, it will not be possible to take as large a deduction for depreciation on the same asset as one would be able to take under traditional, straight-line accounting; most of the depreciation allowance will have been exhausted. Thus, taxes for the later period will be higher. Those higher taxes in later periods are anticipated by setting up an account, called “deferred income taxes” (DIT), which represents the amount that UP deducts from current income beyond traditional straight-line depreciation. The amount is treated as a cash reserve set aside for payment of higher taxes later, although the cash that it represents is available in the interim for other uses.
Because DIT represents an amount of cash available to UP but not included in NROI, the Department argues that NROI is understated. The Tax Court agreed in part, but only *31to the extent that future amounts of DIT would be sheltered permanently in the asset base by ever-increasing asset purchases and offsetting accelerated deductions for depreciation of those future assets. UP argues that no part of DIT should be added to NROI.
The Tax Court explained its view on this point at some length:
“The court finds that both parties failed to properly account for DIT. The provision for deferred taxes, as found in the Form R-ls, is further explained on Schedule 450, entitled ‘Analysis of Taxes.’ That schedule states that under Part B are ‘the particulars which most often cause a differential between taxable income and pretax accounting income.’ Examining Exhibit 1-3, at 62 and 65, the Form R-l for [UP] for 1982, discloses that not all of the deferred taxes are attributable to accelerated depreciation. In fact, a number of items such as contested property taxes are not long-term deferral items. Likewise, the Form R-ls for Missouri Pacific show greater amounts due to special depreciation allowed by the Economic Recovery Tax Act of 1980 than due to accelerated depreciation. Exhibit K-3, at 62, shows that, of $100,565,000 of DIT, only $25,777,000 can be attributed to accelerated depreciation. Likewise, on Exhibit N-3, at 61, of $97,507,000 of DIT, only $18,167,000 is accelerated depreciation. It would appear that specific adjustments underlying the provision for deferred income taxes must be analyzed before adjusting the cash flow.
“The Economic Recovery Tax Act (ERTA), Public Law 97-34 enacted August 13,1981, § 203(c), contained a transitional provision which allowed the railroads to write off their ‘frozen base’ over five years, using accelerated depreciation. It would be error for [the Department] to add back the full amount of that special ERTA depreciation since it will not last indefinitely into the future. Likewise, it would be error for [UP] to subtract all ERTA deductions since they do not entirely represent accelerated depreciation. To the contrary, in many ways the ERTA deductions were catching up with straight-line depreciation.
“The court has additional questions concerning the continuance or permanency of deferred income taxes attributable to accelerated depreciation. [UP] assumes that depreciation equals capital expenditures and, therefore, that there is no benefit from DIT. However, [UP] acknowledges that, due to inflation, capital expenditures will generally *32exceed depreciation. [UP] appears to ignore that difference on the theory that it is caused by property being acquired in the future and, therefore, is not now subject to tax. [The Department], on the other hand, assumes depreciation is less than capital expenditures and so adds back the DIT.
“It is appropriate to recast income to accurately reflect cash flow. * * * In this case, it appears to the court that it would be reasonable to adjust cash flow to . include the deferred income taxes which appear to be permanently sheltered by the ever-increasing asset base. This would exclude deductions attributable to ERTA. * * * To reiterate, what we are looking for here is expected cash flow. The court finds that capital expenditures are .expected to exceed depreciation, which means that the DIT will be permanently deferred. As long as the parties are using perpetuity models to value an existing pool of assets, then deductions from net cash flow such as DIT should have the same long-term implications.”
Union Pacific Railroad v. Dept. of Rev., supra, 11 OTR at 172-74 (citations omitted). We agree with the Tax Court’s conclusion as to the portion of the amounts labeled “DIT” for each of the two years that should be added to NROI in determining the relevant cash flows.
b. Miscellaneous Rental Income (Account 510)
As was true with respect to DIT, the debate over miscellaneous rental income, or income from ICC Account 510, is not over whether it exists or how much it amounts to. As the label suggests, Account 510 is an account reported to the ICC, so it is in any given year a known figure. The issue with respect to this proposed addition to the income stream is whether it appropriately is attributed to the railroad as part of the “operating unit.”
Miscellaneous rental income is income from rail property that is being used, as of the assessment date, for nonoperating purposes. Apparently, it has been the administrative practice of the Department in the past to assess such property separately from the rail transportation unit and then to add the Oregon portion of such property as an adjustment after the railroad’s operating system has been valued and the appropriate portion of that system allocated to *33Oregon. The Tax Court, however, held that such an administrative approach “is inconsistent with the concept of valuing [the railroad as] an integrated whole” and that “there is no evidence that [the] property producing the account 510 income is not part of the integrated whole.” 11 OTR at 169.
UP argues that the Tax Court was in error in its inclusion of Account 510 income because, although the property that produces this miscellaneous rental income is considered rail transportation property for regulatory purposes by the ICC, the property is not, as of the assessment dates, necessary to or a part of the operating unit. UP points out that there was, in fact, testimony from Schoenwald as to the sorts of uses to which such property might be put, and that such uses were not integral to railroad operations. “The essential question,” UP argues, “is why such miscellaneous property should be valued on a system-wide basis when it is not part of the operating unit and when the data specific to Oregon is known?” The short answer to this argument is that Schoenwald’s testimony does not persuade us. Because the Tax Court chose to include this item, the Department does not bear the burden of proof on the issue of whether the property should be included; UP bears the burden of showing that it should not. UP has not satisfied that burden.
UP’s second argument is that the amount of Account 510 income-producing property in Oregon is known and, therefore, it makes more sense simply to add that property “below the bottom line” for ad valorem tax purposes. Of course, to do so would be inappropriate if the property properly is attributed to the operating unit. Railroad property within the operating unit is supposed to be assessed on a unitary basis. In any event, the fact that there is another way that the property theoretically couldbe assessed does nothing to establish that the way the Tax Court chose to assess it is impermissible. So long as UP is not assessed twice for the property — and there is no suggestion here that it has been or will be assessed twice — an answer either way does not offend the purpose of ad valorem taxation.
The Tax Court required that Account 510 (miscellaneous rental) income from railroad operating property be directly capitalized or discounted in the income approach. Because UP does not demonstrate that this was either legal or *34factual error, we also require that Account 510 income be directly capitalized.
3. Identifying the Appropriate Capitalization Rate
Put in its simplest terms, the capitalization rate is the percentage (or “rate”) of return that a prospective investor would expect to receive on his or her investment from the income stream in any particular year. Of course, there is more than one way to invest in a company, and each form of investment carries its own expectations as to a rate of return. For example, one who invests in long-term debt of a company probably would expect a different rate of return than would another investor who purchased common or preferred stock in the same company. The holders of the common and preferred stock might themselves have different expectations. These different forms of investment are called “bands” of investment. Experts from both sides in this case attempted to identify the particular bands of investment applicable to UP and to assign an appropriate capitalization rate to each.
The parties agree that the process involves four steps. First, the percentage of the company’s capital structure in each particular band of investment must be determined. Then, the rate of return expected by investors for each band of investment must be identified. Next, the rate of return expected for each band of investment must be multiplied by that band of investment’s share of the company’s capital structure, in order to “weight” the rate of return for that band vis-a-vis the entire capital structure. Finally, the various weighted percentages must be added together to produce a weighted average rate of return for the company as a whole. This weighted average rate of return then becomes the capitalization rate, the “k,” in the equation V= ^r(or as we have now identified it for the purposes of this case, y— NROI+a+d^ <<a” equais adjustment for Account 510 income and “d” equals adjustment for deferred income taxes).
The parties agreed on the general approach to be taken in identifying a capitalization rate, but disagreed on the result, as the following discussion demonstrates.
*35 a. UP’s Approach to the Capitalization Rate
UP’s expert, Schoenwald, approached the problem by placing emphasis from the outset on the difficult financial circumstances confronting railroads, particularly with respect to their ability to compete for capital. We are satisfied, from the abundance of evidence that Schoenwald amassed on this subject, that he is correct in asserting that, during the years in question, capital was not easy for UP (or other railroads) to obtain. Railroads, as already discussed, were struggling (and commonly failing) to obtain a return equal to their cost of capital. Inflation also was elevating requirements for investment returns. Thus, investment in a railroad would not be one that a potential investor would have regarded as particularly safe when compared with other potential investments. Investors therefore would have demanded a higher return on any investment in a railroad.
One other overall observation must be made. Beginning with the 1983 assessment period, Schoenwald chose to use, for the purposes of assessing the weighted average cost of capital, an average or idealized equity/debt distribution (which he referred to as being that of a “high-quality railroad operation”), rather than the actual equity/debt distribution found in UP. This distribution Schoenwald determined to be 66 per cent equity, 20 per cent equipment trust certificates, and 14 per cent “funded debt” (mortgage bonds). Thus, he projected an idealized ratio of 66 per cent equity to 34 per cent debt. (UP’s actual capital structure differed.) Ultimately, the Department agreed that, in establishing a capitalization rate for an income figure derived by DCF methodology, using that idealized approach was appropriate.
Schoenwald made another pivotal decision in identifying the data on which he relied: He chose to use yearly averages of the various figures that he selected, rather than to use figures as of (or as close as possible to) the assessment dates. Goodwin and Ifflander purported to derive their values from figures near the end of each tax year (and, therefore, closer to the precise value applicable on January 1). We find some significance in the difference, as we shall explain later. We turn now to an examination of Schoenwald’s derivation of the various capitalization rates that, in combination, go to make up his weighted average cost of capital.
*36(1) Equity capitalization rates. Schoenwald’s equity capitalization rate studies considered economic conditions, the capital markets, and the costs of capital for many securities of varying degrees of risk. He examined common stock price/eamings (P/E) ratios — a tool commonly used in valuing companies that issue publicly traded securities — and determined that, for the assessment periods in question, the P/E ratios in the railroad industry were not representative because of the recession that was occurring at the time. Because he believed that P/E ratios would not produce representative results, he sought other means to develop capitalization rates.
Schoenwald examined the “spreads”12 between railroad costs of capital and returns on other, safer investments. Taking 17 per cent as a representative figure for historic railroad equity costs (based on his analysis of capital costs over time), Schoenwald then compared that figure to the rates of safer securities. He determined that the yearly average rate of return for railroad bonds for the 1984 assessment year had been 12.51 per cent, and opined that the additional 4.49 per cent (17.00 per cent minus 12.51 per cent) would be “an inadequate differential compared with historic standards.” That suggested that a rate even higher than 17 per cent was appropriate.
The 17 per cent rate would result in a 5.73 per cent spread between railroad bonds and the safest investments (United States government securities). Schoenwald opined that this spread might be too conservative. History, in his opinion, suggested a spread closer to 7 per cent. Nonetheless, after further comparing his proposed 17 per cent figure with other types of utility companies (electric and telephone), *37Schoenwald selected 17 per cent as the appropriate cost of equity capital for the 1984 assessment. For 1983, he found the equity rate to be higher — 18 per cent. Schoenwald was able to demonstrate that his figures were reasonable when compared with figures derived from other sources, including the ICC, UP itself, a consulting firm, and (from another case involving a similar railroad, Southern Pacific) Goodwin and Ifflander.13
(2) Debt capitalization rates. As a representative form of debt of a high-quality railroad operation, Schoenwald chose an “equipment trust certificate.” (He testified that some other forms of debt instruments commonly issued by railroads carried higher interest rates, but he settled for the trust certificates.) Schoenwald was able to determine from various sources and publications that the average expected return for such instruments during 1982 (the year preceding the January 1, 1983, assessment date) was 13.62 per cent. The average expected return for funded debt (mortgage bonds) of similar railroads during 1982 was 13.63 per cent. Schoenwald used those two figures as his costs of capital for those segments of the ideal high-quality railroad operation as of the 1983 assessment date. After performing essentially the same analysis, using the same approach, in identifying the various parts of the overall capitalization rate for the 1984 assessment, Schoenwald selected figures of 11.86 per cent for railroad trust certificates and 12.51 per cent for funded debt.
The following table summarizes Schoenwald’s proposed weighted capitalization rates for the tax years in question, including his calculation of the weighted average capitalization rate for all the bands of investment:
*38Summary of UP Discount Rate Calculations
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b. The Department’s Approaches to the Capitalization Rate
In attempting to make use of the Department’s alternative methods of establishing an appropriate capitalization rate, we are met at the outset with a problem: Not only do the Goodwin/Ifflander capitalization rates assume growth, they also are not (accordingto their authors) of any use unless the cash flows with which they are compared share the same assumption. Goodwin and Ifflander wrote with respect to their capitalization rate under the DCF method:
“It is important to re-emphasize that a discount rate which includes a growth component must be applied to a cash flow stream which is also growing. One cannot imply growth in the discount rate and zero growth in the cash flow stream. There may be some debate as to what the total growth rate would be in any particular time period, but at the very least, cash flows should be adjusted by the projected inflation rate. To argue that earnings do not change over time is to argue that inflation is zero. Clearly, there is not a shred of evidence to support this contention. Inflation is a fact of life in the U.S. economy; consequently, the discount rate which investors demand is based on inflation and, therefore inflation must be factored into the income stream.”
(Exhibit D-3, at p 108.)
We already have indicated why we reject the Department’s theories justifying projected growth and instead accept (for the purposes of this case) Schoenwald’s model. One way to read that cautionary note from Goodwin and *39Ifflander is that, because we have rejected their income projections, we cannot make any use of their capitalization rates. Upon careful consideration, however, we conclude that there is some utility to the Goodwin/Ifflander projections.
Our acceptance of Schoenwald’s testimony does not mean that we believe that UP’s cash flows cannot go up, at least as raw numbers. We understand Schoenwald to acknowledge that the cash flows may go up. His point (which we accept based on the evidence offered in this case, including some of the Department’s admissions concerning the economic climate) is that UP does not appear to have any chance of obtaining returns in excess of its cost of capital, i.e., it has no present prospects of real growth, which we have identified as being growth of a kind that would increase the present value of UP. Inflation, by itself, may produce higher cash flows, but that is not growth. Nevertheless, we conclude that, at least in theory, Goodwin and Ifflander’s capitalization rate calculations may have some utility with respect to the cash flows projected by Schoenwald. We turn to a closer examination of those capitalization rates.
(1) Debt capitalization rates. As will be explained below, the Department does not make an issue of UP’s debt capitalization rates for the purpose of this calculation.
(2) Equity capitalization rates. Goodwin and Ifflander used two methods to estimate the equity capitalization rate: the dividend growth model and the capital asset pricing model. Unfortunately, neither their appraisal report (Exhibit D-3) nor their testimony fully explains either the sources for their data or the mathematics that produced their conclusions under these models. This omission diminishes the weight to be given to the estimates involved. However, they still have significant value.
(a) The Dividend Growth Model. The dividend growth model recognizes that the return to an investor in common stock will be comprised of the current dividends that the investor is receiving on that stock plus future growth (if any) in those dividends. Accordingly, the model attempts to estimate the dividend yield, i.e., the expected dividends in relation to the current price, and adds the expected growth in *40dividends.14 The total represents the discount rate as it is calculated under this model.
Goodwin and Ifflander explained the derivation of their dividend growth figures as follows:
“The dividend yield was based on average dividend yields for rail equities. These can be found in Value Line[, a generally-available periodic market study,] or in various ICC cost of capital studies. The growth rate was based on growth rates contained in the same ICC studies.”
The difficulty with the appraisers’ explanation is that, when one consults the same data that Goodwin and Ifflander indicated that they had used, one cannot reproduce their reported results. Application of the method to the figures to which Goodwin and Ifflander refer would, by our calculations, produce a lower discount rate for each of the tax years than the rates that Schoenwald projected, hut the figures would be higher than those selected by Goodwin and Ifflander.
(b) The Capital Asset Pricing Model. The idea behind this model is straightforward. First, one determines the return that an investor would be willing to accept on a risk-free investment. Then, one attempts to identify the additional return (the “risk premium”) that an investor would require in order to justify investing in the kind of company under consideration. Once that “risk premium” has been quantified, its value is added to the risk-free rate of return in order to obtain an estimate of the total return that equity investors would require in order to invest in the kind of company under consideration.
The Department’s use of this method is subject to problems similar to those that affected the dividend growth model. Goodwin and Ifflander claim to have utilized data that “was based on current interest rates and risk premiums *41taken from [a well-known publication specializing in identifying risk premiums].” The data is not more precisely identified. We have difficulty making use of the method under these circumstances.
Ifflander and Goodwin combined the results of their two methods of calculating the cost of equity capital. They concluded that the cost of equity capital for the 1983 assessment year should be 15.5 per cent in 1983 and 15.0 per cent in 1984. As the Department observed in its post-trial brief to the Tax Court: “[T]he 2.5 and 2.0 percent difference in the equity cost comprise, essentially, the only issue in regard to discount rate and capital structure issues.” Taking the Department at its word, the following table summarizes the Department’s proposed capitalization rates for the tax years in question, including its calculation of the weighted average capitalization rate for all the bands of investment:
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c. The Tax Court’s resolution of the capitalization rate
The Tax Court professed some difficulties with the approaches taken by each side. UP’s figures, the court opined, were “not particularly persuasive.” 11 OTR at 177. The Department’s calculations did not fare much better: The court expressed the same dissatisfaction that we have expressed concerning the sources of Goodwin and Ifflander’s data and the mathematics that had been applied to that data. *42Ultimately, however, the court concluded that “[the Department’s] weighted average cost of capital for the discounted cash flow method is the most accurate. The cost of capital is primarily a function of risk. [UP] is a high quality, strong railroad with a good reputation. This should be reflected in its cost of capital.” 11 OTR at 178.
d. This Court’s Resolution of the Capitalization Rate
(1) Debt capitalization rates. As already explained, we choose, based on the Department’s concession to the Tax Court, to treat the debt capitalization rates as not being an issue under this approach.
(2) Equity capitalization rates. Schoenwald’s rates are theoretical — the whole DCF model is — but fairly well justified. On the other hand, the Department’s rates have two things in their favor: (1) recent market experience suggested that the historical spreads on which Schoenwald relied may have been a little higher than appropriate when compared with spreads between risk-free investments and railroad investments as of the assessment dates, and (2) UP was one of the best-run railroads in the country, suggesting that its spreads should be at the low end of the range of spreads typical of the industry. Both considerations call for a reduction in the rates selected by Schoenwald. The problem lies in choosing a rate: The data actually utilized by Goodwin and Ifflander in the selection of their own rates is so obscure that wholesale reliance on those rates appears inappropriate. We therefore will do what any other trier of fact might be expected to do in the absence of sufficient underlying data to make the calculation wholly on our own: compromise. We select as our equity capitalization rates 17.0 per cent for 1983 and 16.0 per cent for 1984.
(3) Overall capitalization rate. This court’s calculations of the weighted average costs of capital for the two assessment years are as follows:
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*43[[Image here]]
The weighted average cost of capital used by the court in calculating the value of UP under the income indicator of value for the 1983 assessment date is 15.85 per cent. The weighted average cost of capital used by this court in calculating the value of UP under the income indicator of value for the 1984 assessment date is 14.72 per cent.
4. Summary Under the Income Approach
This court’s calculation of the value of UP, under the income indicator of value, for the 1983 and 1984 tax years, is as follows:
1983 1284
$2,802,300,000 $3,019,700,000
THE STOCK AND DEBT METHOD OF VALUATION
The idea behind use of the ‘ ‘ stock and debt’ ’ indicator of value15 for a company for ad valorem tax purposes is that a company may be said, in a general way, to be worth the total of what investors can be shown to be willing to pay for all the pieces of it. The “pieces” of a company for this purpose are of two kinds: debt, i.e., the various kinds and amounts of loan obligations that the company has outstanding at any one time, and equity, i.e., the various kinds and classes of stock that the company has outstanding at that same time.
While reasonable theoretically, the stock and debt approach encounters difficulties in the present case due, inter alia, to the fact that the debt and equity securities of the parent holding company, UPC, reflect substantially more than the value of the Union Pacific Railroad. As noted earlier, the parent corporation owns three other major subsidiaries: Champlin Petroleum Company, Rocky Mountain Energy, *44and Upland Industries. These subsidiaries are engaged primarily in oil and gas exploration and production, mining of coal and soda ash, and industrial land development, respectively. There also are significant nontaxable assets owned by UP itself. Separating the portion of UPC’s total stock and debt attributable only to UP’s taxable operating unit thus represented a formidable task for the parties’ experts and for the Tax Court.
Broadly speaking, five issues emerged from the testimony with respect to the stock and debt approach to valuation:
1. Should the valuation of UPC’s common stock be made by the use of an annual average of stock prices, or by the use of an average derived from the fourth quarter of each year preceding the assessment date?
2. Should the preferred stock of UPC be valued and allocated among the subsidiaries of UPC in a manner consistent with the allocation of the common stock, or should it instead be attributed solely to the railroad?
3. By what method should the value of the railroad operation be isolated from the value of UPC as a whole?
4. Once the equity value attributable to UP is determined, what method is most appropriate for eliminating nontaxable property owned by the railroad?
5. Should debt values be determined using annual average interest rates, or year-end rates?
We next address the parties’ approaches to these questions, among others, and the Tax Court’s and this court’s responses to them, as we examine the various components of the stock and debt calculation.
1. Calculating the Stock Values; Allocating Values to UP
Making this calculation would be simple if UP’s railroad operations were represented by separate and identifiable common and preferred stock. However, as noted earlier, they are not. Instead, as is generally true concerning wholly owned operating units of large holding companies, the stock value of UP must be extracted theoretically from the *45greater value of the stock of the holding company, UPC, as a whole.
a. UP’s Stock Value Calculations
Schoenwald’s stock value calculations were based on a single approach in which Schoenwald went directly to the available data concerning outstanding numbers of shares, prices, and the reported earnings of the various UPC subsidiaries.
(1) Common stock. Schoenwald estimated the value of UPC common stock by averaging stock prices during the calendar year prior to each assessment date and then applying that average price to the number of shares that were outstanding on the assessment date. Schoenwald justified his use of annual averages, rather than averages taken closer to the assessment dates, because of fluctuations in stock prices over time. This was particularly appropriate for UPC, he testified, because the stock market generally (and UPC stocks in particular) experienced wide swings during the time periods involved.
Goodwin and Ifflander used an average derived from the last three months of each year, although they had used longer averages on some other occasions. Use of the fourth quarter average versus annual average did not make much difference for 1984. For 1983, however, the results were quite different. The annual average for UPC shares in 1983 was $39.81 per share; the fourth quarter average was $44.92. Because there were roughly 114.3 million shares outstanding as of the 1983 assessment date, the difference represented about $584 million in value for UPC.
(2) Preferred stock. UPC had outstanding on each of the appraisal dates roughly 4.3 million shares of preferred stock. This stock had been issued in order to raise money for the purchase of Missouri Pacific. The stock was convertible — each share could be exchanged at any time for two shares of common stock of UPC.
Despite the purposes for which the preferred stock had been issued, Schoenwald did not differentiate between it and UPC’s common stock. He simply added the value of the *46preferred stock to the value of all other UPC stock in calculating total corporate equity to be allocated among the different UPC subsidiaries. He justified his approach on two grounds; (1) the ready convertibility of the preferred stock to common stock and (2) the fact that, although the purpose in issuing it was to finance an expansion of the railroad subsidiary, the preferred stock was backed by, and its dividends would be paid from, the income of UPC as a whole.
Schoenwald determined that the total value of outstanding securities on December 31,1982 (the day before the 1983 assessment), should be deemed to be $4,932,323,000. He further determined that the total value of outstanding securities on December 31, 1983, should be deemed to be $6,614,986,000. In each case, he took the average stock prices for the preceding year and multiplied them by the number of outstanding shares as of December 31 of that year.
Having determined a value for total corporate equity for the two years, Schoenwald then summed the totals with each year’s total of other outstanding corporate obligations. This produced a total for each year that Schoenwald called UPC’s “gross value.” He then calculated deductions from the gross value for, inter alia, affiliates and other investments, non-operating subsidiaries (e.g., Champlin Petroleum), and railroad group non-operating property. After the deductions, the remainder represented his valuation of the railroad system under the stock and debt approach.
b. The Department’s Stock Value Calculations
The Department’s experts, Goodwin and Ifflander, did not attempt to identify a figure for the value of UPC’s common stock as a whole and then, derivatively, a figure for the value of the portion of that common stock that represented UP, by going directly to the applicable figures for stock prices. Instead, the two took an indirect approach to the problem by creating two scenarios, “Case I” and “Case II.”
Under “Case I,” the appraisers did not start with stock or stock prices. Instead, they derived P/E multiples for the railroad only, based on an average of P/E multiples derived from what they considered to be comparable railroads. Goodwin and Ifflander described the process this way:
*47“[The Case I approach d]irectly value[s] the rail equity of the subject [UP] by applying financial ratios from a group of comparable companies. Comparable companies are those in the same fine of business (and therefore business risk) as the subject company * * *. Comparable companies are other railroads as determined by financial services such as Value Line and Standard and Poor’s.”
(Exhibit D-3, p 59.) Goodwin and Ifflander also developed three other multiples, based on cash flow, revenue, and book value for what they deemed to be comparable railroad companies. The appraisers then applied those respective industry-derived ratios to the analogous financial data for UP (i.e., to UP’s reported earnings, revenues, cash flows, and book value). The results were then averaged to obtain an equity value for UP’s common stock under “Case I.” The following tables illustrate the process and the outcome:
CASE I: UNION PACIFIC EQUITY VALUE -1983
Unit Railroad Data Multiple Value
Cash
Flow 407.745.000 5.00 2,038,725,000
Revenue 3.623.897.000 0.70 2,536,727,900
Book
Value 2.690.118.000 0.80 2,152,094,400
Earnings 209.598.000 8.00 2,101,082,825
Average Railroad Equity
Value = 2,061,671,248
CASE I: UNION PACIFIC EQUITY VALUE -1984
Unit Railroad Data Multiple Value
Cash
Flow 375.462.000 7.50 2.815.965.000
Revenue 3.608.709.000 1.10 3.969.579.900
Book
Value 2.861.086.000 1.15 3.290.248.900
Earnings 175.502.000 12.50 2.193.775.000
Average Railroad Equity Value = 3,067,392,200
(Exhibit D-3, p 60.)16
*48In “Case II,” the appraisers valued each subsidiary of UPC by calculating a P/E multiple for that subsidiary and then applying that multiple to the previous year’s earnings (as reported by UPC to its stockholders) for that subsidiary. The individual subsidiaries’ values were then totalled and “scaled” up or down proportionately to a point at which their total value equalled the estimated value of all the outstanding shares of UPC common stock. The UPC stock price then was calculated by multiplying the average monthly price from the fourth quarter of each year by the shares outstanding on December 31 of 1982 and 1983. These calculations produced the following results:
CASE II: UNION PACIFIC EQUITY VALUE - 1983
Segment Earnings EM Price
209.598.000 8.0 1,676,784,000 RR
125.156.000 11.6 1,451,809,600 Oil and Gas
47.289.000 10.9 515,450,100 Mining
21.896.000 8.0 175,168,000 Land
285,125,000 Corporate
4,104,336,700 Calculated UPC Equity Value
Shares Outstanding 14,318,556
Average Monthly Price $44.90
Average Price of UPC Common 5,132,903,164
Market Price to Computed Price 125.06%
Calculated Railroad Price - Adjusted 2,096,986,070
*49CASE II: UNION PACIFIC EQUITY VALUE - 1984
Segment Earnings P/E Price
RR 175,502,000 12.5 2,193,775,000
Oil and Gas 131,000,000 16.3 2,135,300,000
Mining 57,000,000 22.3 1,271,100,000
Land 8,000,000 8.0 64,000,000
Corporate 688,000,000
Calculated UPC Equity Value 6,352,175,000
Shares Outstanding 114,761,691
Average Monthly Price $52.60
Market Price to Computed Price 95.03%
Calculated Railroad Price - Adjusted 2,084,744,383
(Exhibit D-3, pp 63, 64).
After the values from “Case I” and “Case II” were derived, Goodwin and Ifflander then compared and correlated the two into a railroad equity value. To that value they added the values for the preferred stock and long-term debt, and subtracted from the result the estimated value of non-operating property. The result was their value for the taxable railroad subsidiary of UPC: $3,822,789,572 for 1983; $4,414,415,141 for 1984. Goodwin and Ifflander’s calculations raised a number of issues:
(1) Common stock
As noted, Goodwin and Ifflander’s appraisal of the value of the common stock portion of the equity of UPC differed from that used by Schoenwald in its selection of the pertinent period from which to derive average stock price. Goodwin and Ifflander chose an average of stock prices over the last three months of each year, rather than choosing to use an annual average stock price. This produced the significantly different valuation for the year 1983, as previously discussed. Goodwin and Ifflander justified their choice of dates for averaging purposes by pointing out that, because *50the valuation of UP was supposed to be a snapshot of the railroad operation as of the assessment date, stock prices closer to the assessment date were more representative of the railroad’s value at the pertinent moment. Schoenwald argued that such an average had a higher chance of distorting true value, because it was not broad enough to take out unrepresentative jumps or drops in value that might, for example, reflect market volatility as a whole at a time when there was no such volatility in UP.
(2) Preferred stock
As noted earlier, Goodwin and Ifflander treated the value of the preferred stock as an “add on” after they had identified a value for UP’s share of UPC’s common stock.
c. The Tax Court’s Stock Value Calculations
(1) Common stock
The Tax Court criticized both parties’ efforts, but indicated that it believed that common stock values closer to the assessment date should be used in any value calculations. Therefore, at least to that extent, it adopted the view of the Department.
(2) Preferred stock
As to whether to attribute the preferred stock entirely to UP or, instead, to add its value to the equity for UPC as a whole, the Tax Court again sided with the Department. Pivotal to the Tax Court was the purpose for which the preferred stock had been issued:
“The court finds that it is appropriate in this case to attribute all of the preferred stock to the railroad. Except for the presence of the other subsidiaries, all of UPC’s stock would be attributed to [UP]. Where a block of securities can be clearly attributed to one company, there is no need to allocate it among all the subsidiary companies. In the stock and debt approach, it is not a question of where the income comes from to pay the preferred stock dividends. The attempt is to measure the value of the assets by segregating out the value of the securities. Since the preferred stock was issued solely to obtain railroad assets there is no need to try and allocate the preferred stock to other than the railroad.”
*5111OTR at 187 (footnote omitted). Accordingly, the Tax Court included the preferred stock as a whole in its valuation of UP as a subsidiary of UPC. This had the effect of taking the preferred stock out of the court’s calculation of the value of UPC for allocation purposes, but then adding the value of the stock to the value for the railroad after other equity (and debt) had been apportioned to the railroad.
d. This Court’s Stock Value Calculations
(1) Common stock
As noted, the struggle here is between taking an annual average for the price of stock and taking an average for the last three months only. The Tax Court agreed with the Department that the average of the last three months’ prices was the appropriate average to use, because it was closer to each assessment date. The question is a close one but, on balance, we agree with the Tax Court and with the Department. The idea in ad valorem tax cases is to value the taxpayer’s assets as of the date of the assessment. Schoenwald’s desire to take the peaks and valleys out of UPC’s stock values thus is laudable for its attempt at orderliness, but is not necessarily consistent with the “snapshot” nature of ad valorem taxation valuation. The value of UPC equity for each year’s stock and debt calculation should be based on an average of the last three months’ stock prices in each year. The next question is, how is UPC’s preferred stock to be valued?
(2) Preferred stock
This is not an easy problem. Neither side seems to us to have it exactly right. The Department is too mechanistic in insisting that, simply because the preferred stock was issued for the purpose of financing UP’s purchase of Missouri Pacific, the entire value of the preferred should be attributed to the UP subsidiary. Such an approach could send appraisers in the future scurrying through financial records of holding companies to determine whether other debt and equity issues could be attributed, in whole or in part, to particular subsidiaries that were being valued for ad valorem tax purposes. *52The resulting attempts to attribute particular issues to particular subsidiaries seem certain to raise needless side questions in future valuation cases.17
On the other hand, Schoenwald is not entirely right, either. The fact that the preferred stock could be converted to common stock on a 2-for-l basis did not make the preferred stock, in effect, “super” common stock. The key to the preferred stock was that adjective: “preferred.” Its value was different from and greater than the value of two ordinary shares of common stock precisely because it stood ahead of the common stock in its right to receive dividends, and because of its convertibility, i.e., convertibility has an independent, additional value.
Schoenwald comes closer to the mark with the argument that the obligation to “prefer” the stock devolves upon the holding company, UPC, not just upon UP. Even if, in a given year, UP were to earn no money while the other subsidiaries did a land office business, UPC would have to grant a dividend to the preferred stockholders before it could reward its common stockholders with a dividend. An investor buying the preferred stock would know that he or she could look to the diversified holding company, with its somewhat greater safety as an investment, when the investor purchased the preferred stock.
On balance, we conclude that UP has the better of this argument. The Tax Court’s contrary conclusion focused too much on the reason for issuance of the stock and not enough on the stock’s characteristics as an investment.
In summary, we find that the process of calculating the portion of UPC’s equity that is attributable to the operating railroad subsidiary should utilize an equity total for UPC that includes UPC’s preferred stock and is valued based on an average of stock prices for the last quarter of each calendar year prior to the assessment date.
*53 2. Calculating the Debt Values
Of the two segments in the stock and debt approach to value, this one should be the easiest. UP reports what it owes at various times to several audiences, including the State of Oregon, the ICC, and its own shareholders. Nonetheless, differences appeared between the parties, due in part to a disagreement whether the Department had inadvertently “double counted” certain debt obligations for the 1983 tax year and in part due to a disagreement whether debt obligations should be valued on a yearly average or, like UPC’s equity, on a final quarter average.
Concerning the foregoing questions, the Tax Court held (1) that the Department had “double counted” and (2) that year-end values for debt obligations were best. We agree with both conclusions. The Department has not persuaded us that the Tax Court erred with respect to the double counting, and valuing the debt instruments in a manner consistent with the valuing of the corporate stock seems to us to be most consistent with the theory of ad valorem taxation previously discussed.
3. Isolating the Railroad Value
(a) The parties’ approaches
The next issue to be resolved is determining which method should be used for isolating the value of the railroad assets from those of the rest of the corporation. As noted, Schoenwald used a “direct” method, while Goodwin and Ifflander utilized their “Case I” and “Case II” analysis. Both have been summarized, ante.
(b) The Tax Court’s approach
The Tax Court found “problems” with both parties’ determinations of equity value for the railroad. Schoenwald, the Tax Court felt, had “backed into” his appraisal value for the railroad equity by “using the identical calculations [that] he used to find the discounted cash flow indication of value. This dilutes the value of the stock and debt approach.” 11 OTR at 186. The Tax Court also was critical of the way in which Schoenwald had handled the question of how to value Champlin Petroleum for the purposes of deducting it from the gross value of UPC.
*54The Tax Court also had what it called some “basic criticisms” of the Department’s stock and debt calculations. The calculations were very much the same as those used by the Department in its direct capitalization approach to the income indicator of value and had some of the same flaws and defects that the Tax Court had noted concerning that indicator. Moreover, the results of the two case calculations were sufficiently at odds with each other and with the demonstrable value of UPC’s outstanding common stock to undermine seriously the persuasiveness of the calculations. The court also seemed unimpressed with the Department’s use of “income-influence” and “asset-influence” methods to separate out nonrail assets, a process that we need not explain more fully here.
Having offered the foregoing criticisms, the Tax Court seems to have chosen not to use either party’s values under this approach. The court did, in its opinion, make it clear that it felt that UP’s valuation undervalued the railroad assets. On the other hand, the court stated: “[T]he court has also found errors, with [UP]’s assistance, in [the Department’s estimate of values. This requires adjusting [the Department’s estimated market value of the total Union Pacific Railroad system.” Id. at 189. The Tax Court did not define what “adjustments” it made, however. It simply announced its ultimate conclusions as to value.
(b) This court’s analysis
We disagree with both of the Tax Court’s objections to UP’s analysis. UP’s valuation figures under the stock and debt approach differ substantially from those that its expert found under his DCF calculation, and the figures certainly were not reached in the same way. With respect to the valuation of Champlin Petroleum, it is sufficient to note that Goodwin and Ifflander took basically the same approach for which Schoenwald is criticized.
On the other hand, we agree with the Tax Court’s criticisms of the Department’s presentation in its stock and debt analysis. Because the Tax Court did not adopt the Department’s figures, the Department bore the burden here of persuading this court that we should adopt them. It has not done so.
*55UP bore the same burden with respect to Schoen-wald’s approach, which also was rejected in the Tax Court. Subject to the modifications required by our specific rulings on certain subissues, UP has persuaded us. We reach the following results under the stock and debt method of valuation:
1983 1984
$3,149,552,000 $2,995,199,000
AVERAGING THE RESULTS OF THE VARIOUS APPROACHES
Each of the approaches has its own drawbacks and its own advantages. Nothing argued to us by the parties suggests to us any basis for preferring one approach over the other. The Tax Court’s approach does not suggest a basis for assigning a preference, either. Accordingly, we give equal weight to the values obtained through the two approaches. This produces the following results:
1283 1284
$2,975,926,000 $3,007,450,000
IDENTIFYING THE OREGON PORTION OF THE VALUATION
The Tax Court made the following observation in its opinion concerning the allocation of a portion of the value of UP to Oregon for ad valorem taxation purposes:
“A proportion of the total system value must be allocated to Oregon for taxation. Although the differences between the allocation factors used by the parties are not great, there are differences. After reviewing [the Department’s] calculation of its allocation factors and [UP’s] calculation of allocation factors, the court finds that [the Department’s] allocation factor should be used.”
Id. at 189-90. UP has not persuaded us otherwise. We assign the same allocation percentage that the Tax Court assigned, viz., 4.06 per cent in 1983 and 4.76 per cent in 1984. This produces the following results:
1984 1283
$120,823,000 $143,155,000
*56CONCLUSION
The judgment of the Tax Court is modified. The value of UP allocable to Oregon for ad valorem tax purposes is $120,823,000 for 1983 and $143,155,000 for 1984.
This case took 43 days to try before the Oregon Tax Court. The record contains 9,140 pages of transcript and nearly 700 exhibits. We adhere to the view, previously expressed, that requiring that this court decide these cases de novo is an inappropriate expenditure of judicial resources. See United Telephone v. Dept. of Rev., 307 Or 428, 432 n 2, 770 P2d 43 (1989).
We use both abbreviations “UP” and “UPC,” because it will be necessary, at various points in this opinion, to distinguish between the parent holding company, Union Pacific Corporation (UPC), and its wholly owned railroad subsidiary (UP).
See supra note 1.
The total pages devoted to trial briefing exceed 1,000: UP’s opening and reply briefs in the Tax Court totalled 523 .pages, plus appendices; the Department’s brief contained another438 pages, plus appendices. Briefing before this court has been, at least by comparison, relatively modest: 195 pages, together with many appendices, for UP; 146 pages, together with appendices, for the Department. (Both parties before this court cross-reference large portions of their trial court briefs, thereby effectively extending their briefs in this court by many pages.)
This formula is the functional equivalent of the formula V = I/R, discussed in PP&L v. Dept. of Rev., 308 Or 49, 58-59, 775 P2d 303 (1989).
The NROI figures were taken from Interstate Commerce Commission (ICC) data. They are not, as raw data, disputed in these proceedings.
Or, more accurately, the average of the composite NROI of the three railway systems that had merged to form the present UP system as of the assessment date.
As already explained, Schoenwald’s “no growth” conclusion did not mean that UP’s NROI from year to year would not get larger. It simply meant that, as to the next year, a realistic estimate of income was a five-year average NROI, because that figure represented an average of recent past experience and the prospects for the near future did not suggest a sudden upturn in UP’s revenue-generating fortunes. Obviously, applying this same approach to the next year would not (except in the most unusual circumstances) produce precisely the same mathematical result, because the new five-year average NROI would include the actual income experience of the end year and delete the income experience of the sixth preceding year.
The Department’s brief to this court contains many factual propositions that are unsupported by any citation to the record or, in a number of cases, by any citation at all. Citations frequently are given to some portion of the Department’s very long post-trial brief, and that is no substitute for a direct reference to the trial record. *24Several citations give the impression that they are based more on counsel’s substituted expertise than on anything that the Department actually demonstrated through its witnesses at trial. This impression is bolstered by the fact that the Department devoted a portion of its post-trial brief to a partial impeachment of its own principal expert witnesses.
Because our review of these decisions of the Tax Court is de novo, it is entirely possible that this court would refuse to accept particular testimony in one case, but then accept that same testimony in another case, if the surrounding evidence placed the testimony in a different light in each case. United Telephone Co. v. Dept. of Rev., 307 Or 428, 431-32, 770 P2d 43 (1989).
This problem also affects the persuasiveness of the Department’s calculations under the stock and debt indicator of value, discussed post.
‘ ‘Spreads’ ’ are the differences in rates of return that investors are demanding between investments of various risks. By way of illustration, assume two bonds. One is very safe; as to it, investors will accept a rate of return of 10% as adequate to justify investment. The second is very risky; the same investors would require a return of at least 18% before they would be willing to risk their money on the company that issues the second bond. In our example, the “spread” between the two would be 8 per cent (18 per cent -10 per cent). In cases in which the “spread” is that between the safest forms of investment, government securities, and other, more risky, securities, the spread may also be called the “risk premium,” i.e., the premium that an investor demands to take this level of risk with the investor’s money; when the risk is compared with a very safe investment. For a further discussion of this concept, see PP&L v. Dept. of Rev., supra, 308 Or at 61-62.
The following table summarizes the range of equity capitalization rates from the various sources:
1983 1984
ICC 19.8% 16.8%
Union Pacific 18.8% 18.8%
CMA (consultant) (method I) N/A 18.8%
Schoenwald 17.0% 18.0%
Goodwin/Ifflander (re Southern Pac.) 15.6% 17.14%
CMA (consultant) (method II) N/A 16.2%
Goodwin/Ifflander (present case) 15.0% 15.5%
The model is stated formally as dividend yield plus growth. Stated mathematically:
^ Discount Rate = w- +g •M)
Where: Dx = expected dividends
P0 = current price
g = sustainable growth in dividends
As a simplistic example, assuming a stock with a price of $100 and a dividend of $10, plus an expected growth of 5%, the calculation would be: /A" = 10% + 5% = 15 % discount rate. $100
Use of the “stock and debt” approach is authorized by OAR 150-308.205 (A)(2)(d).
If we correctly understand the appraiser’s use of the methodology, there is a *48clear mathematical error here. The figure for “Value” of “Earnings” in the 1983 calculations should be $1,676,784,000 ($209,598,000 x 8.00), not the higher figure ($2,101,082,825) reported by the appraisers. Obviously, a simple transposition of numbers has occurred because, in fact, the latter figure ($2,101,082,825) is the correct “Average Railroad Equity Value” for 1983.
Also troubling in connection with this portion of the Goodwin and Ifflander analysis is the fact that, in addition to issuing the preferred stock to finance the Missouri Pacific acquisition, UPC also issued 17.3 million shares of common stock. Yet, so far as we can determine, Goodwin and Ifflander do not attempt to attribute any of this latter issue directly to the UP subsidiary.