
89 Wis.2d 331 (1979)
278 N.W.2d 487
SOO LINE RAILROAD COMPANY, Plaintiff-Appellant,
v.
DEPARTMENT OF REVENUE, Defendant-Respondent.
No. 77-658.
Court of Appeals of Wisconsin.
Argued September 29, 1978.
Decided March 29, 1979.
*335 For the plaintiff-appellant there were briefs by John S. Best and Willard C. Jackson of Michael, Best & Friedrich, Milwaukee, and oral argument by John S. Best of Michael, Best & Friedrich, Milwaukee.
For the defendant-respondent there was a brief by Bronson C. La Follette, attorney general, and John J. Glinski, assistant attorney general, and oral argument by John J. Glinski, assistant attorney general.
Before Gartzke, P.J., Bablitch, J. and Dykman, J.
[1]
DYKMAN, J.
This is an appeal from a judgment affirming the Wisconsin Department of Revenue's assessment for the 1973 ad valorem tax upon appellant's railroad operating property. Section 76.07 (3), Stats., allows the Department of Revenue to assess the full market value[1] of a railroad's operating property, and then allocate the percent of the assessment to the railroad operating property located in Wisconsin. The Department of Revenue appraised Soo Line's railroad operating property at $143,557,000, with 39.02 percent of that amount, or $56,000,000, allocated to Wisconsin, resulting in a tax of $1,628,164.23. The appellant does not take issue with the 39.02 percent allocation factor applied to its railroad operating property, but contests the total *336 assessment, alleging that the assessment should have been substantially less than as determined by the Department of Revenue.[2]
[2]
It is extremely difficult to determine the value of a railroad, or of its operating property. A railroad is a large, complex corporation. Railroads are seldom if ever bought and sold, making it difficult to apply the traditional test of fair market value.[3] When a railroad is appraised, the willing buyer and willing seller test introduces an alien concept into accounting procedures because it stresses the requirements and desires of non-existent buyers and sellers rather than the realities of the day-to-day financial operation of a railroad. Despite conceptual difficulties in this type of case, the willing buyer, willing seller test is the legal definition of fair market value.
Because it believed previous methods of assessment were too inexact, the Department of Revenue in 1974 developed a formula which it felt could be used to quantitatively assess railroad operating property.[4] The formula *337 combines three conceptually different methods of determining value: (1) The capitalized income approach assumes that a railroad is worth an amount equal to the net income produced by the railroad multiplied by a factor which indicates the rate of return an investor would expect on his investment in the railroad. (2) The cost approach assumes a railroad is worth an amount equal to the original cost of its operating property, adjusted to reflect depreciation and obsolescence. (3) The stock and debt approach assumes that a railroad is worth an amount equal to the total of the value of its outstanding *338 shares of stock plus the value of its outstanding debt.
Because the three approaches used or discussed by the appraisers who testified in this case depend upon certain historical facts, some background and history of Soo Line is important.
Soo Line was formed in 1961 by a merger of three railroads. Construction of the system was substantially completed by 1911. The railroad operates in Illinois, Wisconsin, Michigan, Minnesota, Montana and the Dakotas. It has 1700 miles of main line track and primarily hauls grain, fertilizer, and forest products. The railroad was originally designed to haul lumber and minerals from the mining and logging districts of Wisconsin, Michigan and Minnesota. Since 1911, trucks, pipelines, barges, ships, and airlines have diverted much of Soo Line's business.
Soo Line's net railroad operating income (operating revenues less operating expenses) for each of the 10 years prior to the 1973 assessment was:


   1964 ...... $ 6,856,000         1969 ......   $ 7,790,000
   1965 ......   8,388,000         1970 ......     8,834,000
   1966 ......   9,102,000         1971 ......    10,759,000
   1967 ......   4,616,000         1972 ......    13,808,000
   1968 ......   8,836,000         1973 ......    19,883,000

The increased 1973 net operating income was the result of conditions not likely to reoccur. During that year, substantial purchases of wheat by the Russian government tied up competitors' freight and box cars at gulf coast ports, leaving Soo Line with virtually the only available cars to haul wheat out of its territory. Soo Line handled its increased volume at a relatively small increase in cost, resulting in a substantial increase in its net operating income.
[3-5]
The statutory standard of review in the circuit court under sec. 76.18, Stats., is whether, "in the judgment of *339 the court the assessment should be substantially less or more than the assessment as determined by the department." The standard of review on appeal from the circuit court is whether the court's findings of fact are against the great weight and clear preponderance of the evidence and are clearly erroneous, giving due regard to the opportunity of the trial court to judge the credibility of the witnesses.[5] However, a finding based upon an erroneous view of the law is not entitled to the great weight and clear preponderance standard of review.[6]
Five appraisers gave their opinions of the value of Soo Line's operating property. We examine this evidence *340 to determine if there is credible evidence to support the trial court's finding that the value of Soo Line's operating property was not substantially more or less than the $143,557,000 determined by the Department of Revenue. The evidence relied on by the Department of Revenue consists of its assessment of the Soo Line and also of an assessment by an independent appraiser, John E. Green. We will first consider the department's formula and then examine Green's assessment.

THE DEPARTMENT OF REVENUE'S FORMULA
The Department of Revenue calculated the fair market value of Soo Line's operating property by use of the three methods discussed above. The values reached were:


  1. Capitalized Income            $132,848,000
  2. Cost                          $170,353,000
  3. Stock and Debt                $155,143,000

An arithmetic average of these values is approximately $152,781,000. The Department of Revenue did not use an arithmetic average, but instead used the formula set forth in footnote 4 to weigh each of the three results according to the significance and reliability the Department of Revenue placed on each method. The formula itself is no more valuable than the judgment of the persons who devised it because two items (the 75 percent rejection factor and the standard weights) are arbitrary and judgmental in nature. The formula is merely a quantified method of stating that varying weights will be assigned to each of the three methods.
The results reached by the Department of Revenue's use of their formula were:


*341
                                             ADJUSTED
  METHOD         VALUE           WEIGHT       WEIGHT
  _____          _____           ______      ________
                                              (value ×
                                              weight)
  Capitalized
    Income       $132,848,000    .6622         $87,972,000
  Cost           $170,353,000    .2089         $35,587,000
  Stock & Debt   $155,143,000    .1289         $19,998,000
       TOTALS                   1.00           $143,557,000

Because the income approach valuation is 66 percent of the total valuation, an accurate income approach valuation will tend to minimize inaccuracies in the stock and debt and cost approaches. It follows that a mistake in the income approach valuation will pervade the entire calculation. Even if the income approach valuation is accurate, a mistake in either of the other two approaches may significantly affect the overall valuation because the approaches are mathematically combined and are not severable under the formula.
[6]
Because a formula or system of combining valuation methods is necessary if the results of more than one method of appraisal are used,[7] the use of a formula is not unsound. The ultimate test of a formula is whether it bears a reasonable relationship to reality and conforms to state and federal laws and constitutions. We examine the components of the Department of Revenue's formula in our review of the trial court's decision.

CAPITALIZED INCOME APPROACH TO VALUE
The theory of the capitalized income approach to value is that the greater the net income produced by an asset, *342 the more a willing buyer will pay for the asset. Expressed as the expected rate of return on an investment of the purchaser's capital, this approach can be described as follows:
        I
   V = ___, where V is value, I is anticipated income,
        R
and R is the percentage rate of return the investor demands on his capital. R is also described as the capitalization rate.
All five appraisers who testified at trial agreed that the capitalized income approach is the best or most significant approach to determine the value of Soo Line's railroad operating property. The five appraisers and their appraisals of Soo Line's railroad operating property through the use of the capitalized income approach were:


   For the Department of Revenue
          Robert F. Steffes             $132,848,000
          John E. Green                  141,500,000
   For the Soo Line
         M. D. Ross, Jr.                 101,789,000
         Arthur A. Schoenwald             95,558,000
         John E. Housiaux                102,000,000

Although both Soo Line and the Department of Revenue agree on basic technique of determining value under this approach, they differ substantially in their calculations of both (I) and (R).
The capitalization of income approach to value involves two major steps: A determination of the income to be capitalized, and a determination of the rate at which that income will be capitalized.

Determination of Income  Rail and Tie Adjustment
[7]
To arrive at the income to be capitalized, the appraisers started with Soo Line's 1973 net income after *343 taxes and then made several adjustments to that income.[8] Soo Line contests only a $2,039,596 "rail and tie" adjustment.
Soo Line replaces a large number of rails and ties annually. For the years 1969-73, the annual cost of doing so averaged $2,039,596. The replacements do not increase the value of the railroad but are in the nature of normal maintenance. Because rails and ties have a substantial life, it might seem that usual accounting methods would require them to be depreciated. However, because of the large number of rails and ties used and the necessity of replacing some each year the railroad is in operation, the railroad is required by the Interstate Commerce Commission *344 to treat rail and tie expenditure as an operating expense.
The Department of Revenue added the expense of replacing rails and ties during 1974 back into Soo Line's income because they contended these items must be depreciated, not expensed. The trial court considered this adjustment and approved it.
The result of the rail and tie addback is an increase in the net operating income of Soo Line, and under the
     I
V = --- computation, an increase of about $12,000,000
     R
in the Department of Revenue's capitalization income approach appraisal.

Determination of Capitalization Rate
The Department of Revenue agrees that its rail and tie adjustment to income inflates the income component
            I
of the V = --- formula. It maintains, however, that it
            R
has adjusted the capitalization rate by the use of an investment recovery allowance, or "sinking fund," which will earn at a rate sufficient to provide for rail and tie replacement and depreciation. It contends that its valuation of Soo Line's railroad operating property (V) is accurate because it properly adjusted both (I) and (R). In other words, the first part of the rail and tie controversy has to do with whether, in theory, the Department of Revenue should have made the adjustment to the income component. The more crucial issue is whether the Department of Revenue's corresponding adjustment to the capitalization rate was sufficient to take the income adjustment into account and eliminate the admitted inflation of the income component.
The basic capitalization rate is a combination of two rates. It consists partially of the rate that equity holders *345 would expect on their equity investment in the Soo Line. All witnesses who appraised Soo Line's railroad operating property used a 14 percent return on equity. With the exception of the Department of Revenue's witness John E. Green, all witnesses used a current money rate of 9.50 percent as the rate of return on debt investment. Because equity and debt of Soo Line were almost equal, the 14 percent and 9.50 percent rates of return were averaged, giving a basic capitalization rate of 11.75 percent.[9] The combination of the two rates was termed a "band of investment" by most of the witnesses.
The basic band of investment capitalization rate is applied to Soo Line's net income, after deduction of depreciation and other expenses and income taxes. A prospective purchaser may have different depreciation expenses and income taxes than does Soo Line. For that reason, the income stream to be capitalized may be adjusted to reflect before-tax, before-depreciation income. Once these adjustments are made to the income component, a corresponding adjustment must be made to the band of investment capitalization rate because the prospective purchaser will be meeting additional fixed charges (taxes and depreciation) out of the income stream.
The Department of Revenue added not only depreciation and federal taxes to the income stream, but also the rail and tie replacement expense. Consequently, its capitalization rate had to be adjusted to reflect this expense as well as depreciation and federal taxes.
To adjust for all depreciation and rail and tie expense, the Department of Revenue adjusted the capitalization rate through use of a sinking fund, which will be discussed later in more detail. The department added *346 1.9417 percent to the capitalization rate to cover all depreciation.
The Department of Revenue added a federal tax component of 3.5221 percent to the capitalization rate to recognize the different impact federal income taxes would have on a new purchaser. Soo Line added 6.1385 percent to the capitalization rate to recognize the federal tax impact on a new purchaser.[10] The impact of federal taxes on a purchaser of Soo Line's operating property might be different from the impact of federal taxes on Soo Line. This is because the purchaser's basis for depreciable property would be different, methods of depreciation used by the purchaser could be different, and the tax bracket of the purchaser might be different.
Soo Line's proposed capitalization rate, adjusted for federal taxes and depreciation, was 21.0385 percent. The Department of Revenue's proposed capitalization rate, adjusted for depreciation by the sinking fund component and for federal taxes, was 17.2138 percent. The
                                                   I
capitalization rate is the denominator of the V = ---
                                                   R
formula. A smaller denominator results in a higher value of the Soo Line's railroad operating property, assuming no change in the numerator.
A sinking fund is a method of providing for replacement of an item having a finite life which will eventually *347 be consumed or worn out and rendered valueless. Credits are made to the sinking fund each year in amounts which, with interest, will be sufficient to recover the original investment in each item by the end of the life of the item. This money is invested either internally or externally. Soo Line does not use a sinking fund, but instead expenses rails and ties and depreciates other items. A sinking fund assumes an item (or a composite of items) with a finite life, not the situation with Soo Line because the Interstate Commerce Commission will not allow Soo Line to abandon its business. The actual use of a sinking fund would probably destroy Soo Line by failing to provide enough operating income. This is because both internal and external investment of the fund would not generate a sufficiently high rate of return, and an internal investment that involved a repurchase of Soo Line's outstanding securities would leave the equity investor with less than the required 14 percent return on equity. Under these circumstances, the use of a sinking fund does not conform to the facts of life which Soo Line faces.
[8]
The use of a sinking fund or a similar accounting theory results from the Department of Revenue's decision to use a method of accounting for Soo Line's rail and tie expenses that is different from Soo Line's method. Where a plaintiff taxpayer, a utility, attempted to use straight line depreciation in its attack on an ad valorem assessment, but had used a sinking fund in its actual accounting procedures, the Wisconsin Supreme Court said:
The commission accepted the method and percentage of depreciation set up by plaintiff's books, used by it as a basis of rates and credit, and to sustain plaintiff's contention would require that all accounting systems of estimating depreciation be discarded for the purpose of ad valorem assessments and annual or at least frequent surveys made by the commission of the physical condition *348 of the properties. It is not apparent to us that such a practice would produce superior results. We see no reason why the Tax Commission may not accept whatever method of depreciation is regarded by the utility as sufficient to maintain its investment and which the evidence shows actually does maintain its investment as having a bearing upon actual annual depreciation. Taken over a period of years, this will produce equitable although not perfect results. If it is a satisfactory basis for dealing with investors, creditors, and rate-making bodies, we see no reason why it may not be given weight by a tax commission as a factor to be considered in connection with the capitalization method. Wisconsin Gas & Electric Co. v. Tax Comm., 221 Wis. 487, 503-504, 266 N.W. 186 (1936).
The shoe is now on the other foot. Where a taxpayer has consistently used a generally accepted method of accounting for legitimate business purposes and not as a device the primary purpose of which is to avoid taxation, the Department of Revenue should accept the taxpayer's accounting method when making an ad valorem assessment of the taxpayer's property.
[9]
The trial court found that Soo Line's treatment of rail and tie expense as a maintenance expenditure had the effect of understating both net railroad operating property and depreciation, and that to compensate for this it was necessary to add back rail and tie expenses to net railway operating income. This was error. Soo Line's accounting procedure for rails and ties accurately represents what occurs in fact: rails and ties are constantly wearing out and are constantly replaced. A willing buyer and seller would have no reason to change Soo Line's method of accounting for its rails and ties. There was no need to change Soo Line's accounting *349 methods by adding back rail and tie expense. Wisconsin Gas & Electric Co. v. Tax Comm., 221 Wis. 487, 503-504. This error necessitates a reversal of the judgment appealed from unless the Department of Revenue's assessment can be sustained through the use of a proper alternative method of appraising Soo Line's property.
Normally, we would now review any other evidence to see if it supported the Department of Revenue's assessment. Because the formula used by the Department of Revenue in this case presumably applies to other railroads, and the matter is of significance to all railroads operating in Wisconsin, we will examine other claims of error Soo Line has made.

COST APPROACH TO VALUE
Of the five witnesses who gave their opinions as to the value of Soo Line's operating property, only one, Robert F. Steffes, a tax analyst for the Department of Revenue, placed any significance on the cost approach to value.[11] Mr. Steffes assigned a weighted average of 20.89 percent to the cost approach, because he felt an owner of a railroad would consider cost. However, he agreed with Soo Line's attorney's question:
Q. If the owner looks at cost, he cries, doesn't he?
A. Yes. Yes.
Soo Line's director of taxes, M. D. Ross, Jr., did not use or discuss the cost approach to value. John E. Housiaux, *350 one of Soo Line's expert witnesses, gave the following opinion about the cost approach to value:
Economic obsolescence has reduced the value of certain portions of the property to almost zero. Functional obsolescence affects the value of the remaining portions in varying degrees.
Because of the presence of these negative elements throughout the system, any attempt to develop a current value indicator by means of adjustments to the original cost of the system as a whole becomes so subjective and speculative in nature that the process becomes unreliable as a value indicator.
Arthur A. Schoenwald, another of Soo Line's expert witnesses, gave this opinion about the cost approach to value:
In this Schedule, the physical value evidence  original cost adjusted for obsolescence  is examined. Such a measure, in my opinion, rarely evidences actual market value. . . .
My analysis leads to the conclusion that physical value evidence  based on original costs from another century in some cases  cannot provide any beneficial insights into current market price levels for railroad operations. Therefore, I will assign no weight to any measure which purports to represent "adjusted" original cost in reaching my judgment about the value of the Soo Line Railroad System.
The Department of Revenue used the cost approach. It calculated original cost less depreciation and subtracted a factor for obsolescence. Obsolescence must be subtracted separately because the depreciation rates used by Soo Line take into account only physical deterioration, not economic or functional deterioration.
In computing the amount of obsolescence to assign to Soo Line, the department used the Thatcher-Dubielzig *351 formula.[12] That formula compares a subject railroad with the "best in the industry" or a "blue chip" railroad. A Department of Revenue witness, in explaining the blue chip method, stated:
It must be remembered that the "blue chip" method does not entirely eliminate the obsolescence which is present in the subject railroad. This is due to the fact that the "blue chip" railroads also have some obsolescence so that when these railroads are used as a standard of measurement, the resulting obsolescence figure brings the subject railroad into line with the comparable roads but does not measure the additional obsolescence which may be present in the "blue chip" railroads and thus does not eliminate this portion of the obsolescence which would be present in the subject railroad. Due to this fact, the value indication by the Cost Approach will be the highest value indicator in almost every instance in which "blue chip" method of estimating obsolescence is used.
[10]
We conclude from the testimony of the five expert witnesses that the cost approach, when applied to a railroad's operating property for the purpose of determining an ad valorem tax, is of such little value that its continued use is not justified. The original cost of a railroad has little, if any, relation to its present value. Attempts to adjust original cost for obsolescence appear to be little more than mathematical exercises in speculation.
An examination of the "blue chip" method as an attempt to adjust historical cost to make it resemble present value shows the infirmities of the method.
*352 Part of the Department of Revenue's cost approach to value is footnoted.[13] The department chose the Cincinnati, New Orleans & Texas Pacific as its blue chip railroad. *353 As the department had no 1973 data for this railroad, it estimated the 1973 data on the basis of data for the years 1970-1972. Using the Thatcher-Dubielzig formula, the Department of Revenue compared nine categories of performance for Soo Line with the same nine categories of the blue chip railroad. For example, Soo Line produced $36,560 of gross revenue per mile of road, but the blue chip railroad produced an average of $224,032 per mile. As the Soo Line's gross revenue per mile was 16.32 percent that of the blue chip's gross revenue per mile, this indicated that in this category, Soo Line is 83.68 percent obsolete. Percentages were similarly obtained for eight other categories of performance, and the percentages averaged. The average percent thus obtained was 57.13, which in comparison to the blue chip railroad indicates that Soo Line's operating property is 42.87 percent obsolete. The department then multiplied the depreciated cost of Soo Line's railroad operating property by 57.13 percent, made certain additions,[14] and determined that $170,353,000 is the value of Soo Line's operating property based on the cost approach.
The Department of Revenue's cost approach to value compares dissimilar categories with each other. The Department of Revenue gave each of the items equal *354 weight, and averaged percentages which deviate from the average by 7.69 percent to 42.21 percent. The standard deviation is 29.31 percent, and the coefficient of variation is .513. Although the significance of these statistical indicators is judgmental, in this case we believe that they show that the results obtained by using the cost method fall within the area of speculation.
More serious, however, is the failure of the Thatcher-Dubielzig method, and thus the cost approach, to determine the obsolescence of the blue chip railroad. One of Soo Line's witnesses analogized the comparison of Soo Line's obsolescence with the blue chip's obsolescence to the comparison of a very ill person with a moderately ill person. We do not know how obsolete Soo Line really is, and without this knowledge, the cost approach of determining the value of Soo Line's operating property is of little, if any, significance.

STOCK AND DEBT APPROACH TO VALUE
The stock and debt approach to value is based upon the accounting principle that a company's assets are equal in value to the total of the liability side of its balance sheet. If the liability side of the balance sheet is determined, that amount is also the gross value of the business. It is also based on the assumption that the aggregate market value of all of the company's outstanding stocks, bonds, and other securities fairly represents an appraisal by the investing public as to the value of the property of the company. Wisconsin Gas and Electric Co. v. Tax Comm., 221 Wis. 487, 495. Since the gross value represents the value of both operating and non-operating property, the value of the non-operating property must be subtracted from the total to arrive at the value of the railroad operating property.
*355 [11]
If the total value of the non-operating property is not removed, the Department of Revenue has violated sec. 76.03, Stats., which requires that the Department of Revenue assess only operating property. A second problem exists if Soo Line can show that the Department of Revenue is taxing out-of-state property, because that assessment could not survive a due process challenge. The Department of Revenue cannot tax property which is unconnected with Wisconsin. Northwest Airlines, Inc. v. State, 77 Wis.2d 152, 161, 252 N.W.2d 337 (1977). It may, however, consistent with constitutional principles, value the total utility, including out-of-state operating property, and then apportion the percentage properly allocable to Wisconsin. Braniff Airlines v. Nebraska State Board, 347 U.S. 590 (1954).
The Department of Revenue and Soo Line agree that cash (except for a working capital allowance), receivables, investments in affiliates, unamortized discounts, and certain special funds are non-operating assets and therefore are not subject to assessment.
Soo Line and the Department of Revenue used different methods in attempting to remove the value of Soo Line's non-operating property from the total value of Soo Line's stock and debt. Soo Line deducted the actual value of the non-operating assets, as reflected by the book value or the assessed value of those assets. The Department of Revenue used an "income influence" method of removing the value of the non-operating property. This method calculates the ratio of the non-operating property income to the total income and applies this ratio to the total value of the stock and debt to determine the deduction for non-operating property from the total value of the stock and debt.
The income influence method assumes that an average non-operating asset will produce the same income as an *356 average operating asset. Soo Line has shown, however, that certain non-operating assets of substantial value produced no income. Removal of non-operating property based on amount of income generated by that property understates the value of Soo Line's non-operating property. For example, Soo Line owns all of the outstanding shares of Tri-State Land Company, which owns property for industrial development and an office building in downtown Minneapolis. Those shares are non-operating assets. Although Soo Line received no dividend on the shares of stock, the investment has substantial value. A similar problem exists with respect to investments in other affiliates which produce no income. These include investments in the Sault Saint Marie Bridge Company, Minnesota Transfer Railway Company, St. Paul Union Depot Company, and Belt Railway Company of Chicago.
The Department of Revenue asserts that although the examples discussed result in the values of some assets not being excluded from total value, other assets  whose values are low but which produce substantial income  offset the high value-low income assets.
[12, 13]
Soo Line proved, however, that not all non-operating assets were removed. Soo Line's balance sheet shows that even when viewing working capital as operating property, Soo Line owned cash and temporary investments of $24,615,000. The Department of Revenue and Soo Line agreed that this total represents non-operating property. Since the Department of Revenue reduced the total stock and debt value by only $21,920,000, the Department of Revenue's assessment using the stock and debt approach improperly inflated the value of Soo Line's railroad operating property by a minimum of $2,695,000. This violates sec. 76.03(1), Stats. To the extent the non-operating property is located outside Wisconsin, it also violates the due process clause of the *357 fourteenth amendment to the United States Constitution. Northwest Airlines, Inc. v. State, 77 Wis.2d 152, 160-61. If the Department of Revenue desires to use the stock and debt approach, it will have to devise a way to do so that does not include non-operating property in its valuation.
Soo Line's deduction of the book or assessed value of non-operating property has its own difficulties. Book value is a figure which may have no relation to the present value of an asset. It ignores inflation. It may be distorted by various forms of depreciation. The original basis for Soo Line of an item may not have been its fair market value. However, the assumption that book values will average out appears as reasonable as the department's assumption in its income influence method that incomes from various assets will average out.
Total assessed value of non-operating properties as determined by the municipalities in which the properties are located, even when adjusted by the appropriate appraisal ratios, may not accurately reflect actual value. Assessors have differing degrees of ability, and may not keep their assessments current. However, the difficulties with Soo Line's methods of removing non-operating property appear to err on the side of understating the value of non-operating property and result in an operating property value which exceeds its actual value.
Other items to be subtracted from the total value of the stock and debt with the exception of working capital will not be discussed in this opinion. Because of our decision that this matter must be remanded, these items will be relitigated and their effect upon the Department of Revenue's assessment will be determined by the trial court.
[14]
The stock and debt approach to value assumes that shareholders and debt owners act in an informed and *358 reasonable fashion, that prices paid for shares and debt reflect only the value of the corporation, and that the price paid for a small number of shares is the same as the price paid for the number of shares necessary to assure control of the corporation. This court cannot determine to what degree the inaccuracy of the premise affects the value of the method. We do conclude that in this case, value of the stock and debt approach to value, when used, should be given a weight substantially less than the capitalization of income approach.
A further issue is the department's refusal to exclude $9,103,000, one month's working capital, from the gross stock and debt valuation.
[15]
Soo Line points out that sec. 76.07 (1) and (2), Stats.,[15] require the Department of Revenue to assess Soo Line's property "on the same basis ... as near as may be, as the value of the general property of the state is ascertained and determined." Section 70.112 (1), Stats.,[16] exempts *359 money and intangible personal property from general property taxes. Soo Line contends that sec. 70.112 (1) should be applied to exclude Soo Line's cash and intangibles because to exclude money and intangible property from general property taxes of all taxpayers except railroads (and certain others enumerated in sec. 76.07 (1)), would cause sec. 70.112(1) to be unconstitutional as a denial of equal protection and due process of law as to Soo Line. A statute will be construed to preserve it from unconstitutionality. In Re City of Beloit, 37 Wis.2d 637, 643, 155 N.W.2d 633 (1968).
The Department of Revenue contends that working capital is necessary for the operation of Soo Line and thus is part of railroad operating property, that the exemptions to property taxes under ch. 70, Stats., do not apply to utilities taxed under ch. 76, Stats., and that the strong presumption of the constitutionality of tax statutes allows a distinction to be made between taxpayers whose cash and intangibles are not taxed under ch. 70, and utilities whose cash and intangibles are taxed under ch. 76.
[16, 17]
An exemption from taxation must be clear and express. All presumptions are against it, and it should not be extended by implication. Milwaukee E. R. & L. Co. v. Tax Commission, 207 Wis. 523, 536, 242 N.W. 312 (1932). The argument made in that case by Milwaukee Electric Railway & Light Company was similar to Soo Line's argument. In that case, ch. 70, Stats., exempted motor vehicles from the general property tax levied by that chapter, but ch. 76, Stats., provided, as it does now, the method and manner of levying, collecting and disbursing the taxes on the property of railroads and utilities. The court said:
As far as this case is concerned, it suffices to say that as long as that property is in fact assessed and taxed *360 under ch. 76 it is to be treated, for purposes of taxation and exemption, as special property and not as part of "the general property of the state," which is taxed under ch. 70; and, consequently, the exemptions as to "general property" taxed under ch. 70 are inapplicable. 207 Wis. 523, 543.
Soo Line contends that the inclusion of any of Soo Line's cash and intangibles, which consist partly of working capital, is a denial of due process and equal protection under the fourteenth amendment to the United States Constitution because its cash and intangibles are taxed, while the cash and intangibles of persons not taxed under ch. 76, Stats., are exempted.
Although Soo Line argues that the case of Hillside Transit Co. v. Larson, 265 Wis. 568, 62 N.W. 722 (1954) has no relevance to this case because Hillside dealt with the exemptions from a ton-mile tax imposed on the operations of motor carriers and this case deals with exemptions of cash and intangibles from a general property tax, Soo Line makes the same due process and equal protection attacks that were made in Hillside. The court in Hillside upheld the statute which levied the ton-mile tax although 91.3 percent of the motor carriers by number and 75 percent by volume of goods transported were exempt. The court said:
In passing upon the constitutionality of the exemption of these particular products we must assume that the legislature determined that such exemptions would be of direct economic benefit to the agricultural population, thereby indirectly benefiting the citizens of the state as a whole. We, therefore, are not prepared to hold that the resulting classification was arbitrary or unreasonable because it is not the role of the court to determine economic policy. That is a legislative and not a judicial function. 265 Wis. 568, 580.
[18-20]
In Lehnhausen v. Lake Shore Auto Parts Co., 410 U.S. 356 (1973), the United States Supreme Court discussed *361 the leeway given to states in the area of taxation under the equal protection clause of the fourteenth amendment. The court stated:
The Equal Protection Clause does not mean that a State may not draw lines that treat one class of individuals or entities differently from the others. The test is whether the difference in treatment is an invidious discrimination. ... Where taxation is concerned and no specific federal right, apart from equal protection, is imperiled, the States have large leeway in making classifications and drawing lines which in their judgment produce reasonable systems of taxation. 410 U.S. 356, 359. (Citations omitted.)
Separate treatment of utilities is not a basis for an equal protection claim. New York Rapid Transit Corporation v. New York, 303 U.S. 573, 579 (1938). The presumption of constitutionality can be overcome "only by the most explicit demonstration that a classification is a hostile and oppressive discrimination against particular persons and classes." Lehnhausen, 410 U.S. 356, 364, quoting Madden v. Kentucky, 309 U.S. 83, 88 (1940).
The court in Lehnhausen quoted with approval from Carmichael v. Southern Coal & Coke Co., 301 U.S. 495, 510 (1937):
"A state legislature, in the enactment of laws, has the widest possible latitude within the limits of the Constitution. In the nature of the case it cannot record a complete catalogue of the considerations which move its members to enact laws. In the absence of such a record courts cannot assume that its action is capricious, or that, with its informed acquaintance with local conditions to which the legislation is to be applied, it was not aware of facts which afford reasonable basis for its action. Only by faithful adherence to this guiding principle of judicial review of legislation is it possible to preserve to the legislative branch its rightful independence and its ability to function." 410 U.S. 356, 364-65.
*362 We must assume in this case that the legislature determined that the exemptions given to persons other than Soo Line would benefit all of the state's residents. Furthermore, those exemptions may be offset by the substantial benefits that Soo Line enjoys by being taxed pursuant to ch. 76, Stats., which cannot be obtained by those taxed pursuant to ch. 70, Stats. As an example, were each Wisconsin municipality to tax Soo Line's property within the municipality, the cost to Soo Line of contesting many assessments would be a great hardship and involve much expense.
[21, 22]
The Department of Revenue properly refused to reduce the value of Soo Line's stock and debt by an amount equal to one month's working capital. That sum was properly a part of the value of Soo Line's railroad operating property, and Soo Line has not been denied due process or equal protection of law under the fourteenth amendment to the United States Constitution.
We have discussed the stock and debt approach to value because this approach is used by both the Department of Revenue and Soo Line, and presumably other railroads operating in Wisconsin. We do not disapprove the stock and debt approach to value, or the income-influence method of removing the value of non-operating property. In this case, the income-influence method as applied resulted in an obvious error of law which must be remedied upon remand of this case.

APPRAISAL BY JOHN E. GREEN
The Department of Revenue's evidence consisted of testimony of department employees concerning the assessment of Soo Line's railroad operating property together with expert testimony of an independent appraiser, John E. Green, who specialized in appraising public *363 utility property. If the components of Green's appraisal are not faulty as a matter of law, an independent means of supporting the Department of Revenue's appraisal will exist, and the trial court's finding that the proper assessment of Soo Line's railroad operating property should not be substantially less or more than the $143,557,000 determined by the Department of Revenue must be affirmed.
Green appraised Soo Line's railroad operating property at $142,000,000, 98.9 percent of the Department of Revenue's appraisal of $143,557,000. He considered the cost and stock and debt approaches to value, but based his appraisal almost entirely on the capitalization of income approach to value. The trial court found, and we agree, that he weighted his capitalization income approach to value in excess of 99 percent.
Soo Line contends that Green made two errors in his capitalization of income approach, each of which renders his appraisal valueless. These alleged errors are the use of an "embedded debt" component of the capitalization rate, and the use of a weighting system for averaging income that places an abnormal and excessive stress on one year's income.

EMBEDDED DEBT
                                             I
  The basic capitalization rate (R), in V = ---, is a combination
                                             R
of the rate equity holders would expect on their investment and the rate debt holders would expect on their investment. All witnesses used 14 percent as the equity rate. All witnesses except Green used 9.50 percent as the rate of return on debt investment. Green used 6 percent.
*364 Green used the 6 percent rate because he assumed that a buyer of Soo Line would purchase Soo Line's shares and assume, rather than refinance, its existing or embedded debt. A substantial portion of Soo Line's debt was borrowed when interest rates were low. Soo Line's average interest rate is 5.6 percent on its debt, which Green rounded to 6 percent because a purchaser of Soo Line's railroad operating property might have current money needs that would require some borrowing at a higher rate.
Green's use of a 6 percent cost for debt results in a basic capitalization rate of 10.06 percent, which he rounded up to 10.25 percent. He capitalized Soo Line's income, which he determined to be $14,500,000, at 10.25 percent to arrive at his capitalization of income value of $141,500,000.
Green's use of the "embedded debt" concept in appraising the value of Soo Line's railroad operating property is defective for two reasons.
First, the concept of a willing buyer and a willing seller does not assume, as Green suggests, a buyer and seller of the Soo Line Railroad through acquisition of its corporate stock, but only a buyer and seller of Soo Line's operating property. Shareholders have equity not only in Soo Line's operating property, but in its non-operating property as well. It is not possible to acquire only Soo Line's operating property by purchasing its shares. Second, there is no evidence that a purchaser of Soo Line's assets could assume Soo Line's debt, or that mortgages, security interests and other devices to secure debt cover only operating property, or that secured creditors have no control over what would be a most unusual sale, or that secured creditors would agree to such a sale if their agreement would be necessary.
Should we approve the concept of valuing not only property but the benefit or detriment of indebtedness on property for ch. 76 assessments, it follows that there is *365 no reason why that concept should not be followed in ch. 70 (general property) assessments. The notion that municipal tax assessors, in addition to the duties they now perform, might be required or might choose to begin investigating real estate mortgages so that they might appraise identical real estate at differing amounts because the underlying mortgages bear different rates of interest is unique at best. Should that result be desired, the legislature, not this court, must require it.

WEIGHTED AVERAGE OF PAST INCOME
Green used $14,500,000 as the income component of his capitalization of income approach to value. He arrived at this figure by averaging Soo Line's net railroad operating income for the years 1969 to 1973. All expert witnesses except Green used the arithmetic average of the incomes for those years. The arithmetic average is approximately $12,214,800. Green used a weighted average:


         Income        Weight         Total
1973   19,883,000     ×    5       99,415,000
1972   13,808,000     ×    4       55,232,000
1971   10,759,000     ×    3       32,277,000
1970    8,834,000     ×    2       17,668,000
1969    7,790,000     ×    1        7,790,000
                                ___      ___________
                  TOTALS        15       212,382,000

An undisputed adjustment changed these figures so that the weighted total was actually $216,244,321. The average ($216,244,321 divided by 15) was $14,416,288. Green felt the $14,416,288 figure was too low, and adjusted it to $14,500,000. On cross-examination, he maintained that he had actually discounted 1973 earnings by 30 percent. While it is true that the $14,500,000 used by Green is about 73 percent of the 1973 income of $19,883,000, the only significance of the alleged 30 percent *366 discount is the arithmetical fact that $14,500,000 is about 70 percent of $19,883,000. What Green did in fact was to weight 1973 earnings by 5 and then increase his total because he felt the resulting figure was not high enough.
Green recognized the cyclical nature of railroad income. In his written appraisal he stated:
Due to the erratic earning pattern of railroads, most states use five years [sic] average earnings. The number of years to be used is a matter of judgment; however, the principal reason for using several years is to eliminate the peaks and valleys in the erratic earning pattern.
Despite this statement, and despite Green's knowledge that 1973 was an abnormally good year for Soo Line because of the Russian wheat purchases, he weighted 1973 income over 5 times as heavily as an arithmetic average would have weighted it. He stated that he did this because an investor would give most weight to recent earnings.
[23]
If the purpose of an average is to eliminate peaks and valleys, this purpose is totally defeated by a method of averaging that emphasizes the peak to the substantial exclusion of the rest of the mountain and the total exclusion of the valleys. Green's use of a weighted average for this purpose is contradictory, and the trial court's finding that Green's weighted average of Soo Line's income was proper and reasonable is against the great weight and clear preponderance of the evidence.
Soo Line argues that Green capitalized some income derived from non-operating property, violating the statutory requirement that the Department of Revenue assess only Soo Line's operating property. As we have pointed out, it is essential that an assessment not include non-operating property. Whether a particular method of appraisal does include non-operating property is a matter the trial court will determine on remand.
*367 Because Green's appraisal of Soo Line's railroad operating property contained the errors we have noted, it cannot support the trial court's approval of the Department of Revenue's assessment.
By the Court.  Judgment reversed and cause remanded to the Dane County Circuit Court with directions to refer the cause to the Wisconsin Department of Revenue to recalculate the ad valorem tax assessment in a manner consistent with this opinion.
NOTES
[1]  The parties to this action used "full market value" interchangeably with "fair market value," and we find that the terms have the same meaning.
[2]  Section 76.18, Stats., sets forth the circuit court's standard of review of the Department of Revenue's assessment:

Nothing in this chapter shall preclude the court in any proceeding before it under s. 76.08 from redetermining the assessment of the property of any company defined in s. 76.02 when in the judgment of the court the assessment should be substantially less or more than the assessment as determined by the department.
[3]  Fair market value is the amount the property will sell for "upon negotiations in the open market between an owner willing but not obliged to sell and a buyer willing but not obliged to buy." Rosen v. Milwaukee, 72 Wis.2d 653, 661, 242 N.W.2d 681 (1976).
[4]  The overall formula, as applied to Soo Line, was:



               Soo Line Railroad Assessment Data 1974
                      Indicated System Value
                           Stock
                           & Debt       Cost        Income       Total
                          ________      ____        ______       ______
  A. System Indicator
     (000)                155,143      170,353     132,848
                          ________     ________    _______
  B. Percent Deviation     +17.00        +28.00
  C. 75% Rejection (100)   1.3333        1.3333
                   _____   ______        ______
                   ( 75)
  D. Adjustment Factor
     To Standard
     Weights (B × C)       .226661      .373324
  E. Standard Weight         .1667      .3333      .50
  F. Factor Applied
     (D × E)                (.0378)                 .0378
                                        (.1244)    .1244
  G. Adjusted Weight        .1289      .2089       .6622
                            _____      _____       _____
  H. Weight to System
     (A × G) (000)         19,998      35,587     87,972         143,557
                                 ______      ______     ______         _______
  I. Wisconsin Allocation                                        .3902
                                                                 _____
        Amt. to Wisconsin (H × I)                                56,015,941
        Rounded to                                               56,000,000

[5]  Section 805.17(2), Stats. In a case similar to the one before us, the Wisconsin Supreme Court said:

It follows that the review of such an assessment as is here involved is a review of the commission's judgment, a judgment which is presumably correct and not subject to being overthrown except by evidence clearly showing that it was exercised upon some gravely erroneous basis. Since the members of the commission are not subject to cross-examination as to the operation of their mental processes in arriving at an assessment (in connection with which see Chicago, B. & Q. Ry. Co. v. Babcock, supra, and Appleton Water Works Co. v. Railroad Comm., 154 Wis. 121, 142 N.W. 476), the review must necessarily consist of a rationalization of the assessment by application to the facts of standard and approved methods of valuing such properties. If, by the application of such methods to the facts, the assessment is shown to be grossly excessive because substantially out of line with all of them, after allowing a reasonable margin for the exercise of judgment, the tax collected upon the excess must be held to have been inequitably and unjustly levied. The task of ascertaining with anything more than approximate accuracy the full market value of the property of large public service corporations is extremely difficult and probably impossible. The property of such a corporation, due to its size and other peculiar incidents, is not bought and sold under such conditions as will establish its market value, and thus assessing bodies have not the benefit of data which is usable in connection with smaller units of property. Wisconsin Gas & Electric Co. v. Tax Comm., 221 Wis. 487, 494-95, 266 N.W. 186 (1936).
[6]  Posnanski v. City of West Allis, 61 Wis.2d 461, 466, 213 N.W. 2d 51 (1973).
[7]  John E. Green, an appraiser and one of the Department of Revenue's witnesses, testified that he gave "minimum consideration" to the stock and debt approach, and "minimal weight" to the cost approach. The Department of Revenue's formula attempted to be more specific.
[8]  Soo Line made adjustments to income which deflated the capitalization of income approach value of its railroad operating property. These were termed "Reclassifications and Restatements," and were for certain items that were shown as nonoperating expenses on Soo Line's books but were allegedly railroad operating costs. A witness for Soo Line also adjusted net income to reflect certain benefits that a purchaser of the railroad operating property would not enjoy.

These reclassifications and restatements were not made by the Department of Revenue in arriving at its assessment. Soo Line alleges that the "reclassifications and restatements" reduced Soo Line's net railroad operating income by $724,082 and that consequently the value of Soo Line's net operating property, using the capitalized income approach, should have been lower. The trial court did not make findings as to whether the reclassifications and restatements would have been agreed upon by the willing buyer and seller as adjustments to income that logically accompanies the sale. We therefore cannot determine whether there was a need to change Soo Line's accounting methods by adjusting its net railroad operating income to reflect the reclassifications and restatements. We note however that Soo Line is suggesting the very thing for which it criticizes the Department of Revenue  a change in accounting methods for the purpose of computing the amount of an ad valorem tax. The trial court's failure to consider the effect, if any, that the suggested reclassifications and restatements had upon the Department of Revenue's assessment is error.
[9]   50 percent × .14 (cost of equity) =  .07
  50 percent × .095 (cost of debt)  =  .0475
                                       _____
  Composite capitalization rate        .1175 or 11.75 percent

[10]  The Department of Revenue computed 92 percent of the assets as depreciable because it added rails and ties into the income stream. The department concedes that only 63 percent of Soo Line's assets would be depreciable for federal tax purposes. The department submits that because of the nature of the algebraic equation used to determine tax liability, the mistake is very nearly cancelled out by the use of the higher income figure (adding in rail and tie replacement expenses). We do not address this issue because, in light of the decision of this court, the federal tax adjustment to the capitalization rate will have to be recalculated in any event.
[11]  John E. Green, one of the Department of Revenue's expert witnesses, testified that he placed minimal value on the cost approach. The trial court correctly found that Green's appraisal weighted the combined total of the cost approach and stock and debt approach at one percent.
[12]  This formula is apparently based on W. Thatcher and R. Dubielzig, Obsolescence in Railroad Ad Valorem Tax Assessments (University of Wisconsin, Bureau of Research and Service, 1967). This study was marked as an exhibit but not introduced into evidence.
[13]                              ESTIMATED
                        BLUE    RESPONDENT   PERCENT
                        CHIP                   TO
                      STANDARD   RAILROAD    STANDARD
1. Gross Revenue Per
     Mile of Road           224,032   36,560       16.32
2. Rate of Return            10.5      7.65        72.86
3. Gross Profit Margin       30.5     15.08        49.44
4. Freight Traffic
     Density                 16,300    2,432       14.92
5. Transportation
      Performance           106,212    71,851       67.65
6. Load Factor                2,125     1,966       92.52
7. 100  Operating
     Ratio                     37.5     31.68       84.48
8. 100  Transportation
     Ratio                     74.5     65.92       88.48
9. Maintenance of Way/
    Mile of Road             21,139     5,806       27.47
                                                   ________
                  Weighted Average Ratio             57.13
A. Depreciated Cost of Trans.
    Property (ICC SCH. 211N-1
    L 39d-L39e)                         259,785,000
B. Less: Other Elements of Value
     (ICC SCH. 211N-2 A/C 80)
C. Other Adjustments (Leased
    Equip.) (WAR. SCH. 17
    Col. D2)                                862,000
                                            ________
D. Net Cost Before Adjustment for
    Obsolescence (A + C)                                $260,647,000
E. Sound Value of Productive
    Transportation Plant
    (D × 57.13)                                    148,908,000
F. Materials and Supplies (ICC
     SCH. 200A L12)                                       12,342,000
G. Working Capital (UT SCH. 2.3)                           9,103,000
      Total Cost After Adj. for                          ____________
        Obsolescence (Est.)                              $170,353,000
                                                         =============

[14]  The Department of Revenue added $12,342,000 for materials and supplies and $9,103,000 for working capital to the sum reached by multiplying Soo Line's depreciated cost of its railroad operating property by 57.13 percent to reach the total of $170,353,000. These sums do not directly pertain to a discussion of obsolescence.
[15]  76.07 Assessment. (1) DUTY OF DEPARTMENT. The department on or before June 15 in each year in the case of railroad companies, telegraph companies and sleeping car companies, and on or before August 15 in the case of light, heat and power companies, air carrier companies, conservation and regulation companies, and pipeline companies, shall, according to its best knowledge and judgment, ascertain and determine the full market value of the property of each company within the state.

(2) RELATION TO STATE VALUATIONS; DESCRIPTION. The value of the property of each of said companies for assessment shall be made on the same basis and for the same period of time, as near as may be, as the value of the general property of the state is ascertained and determined....
[16]  70.112 Property exempted from taxation because of special tax. The property described in this section is exempted from general property taxes:

(1) Money and Intangible Personalty. Money and all intangible personal property, such as credit, checks, notes, bonds, stocks and other written instruments.
