#### In re APPLICATION OF EDWARD J. ROSEWELL, County Treasurer. — (THE PEOPLE ex rel. EDWARD J. ROSEWELL, Appellee, v. UNITED STATES STEEL CORPORATION, Appellant.)

First District (4th Division)

No. 78-1818

Opinion filed June 26, 1980.

William Fullagar, of Chicago, for appellant.

Bernard Carey, State’s Attorney, of Chicago (Michael F. Baccash, Assistant State’s Attorney, of counsel), for appellee.

Mr. JUSTICE JIGANTI

delivered the opinion of the court:

The United States Steel Corporation (U. S. Steel) appeals from orders entered by the circuit court of Cook County overruling its objections to the 1971 quadrennial assessment and 1972, 1973 and 1974 assessments of its South Works steelmaking plant located in Hyde Park Township in Cook County. The 1971 objection was tried in one proceeding and the 1972-74 objections were tried in a second proceeding. All objections for the years 1971 through 1974 have been consolidated on appeal.

On appeal U. S. Steel argues the assessments imposed on its South Works for the years 1971-1974 were not made in accordance with the law or in amounts which bore a proper relationship to the actual value of the property, or to property generally.

The 1971 quadrennial assessment of U. S. Steel’s. South Works increased the 1970 assessment from $45,754,781 to $82,589,679. The 1972 assessed value was $79,350,110, the 1973 and 1974 assessed values were each $79,402,766.

South Works is a plant which produces iron, steel and steel products, *118located on 416 acres of land on Lake Michigan at the Calumet River. At the time of the assessments there were 11 blast furnaces at South Works, although only eight were capable of production and all eight could not be operated at one time.

In the 1971 case, U. S. Steel contended the actual value of South Works was not in excess of $134,170,000 and that the lawfully assessed value was not more than 50% of that figure, or $67,085,000. In the 1972-1974 case, U. S. Steel contended that the 1972 actual value was not in excess of $136,570,000, and the total lawfully assessed value was not in excess of $65,285,000. The values asserted for 1973 were not in excess of $135,500,000 and $40,650,000 respectively; for 1974, $132,000,000 and $52,800,000.

U. S. Steel hired the American Appraisal Company (American) to determine the actual or market value of South Works as of January 1, 1971, 1972, 1973 and 1974. Richard Nichols, assistant vice-president of American, was in charge of the work and testified in both trials. The appraisal reports were introduced in each case.

Nichols testified that there are three basic approaches for determining the fair market value of a parcel of real estate: (1) cost approach, (2) income approach, or (3) market approach. The market approach was not used because industrial complexes such as South Works infrequently- change ownership. An income approach was also deemed inappropriate because the segregation of an earnings stream which would be attributable only to South Works is difficult due to the many facets of the business, the many locations of other of U. S. Steel’s steel producing real property, and the difficulty of making a profit determination for any single component of the “production line.” Nichols thus determined that a cost approach was most appropriate in this situation. Replacement rather than reproduction cost was considered the better measurement. The American appraisal involved the estimate of the cost of a “model” replacement plant, located on the site of South Works, which would produce like products and would have a design capacity of 3,780,000 shipped tons. That capacity is 28% greater than the previous five years’ average shipments, and 22% greater than the 1970 shipments, the year in which the greatest volume was produced during the five-year period.

Nichols further testified that the actual production of a blast furnace is usually less than rated capacity. He said that each of the conceptual replacement furnaces would have to be relined after 3,000,000 tons of production and that the downtime for relining would be three to four months. The conceptual replacement plant permitted a determination of the cost of replacing South Works and allowed the differences in the operations of the existing plant and its replacement to be measured so as *119to determine the functional obsolescence of South Works. The total cost of all the facilities envisioned as part of the conceptual replacement plant established the upper limit of what someone would pay for South Works. Present replacement cost is $363,900,000. From this was deducted a percentage representing observed physical deterioration. Replacement cost less observed deterioration produced the figure of $181,200,000.

Nichols explained that functional obsolescence was dealt with in part in the replacement facility by doing away with excess construction. Additionally, the difference in operational efficiency between the current and replacement facilities was analyzed and a penalty cost developed, representing the excess costs of operating South Works. Excess costs were estimated at $39,270,000 per year. Economic obsolescence was reflected in the curtailment of the remaining life of facilities in plant areas which were affected by the market.

Only half of the excess operating costs, or $19,635,000, was considered savings in light of the tax consequences. Such costs were assumed to continue for the remaining life of the facilities which created them. The present value of $19,635,000 for an eight-year remaining life at an 8% capitalization rate is $113,100,000. The discount factor and the economic remaining life were applied to the excess operating costs to develop the total operating obsolescence penalty for each year in issue.

Sixty-two percent of the assets contributing to the cost differential were attributed to real estate. Therefore, the present value of the functional obsolescence attributable to real property is $70,200,000.

The appraisal then combines the improvement appraised value ($181,200,000), the land appraised value ($6,870,000), the construction in progress appraised value ($16,300,000), and subtracts the functional obsolescence figure ($70,200,000), to arrive at American’s opinion that the fair cash value was $134,170,000 as of January 1, 1971.

A similar approach was used to arrive at the fair cash values of South Works for the years 1972 through 1974:

January 1, 1972 — $132,423,000

January 1, 1973 — $132,580,000

January 1, 1974 — $129,700,000

David H. Belt, manager of taxes for U. S. Steel, testified in each case. He said the assessor had not included a sufficient depreciation factor in making his assessments because a chart was used which related to age alone as a deduction from reproduction costs. Irrespective of age, a 30% floor prevents any depreciation allowance in excess of 70%. He also said the chart is not designed for industrial facilities. As computed, the reproduction cost created duplications of value. New facilities intended to replace old ones were fully assessed in addition to a full assessment of *120the old ones which would be replaced. Also, some major facilities which were assessed were inoperable due to physical deterioration and because of city ordinances requiring their termination.

Belt also testified that U. S. Steel had not complied with the assessor’s request for cost information pertaining to four new facilities because of difficulty in determining which portions of them constituted real property as opposed to personal property. Belt conceded the cost records did exist and that U. S. Steel had been able to develop cost data for its 1971 personal property tax return.

Victor Lindberg testified in each case. At the time of the 1971 trial he was assistant general superintendent of South Works. When he testified in the second case he was general superintendent of South Works. Lindberg described the maximum productive capacity of the blast furnaces as compared to the formula used by the assessor. Lindberg said the maximum output which was ever achieved at South Works was 10,890 tons per month. In Lindberg’s opinion, the assessor’s formula failed by some 200% to reflect accurately the production. Lindberg also testified that since the time the assessed value of South Works was doubled in 1971, there had been a decrease in the utilization of South Works’ facilities. The plant had become an uncompetitive high-cost operation, although it was competitive with other U. S. Steel plants prior to 1971.

Herman Walther, a real estate appraiser, testified in the 1971 case that the actual value of the land without any improvements was 45 cents per square foot. American’s report for 1971 shows the land to have a market value of 37.9 cents per square foot.

Mr. Suits, a land appraiser, appraised South Works’ land for each of the years. His opinion was that the market value of the land was the same in each of the four years, that value being 37.9 cents per square foot.

In the 1971 case, the assessor valued the land as having an assessed value of 40 cents per square foot. This represented a 14% increase over the prior valuation. The county assessed value of land was subject to equalization which in 1971 was a factor of 1.59. On a tax payment basis the land was valued at a rate of 63 cents per square foot in 1971 and varied in the other years only by reason of the equalization factors.

John H. Brierly testified in the 1971 case. He is an appraiser and is familiar with South Works. In his opinion, the assessor’s reproduction method of valuation would not produce an accurate estimate of functional obsolescence because it would not permit overall plant obsolescence to be taken into consideration. He believed the replacement cost basis was the proper method to use in determining the value of South Works. The 1959 manual, which was used by the assessor, did not contain data concerning industrial properties and did not have any explanation of depreciation.

*121Norman J. Beatty, the executive vice-president of the Civic Federation, testified in the 1971 case. He said the Civic Federation had made a study of the relationship between 1971 assessed valuations and fair cash values of Cook County real property. The study showed that the overall assessed value of property in Cook County in 1971 was 30% of actual value. The average assessed value of industrial property was approximately 50% of fair cash value.

Theodore Swain, chief deputy assessor of Cook County, testified for U. S. Steel in the 1972-1974 trial. Swain said the practice of the assessor was to assess property from a manual. The assessor’s office would determine the physical characteristics of the property, apply a unit cost from the manual, and then deduct a depreciation factor from an age and condition chart. No effort was made to relate that process to any proportion of full value. If the property being assessed was not covered by the manual, the assessor would rely upon a staff member to arrive at an appropriate unit cost on the basis of experience with comparable properties.

Swain testified that proper application of the manual procedures would produce an assessed value which would bear the 40% relationship to market value required by the Cook County ordinance for industrial property. Prior to the adoption of the 1973 ordinance, the assessor had no knowledge of the percentage which assessed industrial property bore to actual valué. South Works was classified Industrial No. 93 for the years 1971 through 1973. For 1974 the property comes within the County Classification Ordinance Class 5. Swain also testified that Professor Richard Michael’s study indicated that for the years prior to 1974, class No. 93 property was assessed at an average of 40% of market value. Swain said he instructed the appeals staff in the assessor’s office to reduce assessments of industrial property to 40% if in any case evidence was presented indicating a higher assessment.

The assessor’s assessed valuation, the State’s equalized valuation, and the tax levied for the years in question are as follows:

Assessed State Equalized

Year_Valuation_Valuation_Tax_

1971 $82,589,679 • $131,317,590 $10,314,522.60

1972 79,350,110 126,166,695 10,101,353.08

1973 79,402,766 117,619,813 10,015,458.54

1974 79,402,766 114,760,819 9,823,709.82

Gregory Lafakis testified for U. S. Steel in the 1972 case. Prior to 1975, Lafakis was the property assessment and equalization supervisor of Illinois’ Department of Local Government Affairs. He testified that his office made assessment/sales ratios studies for the years 1972 through *1221974. Each study compares the assessments for the year of the study with sales in Cook County which occurred in the same year. The 1972 study showed a median assessment ratio of 38.95 for Cook County industrial property. The 1973 study showed a median assessment ratio of 32.50, and the 1974 study showed 37.84.

Martin Miller testified for U. S. Steel in the 1972 case. He is chairman of the Jacobs Company, a firm engaged in property tax consulting and mass appraisal work. Miller is the principal author of real property appraisal manuals for various States. He gave his opinion of the methodologies used by American and the assessor in appraising South Works. Miller said an integrated steel producing plant could only be appraised by use of the summation approach to value, that is, the cost of replacement less depreciation due to all causes plus land value. He would have used the same approach as that used by American because it provides a full and complete methodology for the valuation of an industrial plant. He does not believe that original cost was a significant factor in determining the value of South Works. Miller testified that the assessor’s manual indicated basically a cost approach to value. Obsolescence did not appear to have been considered.

George Haddad, U. S. Steel’s manager of engineering services, testified in the 1972 case. He described the limited utilization of modem technology at South Works. In his opinion, South Works is a substantially uncompetitive plant.

Joseph Florence, deputy assessor/industrial building appraiser, testified for the county collector. He made the assessments of South Works for the years 1971 through 1973. Florence said that 1971 was a quadrennial assessment year for South Works. He visited the site at least 17 times in 1971 while he was making the assessment for that year. South Works was reassessed by a formula calculation of reproduction costs. Florence stated he had determined assessed value only. He did not determine either the fair cash value or the actual value of either the furnaces or South Works as a whole. He could not state the relationship which the assessments bore to the actual or fair cash value of the property. Florence and Thomas M. Tulley, the chief deputy assessor, asked U. S. Steel for the construction costs of blast furnace No. 8, the continuous casting facility, the No. 4 electric furnace and the basic oxygen processing shop. These four facilities were either under construction on January 1, 1971, or had commenced operation since April of 1969. U. S. Steel failed to provide the requested information. Belt, manager of taxes for U. S. Steel, told him the cost records were “unavailable.”

Florence said the reproduction costs used in each year’s assessments were derived in part from the 1959 Cook County assessor’s manual. He *123was not supplied with any factor with which to update those costs. He used his judgment which he recognized would be different from that of another assessor. In the absence of the requested information, he assessed South Works as uniformly as possible, consistent with the assessment of the other three steel producing facilities in Cook County.

The assessor’s manual applies to commercial and residential real estate, and to industrial buildings. It makes no reference to the pricing of industrial facilities or to the special purpose buildings of South Works. Florence would determine the reproduction cost and then adjust for depreciation by applying a condition factor. Florence conceded that the depreciation chart for 1971 carried the same depreciation for certain buildings as was applied four years previously on the 1967 chart. The new cost multiplied by the condition factor gives the full value for an item. The full value for all items on a parcel is combined to obtain the assessed valuation of a parcel. The bulk of the dollars of assessment represent values determined without reference to any manual.

The assessed values for each blast furnace were calculated by squaring the diameter of the hearth, multiplying that figure first by .75854 and then by 3.4 to reach an estimate of the rated capacity of the furnace in tons per day. This formula was developed by the assessor’s office through its work with Interlake Iron Company where the formula was corroborated. The productivity figure was then multiplied by a unit cost factor of $3350 per ton for each furnace capable of producing, with the exception of No. 8, the newest furnace, which was multiplied by $4000 per ton. The unit cost factor was applied to furnaces of all ages although Florence derived it from an assumed construction cost of the new No. 8 furnace which he said was entirely different from the other furnaces. In the previous quadrennial reassessment, the unit cost assigned to the furnaces was $2250 per ton.

A condition factor was then applied, which Florence said was in accordance with an “office rule.” U. S. Steel requested a copy of the rule but never received it. The factor was 50% for operating furnaces, something less for nonoperating furnaces, and 75% for the new No. 8 furnace. The three abandoned furnaces were assigned condition factors of either 5% or 10%. Florence could not say why there was a difference as to the factors applied to these three furnaces. The condition factor for the operating furnaces was increased for the 1971 quadrennial assessment from 27% to 50%.

William Wecker, a statistician, testified for the collector. He testified that the assessment/sales ratio studies which were put in evidence by U. S. Steel were not done by a random sampling. He also said that when estimating assessment ratios as of a certain date, the effect of inflation *124would be balanced only if the study included sales occurring both before and after the certain date rather than using only sales which occurred after that date.

J. Fitts also testified for the collector in the 1972 case. Fitts, a valuation expert, criticized American’s appraisals. He said he recognized the technique used in the reports but that he had never used it himself. He had never appraised a steel plant and he had not seen South Works. He had some criticisms of the appraisals. First, he thought there was a failure to explain what is obviated by the technique of going from a reproduction cost to a replacement cost. He also thought the use of replacement cost was unjustified as it was not well documented.

Before addressing the issues raised on appeal, it is necessary to discuss the standard of review applicable to real estate tax cases. The courts have no power to review the valuation of property which has been fixed for purposes of taxation by appropriate administrative officers in the absence of a showing of actual or constructive fraud. (People ex rel. Munson v. Morningside Heights, Inc. (1970), 45 Ill. 2d 338, 259 N.E.2d 27.) The supreme court discussed constructive fraud in Clarendon Associates v. Korzen (1973), 56 Ill. 2d 101, 104-05, 306 N.E.2d 299, 301:

> “In administering the legal remedy 0 * * the courts must presume, in the absence of evidence to the contrary, that the assessing officials performed their duty, and the court will not set aside an assessment merely because of a difference of opinion as to value. [Citation.] It is only where the valuation has been fraudulently made that it is subject to judicial review. [Citation.] Overvaluation may be so excessive, under some circumstances, as to justify the conclusion that it was not honestly made and is thus constructively fraudulent. [Citations.] Similarly, when property is assessed disproportionately higher than other similar property [citation] or the assessed value is reached under circumstances showing either a lack of knowledge of known values or a deliberate fixing of values contrary to known value, fraud will be inferred. [Citation.] In such cases courts will grant relief.”

U. S. Steel’s first argument on appeal is that the assessment procedure disregarded the Illinois Revenue Act of 1939. (Ill. Rev. Stat. 1971, ch. 120, pare 482 et seq.) The statute requires the assessor or his deputy, in a quadrennial assessment year, to “actually view and determine as near as practicable the value of each tract or lot of land listed for taxation as of January 1 6 0 (Emphasis added.) (Ill. Rev. Stat. 1971, ch. 120, par. 524.) In other years the assessor is to return a list of the new or added improvements and “the value which, in his opinion, has been added to such tract or lot by the erection thereof.” (Emphasis added.) Ill. Rev. Stat. 1971, ch. 120, par. 525.

*125U. S. Steel relies on the testimony of Swain and Florence in arguing that the statute was violated. Florence testified that he determined only the assessed value of South Works and that he did not determine either the fair cash or the actual value of the property. Swain testified that no effort was made to relate the assessment process to any proportion of full value. Swain also testified that it was not until the adoption of the Cook County Real Property Assessment Classification Ordinance, effective for tax year 1974, that the assessor’s office was able to determine the •relationship existing between the assessment of a property and its actual value. From this testimony, U. S. Steel argues the assessments were made “in ignorance of the value” of its property.

We cannot accept U. S. Steel’s assertions that the statute requires the assessor to determine full value before determining assessed value or that the statute was violated because full value was never determined. The statutory requirement that assessments be made on the basis of the “value” of each parcel is obviously intended to assure that taxpayers are treated equitably and that each undertake his or her just share of the tax burden. The court had a right to rely on Swain’s testimony that proper application of the assessor’s manual would produce an assessed value which would bear the 40% relationship to full value as required by the ordinance for industrial property.

U. S. Steel next argues the appraisal reports prepared by American should be accepted as stating the actual or full value of South Works for the years in question. The trial court’s rulings in each of the cases accepted the replacement cost method of appraising the value of South Works and also accepted the technique of using the conceptual plant as a guide. However, the court determined that the values found by American were understated due to certain omissions. Therefore, the court made certain adjustments to the American appraisals. As adjusted, these figures so closely approximated those of the assessor’s assessments that the court then concluded U. S. Steel had not demonstrated constructive fraud.

U. S. Steel makes a number of arguments directed at the trial court’s “corrections” in its computation of the replacement cost of South Works for the years in question.

U. S. Steel contends the trial court erroneously determined that the production figures for the American conceptual plant did not take into account the downtime for relining of the blast furnaces and that this error contributed to its eventual conclusion that the conceptual plant was insufficient in its productive capacity. In making this argument U. S. Steel relies on the testimony of Nichols where, in response to a question from the court, he said the downtime “is figured in, part of the factor that is in the capacity on developing, you are assuming down.” Nichols also said “the rated capacity of any furnace involves a certain amount of down *126time, because it is known at the time it is commissioned the first time that every so often it will have to have relining, so that figure is in there also.”

The written appraisals prepared by American fail to discuss downtime for relining the furnaces. Although Nichols’ testimony lends support to U. S. Steel’s argument that relining was taken into account, the trial court was not obligated to accept this testimony, particularly in light of the fact that the American appraisal reports never mention this factor.

U. S. Steel next contends the court erred in concluding that the primary mills of the American conceptual plant were deficient in productive capacity. It contends the testimony shows that the casters in the model plant were intended to produce the same product but more efficiently than South Works’ primary mills.

The trial court concluded there was a shortfall in the productive capacity of the primary mills of the conceptual plant because the replacement mills were designed to produce a smaller quantity of end product than the existing primary mills at South Works. U. S. Steel argues this conclusion overlooks the testimony, which is supported by the appraisal reports, that the continuous casting provided by the conceptual plant would have a significant effect on the efficiency of the process. Regardless of the merits of this argument, U. S. Steel has not demonstrated that this is a significant factor in concluding there is constructive fraud.

U. S. Steel next argues the trial court erred in concluding there was a shortfall of productive capacity in the finishing mills of the conceptual plant. The trial court found that the testimony concerning the productive capacity of the existing finishing mills was inconclusive.

The disputed testimony was given by Lindberg. Lindberg testified that the finishing mills at South Works consist of the continuous plate mill, the structural mills and the bar mills. The 52-inch structural mill averages 800 tons per turn, and the 34-inch structural mill averages about 450 tons per turn. The mills can be run 18 turns per week if there is enough “semi-finished” and if the blast furnace gas is available. The plate mill averages about 800 tons per turn, but Lindberg said there is a bottleneck in the finishing end on that mill and so the maximum turns that can be run is about 15 or 16 per week. Concerning the bar mill, Lindberg testified that it had “been down so long” he could not think of the numbers. He then said “I think we used to do on that mill 200 tons a turn maximum capacity.” This testimony presented a question of fact as to the productive capacity of the finishing mills. The trial court therefore was justified in concluding there was a shortfall which required correction.

In terms of the shortfall of productive capacity generally, the trial court noted that the conceptual plant is based upon end-product shipments over the five-year period ending in 1971. Those shipments do *127not necessarily equate with productive capacity for various reasons, including the fact that a producer may be accumulating inventory or liquidating inventory. The trial court also noted that shipments do not necessarily equate with ability to produce because market demand may limit actual production. Additionally, demand for the various end products will vary according to various factors. In light of these considerations, we believe the trial court was justified in concluding that the overall productive capacity of the conceptual plant was insufficient.

U. S. Steel next argues the trial court erred by including a residual value for each facility which has a remaining life in excess of eight years. U. S. Steel explains that the value of the facilities’ remaining lives to their terminal dates was not included in the appraisal’s figures because the appraisals as of January first for each year represent the value at that time of the continued use of the facility.

The dispute here seems to involve whether it was proper to use an average eight-year remaining life, at which point, in the appraiser’s opinion, the facilities would be replaced with equipment which was more technologically efficient, or whether, as the trial court concluded, the facilities’ replacement cost should be determined on the basis of their full remaining lives regardless of efficiency.

U. S. Steel has not cited any authority for the proposition that it was improper for the court to assign a value to the residual lives of the facilities beyond eight years. The trial court noted that the American appraisals measure economic loss to be suffered by U. S. Steel from continued ownership of the property and this would be valid if all the property had the same remaining useful economic life. However, most of the facilities have admitted useful lives in excess of eight years, and American did not measure the benefits of ownership which would accrue beyond the eight-year period. U. S. Steel has not proved by clear and convincing evidence that the trial court erred in determining that the residual lives of the facilities beyond eight years was a proper component of replacement cost.

U. S. Steel also objects to what it calls a “spurious valuation approach” by the trial court. It takes exception to the court’s use of an income approach in its adjustment of the figures as calculated by the appraisals. The trial court’s memoranda found this justifiable because the appraiser used an income approach in its reports. U. S. Steel says American’s capitalization of excess operating costs was used only for the purpose of discounting to a January 1st value the excess expense of operating South Works.

The appraisal report stated that it considered the “productivity of earning capacity” and “the capitalization of income received from the use” of South Works. The trial court also noted that “costs” and “earnings” *128have a direct relationship. We agree with the collector’s argument that to the extent American could and did determine an expected rate of return for investments in the industry, the court was justified in determining the expected return on an investment in the model plant.

U. S. Steel’s next argument is that the assessor made certain arbitrary increases in its assessments which demonstrate that they were made in ignorance of the value of the property and on judgments not based upon readily ascertainable facts or on a designedly excessive basis. The “arbitrary increases” which U. S. Steel objects to involve the use of a formula to estimate blast furnace production. U. S. Steel contends the use of the formula resulted in two errors: (1) use of the formula indicates that the assessor arbitrarily ignored the production data which was supplied to him annually, and (2) the assessor erroneously used the cost per ton of constructing the new No. 8 furnace in determining a unit factor for the old furnaces which were unlike No. 8.

We agree with the trial court’s conclusion that U. S. Steel did not prove the assessments were made arbitrarily. First, U. S. Steel did not provide some of the requested cost information pertaining to the recently constructed facilities. Although Belt explained that this omission was due to U. S. Steel’s difficulty in distinguishing between real and personal property, it nevertheless lends some justification to the assessor’s decision to use a formula for determining blast furnace production rather than the incomplete figures provided by U. S. Steel. Additionally, using a totally different method of calculating the value of South Works, the trial court’s figures were close enough to those determined by the assessor as to warrant the conclusion that constructive fraud had not been demonstrated. This fact also lends support to the trial court’s conclusion that the assessments were not arbitrarily made.

U. S. Steel also argues the assessor was arbitrary in its increase in the size of the “condition good” factors which it applied to the blast furnaces. A 50% condition good factor was used on all the furnaces except for the new No. 8, to which a 75% condition good factor was used. U. S. Steel points out that the unproductive furnaces Nos. 1, 3 and 5 were given 5 or 10% condition good factors even though Nos. 3 and 5 had been removed from the assessment rolls at the time of the previous quadrennial reassessment.

In response, the collector points out that a number of the blast furnaces had been refined since the last quadrennial assessment, with the result that their estimated useful fives had been extended. Additionally, the increase in condition factors was applied uniformly to all steel-making firms in Cook County. In fight of this evidence we cannot say U. S. Steel has proved its argument that the assessments were arbitrarily made.

U. S. Steel next makes a constitutional argument based on article IX, *129section 4(b) of the 1970 Illinois Constitution which provides that “classification shall be reasonable and assessments shall be uniform within each class. The level of assessment * * * of the highest class in a county shall not exceed two and one-half times the level of assessment “ * * of the lowest class in that county.” In making this argument U. S. Steel relies on the annual sales/ratio studies of the Department of Local Government Affairs (the Department).

U. S. Steel concedes that when the court’s determinations of fair market value for each year are used the assessments were in proper relation to the actual value of the property. Because we have previously found that U. S. Steel has not proved the court’s calculations were erroneous, we need not address the argument based on that part of the constitutional provision.

For tax year 1974, the trial court found the constitutional 2/2 times requirement had been exceeded by three percent. Rather than applying a per se rule which would require that the assessment be struck down, the court applied what it termed a “rule of reason” and found the variance was not in violation of the constitutional requirement.

U. S. Steel argues on appeal that the court should not have applied a “rule of reason” and that the three-percent variance establishes that the 1974 assessment was unconstitutional. U. S. Steel argues a three-percent variance does not justify its occurrence any more than if it had been 30 percent or 90 percent. It offers no authority for the proposition that it was improper to apply a “rule of reason.”

The trial court gave a number of reasons for its conclusion that a per se rule was not appropriate: reassessments are made every four years, and the 1974 sales/ratio figures reflect assessments which were made during the years 1971 through 1974; inflation necessarily created some distortion in the assessment levels of properties assessed as much as four years apart; the Department’s statistics are probably accurate enough to show broad deviations from the constitutional levels but are not accurate enough that a three-percent variation should be relied on; and, finally, the statistics show a good faith effort on the part of the assessor to comply with both the ordinance and the constitutional requirement. In light of these sound reasons for applying a “rule of reason” we cannot say that U. S. Steel has proved by clear and convincing evidence that the court erred.

We affirm the trial court in both of these consolidated cases.

Judgment affirmed.

JOHNSON and ROMITI, JJ., concur.