
144 N.W.2d 161 (1966)
180 Neb. 571
GRAINGER BROTHERS COMPANY, a Corporation, Appellant,
v.
COUNTY BOARD OF EQUALIZATION OF the COUNTY OF LANCASTER, State of Nebraska and County of Lancaster, Nebraska, Appellees.
Nos. 36111-36114.
Supreme Court of Nebraska.
July 15, 1966.
*163 Mason, Knudsen, Berkheimer & Endacott, Lincoln, for appellant.
Paul Douglas, County Atty., William D. Blue, Deputy County Atty., Floyd Sterns, Ronald D. Lahners, Walter D. Weaver, Janice L. Gradwohl, Lincoln, for appellees.
Heard before CARTER, SPENCER, BOSLAUGH, BROWER, SMITH, and McCOWN, JJ., and RONIN, District Judge.
BROWER, Justice.
These cases involve the assessments on stocks of merchandise, being tangible personal property of the plaintiff and appellant, Grainger Brothers Company, for the years 1959, 1960, 1961, and 1962.
Protests were filed with the defendant and appellee board of equalization of the county of Lancaster for each of the years mentioned. The protests were each denied. On appeal the cases were consolidated for trial in district court as was done for briefing and argument here. The trial in district court resulted in a finding and judgment that the plaintiff's inventory was fairly and properly equalized by the county assessor and the board of equalization for each of the years involved and a dismissal of plaintiff's petitions. Plaintiff has appealed from an order overruling its motion for a new trial.
Plaintiff assigns error to the trial court in determining the assessed and actual value of its inventories and establishing them as set by its order; in failing and refusing to equalize assessed and actual values thereof with that of other properties in Lancaster County; and in failing to reduce the assessed values thereof.
Plaintiff's inventory for all of the years in question consisted of a full line of dry groceries and perishables sufficient to supply the needs of its retail grocery customers in the Lincoln trade area. In its amended petitions for the several years plaintiff contended that the equalized assessed value of its inventory should be no greater than the following: 1959$186,449; 1960 $180,280; 1961$211,878; and 1962$205,369.
The assessor raised the actual value as originally reported by plaintiff and set the *164 assessed value at 35 percent thereof, as follows:


   Year             Actual              Assessed
   1959           $821,360              $287,476
   1960            794,185               277,965
   1961            904,710               316,650
   1962            933,385               326,685

The county assessor testified he determined actual value of plaintiff's property for each year involved by simply taking the same value as shown on form 2A of plaintiff's personal property tax return for each of said years. This value is the dollar amount of the inventory as set out in the taxpayer's latest federal income tax return which is required under section 77-1231.01, R.R.S.1943, to be stated in the personal tax return. He did not in any way inspect the merchandise in the inventory. The assessor speaks of this as "book value."
The plaintiff here, however, does not contend the actual value of its inventory as determined by the assessor and board of equalization is in excess of its value. It is stipulated that if present, one S. A. Wilson, who was the executive vice president and general manager of plaintiff from 1950 to 1962 and president in 1962, would testify that the fair market value of plaintiff's inventory for the respective years was practically identical with that fixed by the assessor as actual value heretofore set out.
Plaintiff's objection is that the great proportion of the tangible property in Lancaster County is systematically assessed for less than its actual value, and that the failure to fairly and proportionately equalize plaintiff's inventory in relation thereto results in a discrimination and an unjust and unfair assessment.
Plaintiff calls attention to Article VIII, section 1, of the Constitution of this state which, with certain exceptions not applicable to the case before us, requires that taxes on all tangible property and franchises are to be levied by valuation uniformly and proportionately. Homan v. Board of Education, 141 Neb. 400, 3 N.W.2d 650. The rule of uniformity applies to both the rate of taxation and the valuation of property for tax-raising purposes. Gamboni v. County of Otoe, 159 Neb. 417, 67 N.W.2d 489; State ex rel. Morton v. Back, 72 Neb. 402, 100 N.W. 952, 69 L.R.A. 447; Chicago, R. I. & P. Ry. Co. v. State, 111 Neb. 362, 197 N.W. 114.
Plaintiff maintains that the actual value of real estate in Lancaster County, which constitutes by far the major portion of tangible property, is systematically undervalued, resulting in the discrepancy claimed.
To understand the valuation placed upon real estate in the county involved, it is here necessary to relate some of the history of its assessment which antedates the years involved in the present case.
In 1953 E. T. Wilkins & Associates, hereinafter called Wilkins, a professional appraisal company, reappraised all real estate and improvements in Lancaster County. The county assessor testified that Wilkins did a good and thorough job. In 1953 the State Board of Equalization and Assessment increased the value of all lots and improvements to a total valuation of $216,981,750. This figure represented 100 percent of value. For the taxable year 1954 the county board of equalization reduced the Wilkins appraisal figures on real estate and improvements in Lancaster County to correspond to the total valuation placed on real estate by the State Board of Equalization and Assessment the year before. The board of equalization in 1954 in the county assessor's presence reduced the value of real estate in the following amounts: Urban commercial property to 70 percent, rural property to 65 percent, and urban residential property to 60 percent. Actual value then became the Wilkins appraisal adjusted to the 70, 65, and 60 percent values. The 50 percent assessment law then being in effect, the assessd value of each of these kinds of real estate was assessed at 50 percent. While still in 1954 the State Board of Equalization and Assessment reduced the *165 actual value of urban residential property (60 percent) and urban commercial property (70 percent), by 10 percent without changing the value of rural property. In 1957 the law was changed, making the level of assessment 35 percent of actual value. Lancaster County, however, did not change the assessed value figures accordingly. What figure had been 50 percent assessed value then became 35 percent.
The actual value was not thereafter placed on the assessor's records, but the assessed value alone was shown. The assessed value was computed, however, by applying different percentages to the Wilkins appraisal, viz: 32½ percent to rural real estate, 31½ percent to urban commercial property, and 27 percent to urban residential property. The result, however, is the same as if the various changes made by the board of equalization and the State Board of Equalization and Assessment, and the shifting of the 50 percent assessed valuation to 35 percent had been spelled out in actual values. These changes are illustrated by exhibits 21, 22, and 23 with respect to the three types of real estate. Exhibit 23, which deals with urban real estate, is here set forth.


                          EXHIBIT 23
                  URBAN RESIDENTIAL PROPERTY
   1954   Property valued by Wilkins                         $10,000.00
          County Board placed this at 60%                      6,000.00
   1954   50% law in effectassessed value of            3,000.00
                                                             __________
          30% of Wilkins                                       ________
   1957   50% changed to 35% but Lancaster County made
          no change
   1954   State Board reduced 10%                            $   300.00
                                                             __________
          making assessed value                              $ 2,700.00
                                                             __________
          or 27%                                              _________
        Could have changed all Wilkins on basis of
          reducing each $10,000.00 to                        $ 7,714.00
         Then apply 35% making same assessed value           $ 2,700.00

Exhibit 21 is similar for a rural property appraised for $10,000 by Wilkins. It shows the reductions heretofore mentioned applied to that type of property and the change from 50 percent to 35 percent in assessed value, and ends by showing that 32½ percent of the Wilkins appraised value is the same as 35 percent on a like computed actual value of $9,285.
Exhibit 22 covers a $10,000 urban commercial property as affected by the changes pertinent to such property, the result being that 31½ percent of the Wilkins appraisal is the same as 35 percent on a similarly computed actual value of $9,000.
The only occasion in which the county assessor computes actual value is when he makes a report to the State Board of Equalization and Assessment. He then multiplies the assessed value by 2.857 which transforms the 35 percent to 100 percent and writes the result on this report as the actual value.
The county assessor testified that if nothing was done to affect "their character or *166 their construction, * * * or buildings, or something of that sort," these assessments remained the same after the adjustment made by the State Board of Equalization and Assessment in 1954. The level was set by the State Board of Equalization and Assessment and the three levels between urban residential, urban commercial, and rural real estate were maintained from 1959 through 1962. This was done in order to keep the assessed valuations in line with those determined by the State Board of Equalization and Assessment in 1953. He stated this was done although real estate after 1958 was steadily rising in value. The defendants were served with requests to make admissions which includes the following: 3. "It was the policy and practice of the County Assessor of Lancaster County to maintain the evaluation for tax purposes of real property in Lancaster County at the same levels established by E. T. Wilkens & Associates as adjusted by the State Board of Equalization in 1954 for the years from 1954 through 1962." To this the defendants replied: "Admit Request No. 3 with the qualification that in the year 1954 the Board of Equalization of Lancaster County, Nebraska, upon the recommendation of the Lancaster County real estate classification and reappraisal committee also made an adjustment in real estate values."
The testimony of both the assessor and an employee engaged in the appraisal work in that office with respect to the assessment of newly constructed improvements on property is enlightening. Their two stories are in complete agreement. They show that new construction was appraised and assessed on cost levels prevailing in 1952 which Wilkins used in 1953. On obtaining information from the authorities of the city of Lincoln that new construction had been authorized, an appraiser went to the premises and examined the improvement as it was being constructed. He measured the building and noted the type of construction. He procured the cost thereof from a detailed cost data book, exhibit 24, left by Wilkins after the completion of its appraisal in 1954, referred to at times as the "cost guide." It is based on 1952 costs. The cost of the improvements at the 1952 value thus obtained was placed on the appraisal. In many instances new types of construction had become prevalent since 1952 which were not specified in this cost data book. As to them the appraiser procured the costs either from the contractors, or from others engaged in construction or the furnishing of materials. These new costs were then discounted 15 percent to 20 percent to bring them down to the 1952 level of the costs as set out in the cost guide book. The new costs as discounted were then added to the appraisal procured through the cost guide. Then the sum was further reduced by 5 percent for depreciation. This discount for depreciation was made even before the building was completed. No other allowance for depreciation appears to have been ordinarily given. The sum so added as discounted was designated on the appraisal card as the appraised value. It was not, however, either the assessed value or actual value. The assessed value was obtained by multiplying this appraised value by the same percentages applied to the original appraised value of Wilkins, to wit: 32½ percent for rural property, 31½ percent for urban commercial property, and 27 percent for urban residential property. There is no dispute as to this manner of appraising new construction, nor its assessment thereafter. Neither is it disputed that its purpose was to keep the valuation of new construction on the level of the Wilkins appraisal and at 1952 prices. All this is conceded by other answers of defendants to requests for admissions.
An example of this method of appraisal applied to residential property was received in evidence as exhibit 25. The exhibit itself contains a diagram showing the dimensions of the house being constructed and figures used by the appraiser in his computation of the appraised value from the Wilkins cost data. An abbreviated abstract of this exhibit shows the ultimate compilation *167 of the results of the appraisal as well as its application to actual and assessed value with the detailed figures omitted. It is here set forth:


                                             Appraised --- 1959
   1 Cost guide                              10,230
       (1952 prices)
   2 Non-cost guide
      (minus 15-20%)
      A. Split level                            700
      B. Carport                                600
      C. Storage                                 50
                                             _____________________
   3 Replacement value                                    11,580
   4 Less: 5% dep'n                              580
                                            ______________________
   5 "Appraised value"                                    11,000
   6 Assessed value                             2,970
   7 % of appraisal                                27%
   8 Computed Actual (Value)                                8,485
        (2.857 X 2,970)

Similar appraisals are in evidence. Not only the new buildings were adjusted to the Wilkins values, but in case of new additions, the land was also. This was done by consulting values as to lots in previously existing additions on the appraisal cards on file in the assessor's office and by consulting tables in the Wilkins guide with respect to standard depth in the measurement of lots and variations therefrom with values set out with respect to different depths.
Dr. James B. Hassler, a professor at the University of Nebraska with degrees from the University of California in agricultural economics and with a minor in statistics, testified with respect to an unbiased appraisal made between assessed value and sales value of real property in the city of Lincoln. He used as data exhibits 1, 2, and 3 which were transcripts prepared by the register of deeds of Lancaster County for the use of the State Board of Equalization and Assessment. These transcripts contained five percent of all real estate sales in the city of Lincoln for the years 1959 through 1962. The data was selected from every addition and subdivision. He also used exhibit 12 which is a compilation of all sales in Lancaster County in 1960 where the consideration exceeded $40,000 and was less than $1,000,000.
Dr. Hassler testified the raw data for the years 1959 to 1962 was carefully screened by him. He rejected sales where the assessed value was very small compared to the sales price because these indicated a sale of residential property that had not been finally assessed. He excluded items where the names indicated relationship between grantor and grantee. Items having assessed valuations higher than 60 percent and less than 10 percent were excluded because he felt they might be questionable. There were very few above 60 percent and most of those under 10 percent were partial assessment situations. He took steps to prevent duplication between items on exhibit 12 and those on exhibits 1, 2, and 3.
The doctor used 100 items for the years 1959 and 1961 and all items for 1960 (431) and 1962 (693). He compared results in exhibit 12 with the other exhibits for the several years to determine whether there was bias in favor of low valued over high valued property. The doctor considered *168 there was no significant variation between high and low valued properties. The sales price was computed from revenue stamps on the deeds. He tested each of the several exhibits by using two methods, one the aggregate ratio used by the Tax Commissioner (consisting of dividing the sum of the values of the actual sales into the sum of the actual assessed value), and the simple average assessment ratio (computing the ratio between sales and assessments on each sale, adding them together, and dividing the result by the number of cases considered). Dr. Hassler determined from the samples the ratio of assessed values to sales values for each of said years. Using an estimated standard of error for both types and for all years involved where annual random samples had been taken, Dr. Hassler testified he was able to state that the estimates, which are hereafter listed, would not deviate more than 1.5 to 2 percent plus or minus from the averages found. He stated that the sample sized was significantly large and the estimates were statistically sound. He prepared an analysis of the ratio of sales values with his estimated standard, which follows:


                    ANALYSIS OF THE RATIO OF
                 SALES VALUES TO ASSESSED VALUE
                  Lancaster County1959-62
                           * * * *
                               Estimated                   Estimated
          Sample                Standard                    Standard
Year       Size      Rw          Error            Rs          Error
---------------------------------------------------------------------
1959        100      .2477       .0091           .2451         .0051
1960        431      .2466       .0049           .2434         .0023
1961        100      .2407       .0051           .2243         .0057
1962        693      .2397       .0054           .2319         .0024
---------------------------------------------------------------------

In the above table Rw refers to the aggregate ratio system and Rs to the simple average ratio. The doctor concluded that to equalize the inventories of the plaintiff for the 4 years they should be assessed at 24.03 percent of value.
The defendants contend the sales assessment ratio as presented by Dr. Hassler should not be considered. They call attention to the case of Carpenter v. State Board of Equalization & Assessment, 178 Neb. 611, 134 N.W.2d 272, where, because of deficiencies in their preparation, sales assessment ratios were not accepted. Here, however, there is detailed testimony by an expert concerning their preparation and their dependability. They are related to four such separate ratio studies in four succeeding years and tested by applying a special one designed to test the 1960 ratio and inferentially the others. Moreover, the testimony of the county assessor and the appraiser from his office lends strength to the conclusions inferable from the sales assessment studies which in turn give weight to that of the assessor and his appraiser. When a study of sales assessment ratios is shown to be statistically reliable, it is entitled to probative value. Sioux City Bridge Co. v. Dakota County, 110 Neb. 597, 194 N.W. 729; In re Appeals of Kents 2124 Atlantic Ave., Inc., 34 N.J. 21, 166 A.2d 763; Baken Park, Inc. v. County of Pennington, 79 S.D. 156, 109 N.W.2d 898; People ex rel. Hillison v. Chicago, B. & Q. R. R. Co., 22 Ill.2d 88, 174 N.E.2d 175.
Under the Constitution of Nebraska, Article VIII, section 1, business inventories and real estate are in the same class for taxation purposes, and properties within *169 the same class are required to be valued and assessed uniformly and proportionately in order that equalization obtain. Homan v. Board of Equalization, 141 Neb. 400, 3 N.W.2d 650; Chicago, R. I. & P. Ry. Co. v. State, 111 Neb. 362, 197 N.W. 114; H/K Company v. Board of Equalization, 175 Neb. 268, 121 N.W.2d 382.
In Newman v. County of Dawson, 167 Neb. 666, 94 N.W.2d 47, the following rules are set forth: "An appeal to the district court from action of the county board of equalization is heard as in equity, and upon appeal therefrom to this court it is tried de novo. * * *
"The burden of proof is upon a taxpayer to establish his contention that the value of his property has been arbitrarily or unlawfully fixed by the county board of equalization in an amount greater than its actual value, or that its value has not been fairly and proportionately equalized with all other property resulting in a discriminatory, unjust, and unfair assessment. * * *
"To secure a reduction in the assessed value of tangible property it must be demonstrated by evidence that the assessment is grossly excessive or that its value has not been fairly and proportionately equalized, and is a result of arbitrary or unlawful action. The evidence must be such as to indicate the exercise of arbitrary action or the failure of plain legal duty, and not a mere error in judgment."
Where the county assessor does not act upon his own information, or does not make a personal inspection of the property, any presumption as to the validity of the official assessment does not obtain. H/K Company v. Board of Equalization, supra.
"The presumption obtains that a board of equalization has faithfully performed its official duties, and in making an assessment it acted upon sufficient competent evidence to justify its action. However, the presumption that a board of equalization in making an assessment acted upon sufficient competent evidence to justify its action disappears when there is competent evidence on appeal to the contrary, and from that point on the reasonableness of the valuations fixed by the board becomes one of fact based upon evidence unaided by presumption." L. J. Messer Co. v. County Board of Equalization, 171 Neb. 393, 106 N.W.2d 478.
We now apply these rules to the evidence previously outlined. It clearly appears that the assessor and taxing authorities of Lancaster County have kept real estate values therein on a level with those fixed by the State Board of Equalization and Assessment in 1953. This is done designedly and systematically. It is done although the assessor testified there has been a steady rise in real estate values. The value of new construction is appraised in relation to replacement value from Wilkins cost guide where possible. The Wilkins cost guide lists prices of 1952. Where information concerning new materials or construction is not shown in the guide, it is discounted 15 to 20 percent. A depreciation of 5 percent is immediately given before construction is complete. If an improvement is only 50 percent completed on the date of assessment, the partial structure is listed at 50 percent of the appraised value with the discounts and depreciation already allowed. Then the rate on the new improvement is applied, not at 35 percent, but at 27 percent, 31½ percent, or 32½ percent by reason of a reduction made by the State Board of Equalization and Assessment in 1953. This is done for the purpose of equalizing real estate values. Indeed the systematic plan seems to have resulted in establishing uniformity and equality in the valuation of real estate for taxation. We conclude, however, that as it affects valuation of the plaintiff's inventories of merchandise here valued for taxation at its true actual value, it perpetuates a systematic and unlawful discrimination. Plaintiff has established that the value of its property has not been fairly and proportionately equalized *170 with other property, resulting in a discriminatory, unjust, and unfair assessment.
It is now necessary to determine the extent and nature of the relief to be granted. From the evidence the total actual value of real estate and of inventories assessed in Lancaster County for three of the four years in question appears. They are here set out for each year, the first figure being the real estate: 1959, $449,420,485 and $30,381,240; 1960, $461,924,270 and $39,384,435; and 1961, $476,922,060 and $40,615,225. Apparently the 1962 figures were not available. The breakdown between urban and rural lands and improvements is not shown except as set forth in the order of the State Board of Equalization and Assessment in 1953, which separates the different types of tangible property as follows: Lands and improvements, $57,600,900; lots and improvements, $216,981,750; business schedules, $29,482,880; and household goods and personal effects, $4,180,990. From the evidence it is clearly inferable the great portion of increase in total value of real estate arises from new construction and new additions in and to the city of Lincoln.
A separate valuation of rural lands upon which the percentage of variation from the Wilkins appraisal is somewhat higher is not shown for the years involved. The intent to hold such valuation to 1953 levels is clearly shown, however. Such value of urban commercial property is likewise not shown although maintained at the same level. Dr. Hassler did not attempt to segregate urban commercial from urban residential because, he testified, it was extremely difficult to do from the descriptions, and because he assumed with the passage of time economic values would have altered on individual properties and the assessed value-sales value ratio would tend to mix for all types of property over the period.
In the case of Baken Park, Inc. v. County of Pennington, 79 S.D. 156, 109 N.W.2d 898, the South Dakota court had under consideration the value for assessment purpose of a shopping center which the owner contended and the court found was assessed higher than downtown business property, resulting in discrimination. The court there considered sales assessment ratios with other evidence. Holding the plaintiff had established such discrimination, it stated: "If discrimination exists the remedy of the taxpayer is the reduction of his valuation to such amount as may be necessary to remove it. In re Appeals of Jepsen, 76 S.D. 421, 80 N.W.2d 76. This court has recognized that perfect uniformity of taxation is a dream unrealized and exact uniformity or mathematical accuracy in valuations are impossible, yet quoted with approval a statement to assess the property of one person or class at 40%, another at 30% and still another at 25% without legislation under appropriate constitutional authority to so classify was the result of deliberation or intention. Sioux Falls Savings Bank v. Minnehaha County, 29 S.D. 146, 165, 135 N.W. 689, 693. Constitutional uniformity is then lacking. Chicago, R. I. & P. Ry. Co. v. Young, 60 S.D. 291, 244 N.W. 370. The record here shows more than mathematical inaccuracy. It was not necessary to prove the basis used in assessing every other piece in the city." The court then cited In re Appeals of Kents 2124 Atlantic Ave., Inc., 34 N.J. 21, 166 A.2d 763, and further said: "In the Kents case, the court decided proof of a common level or ratio was not required, stating the remedy must be within the practical reach of a taxpayer, that he must not be required to prove more than sensibly can be expected of him and until a better technique appears an average ratio could be used as evidence of a ratio at which an assessment above it should be reduced. Requiring proof of a common level or general percentage of true value would in many cases deprive a taxpayer of a remedy and cannot be sanctioned." In the Baken Park case it appears the appellate court was without jurisdiction to determine issues of fact or direct the decision of the trial court except where the facts were undisputed and were such that only one conclusion could be drawn. It did reduce the value, however, *171 because of its finding of undisputed facts and the appellant's willingness to accept the undisputed reduction.
We are considering the present case de novo. From the ratio studies, Dr. Hassler concluded the assessed value of plaintiff's inventories should be 24.03 percent of actual value to be equalized with real estate. He admitted a possibility of very small error. From the testimony of the assessor and his appraiser new construction was discounted 15 to 20 percent to equate it with 1953 values. New construction was immediately given a 5 percent depreciation not accorded to other real estate or at other times. We conclude also that this is by way of equalizing. The 20 percent would reduce 35 percent to 28 percent, and 25 percent to 26¼ percent. The percentage cannot be exact. We conclude that the assessed value of the plaintiff's inventories should be determined by taking 26 percent of the actual value as determined by the county assessor for each of the years in question.
The judgment of the trial court is reversed and the cause remanded with directions to enter judgment in accordance with this opinion.
Reversed and remanded with directions.
