The opinion of the court was delivered by
Kaul, J.:
Plaintiffs-appellants brought this action pursuant to K. S. A. 79-2005 to recover ad valorem taxes for the year 1965 paid under protest on ten oil and gas leases. After a trial in district court, resulting in an adverse decision, plaintiffs perfected this appeal.
The leases in question were rendered for taxes as of January 1, 1965. In April 1965 the leases were assessed for ad valorem purposes by the county clerk-assessor at a total of $669,515.00. Plaintiffs appealed to the Haskell County Board of Equalization which sustained the assessments. An appeal was taken to the State Board of Equalization which reduced the assessment approximately six percent to $629,200.00 on which the taxes in question were levied. On December 9, 1965, plaintiffs paid the taxes amounting to $27,-087.07, protesting $23,268.32 and claiming $3,818.75 to be the correct amount due for 1965. Plaintiffs alleged the protested portion was illegal due to an excessive valuation. There is no controversy concerning the form or filing of the protests.
After filing their protests, plaintiffs instituted this action within thirty days pursuant to the provisions of K. S. A. 79-2005. Anne M. Murphy was substituted as County Treasurer after the resignation of L. G. Phoenix, and the State Property Valuation Department and Alvin E. Jones (Ronald F. Dwyer substituted) Director were made additional parties.
Plaintiffs’ petition, to which their protests were attached, alleged that each of the defendants was shown by clear and convincing evidence that plaintiffs’ property was being assessed at an assessment ratio many times greater than other real and personal properties in Haskell County; and that defendants, by failing to grant plaintiffs the relief asked for, acted in an arbitrary, capricious and unlawful manner and contrary to law and fact to such a degree that such actions amounted to constructive fraud on the part of defendants and a denial of due process of law and equal protection of the laws to the plaintiffs and that defendants’ failure to reduce the assessment did not result from error in judgment, but was intentional unlawful discrimination against plaintiffs and subjected them to an excessive and disproportionate share of the tax burden in Haskell County.
[284]*284Plaintiffs further alleged that the excessive assessments were not made in accordance with the provisions of K. S. A. 79-101, 79-330, 79-331, 79-1406, 79-1409, 79-1439 and 79-1602.
Plaintiffs prayed that the orders of the Board of Tax Appeals, sitting as the State Board of Equalization, be modified to reflect the values of plaintiffs’ leases, as established by the plaintiffs, and that the court direct the county treasurer to refund to plaintiffs taxes unlawfully collected.
The director of property valuation answered plaintiffs’ amended petition asserting that it failed to state a claim upon which relief could be granted; that the property was assessed in accordance with statutes of Kansas; that the use of schedules was lawful and proper and the preparation thereon was directed by K. S. A. 74-2441; that the schedules prepared for assessing oil and gas leases for 1965 show on their face that all of the factors to be considered, as set forth in K. S. A. 79-331, are considered therein, and that plaintiffs’ property was asseseed for the year 1965 in compliance with K. S. A. 79-1439 and all other applicable laws relating thereto.
Other defendants filed separate answers generally alleging that plaintiffs’ property was assessed in accordance with the statutes relative thereto and in accordance with the Kansas Price Schedule of Oil and Gas Properties for 1965, promulgated by the Director of Property Valuation under the authority of K. S. A. 74-2441.
The county treasurer prayed that the order of the State Board of Equalization be upheld and confirmed and that she be instructed to disburse, according to law, the sum now held in suspense under the protested payment of the plaintiffs.
The case was tried to the court which made comprehensive findings of fact and concluded that plaintiffs had not met their burden of proving conduct on the part of defendants constituting fraud, or that the assessments complained of were unequal or not uniform.
Both plaintiffs and defendants offered the testimony of petroleum engineers as evidence of values.
Essentially, plaintiffs contend the trial court erred (1) in not adopting the values established by their expert Mr. Yates, and substituting them for the values arrived at by the defendants in the application of the state price schedules; and (2) in failing to give consideration to the real estate assessment ratio study prepared by the property valuation director in establishing the ratio of assessment to one hundred percent justifiable value in Haskell County.
[285]*285This controversy, like many other matters concerning taxation recently before this court, stems in part from legislative enactment in 1963 of laws relating to uniform assessment rates of property subject to ad valorem taxes. We refer in particular to K. S. A. 79-411, 501, 503, 1406 and 1439 providing that after January 1, 1964, all real and tangible personal property shall be assessed at thirty percent of justifiable value and establishing factors to be considered in the determination of justifiable value.
The evidence disclosed that the original assessment of the leases in question was made by the Haskell County assessor by following schedules furnished to her by the state director of property valuation. The assessor testified that two adjustments were made to the renditions filed by Cities Service Oil Company and that daily average was adjusted to 366 days instead of 365 and that operators’ allowance was credited. Both adjustments were small and lowered the valuations slightly. The assessor further testified that she used manuals and schedules prepared by the property valuation department for assessing other personal property in the county at thirty percent justifiable value. A comparison of assessments of 1964 and 1965 made by the assessor disclosed that, disregarding a lease not owned by plaintiffs in 1964, the assessments of the other nine leases decreased $32,675.00 in 1965. The assessor also testified that the board of county commissioners of Haskell County, on August 5, 1965, contracted with an appraisal firm, to reappraise all real estate at thirty percent justifiable value; that such appraisal was completed but hearings had not been held thereon at the time of trial.
The evidence disclosed that for a number of years prior to 1965 Kansas oil and gas leases were assessed by the use of a schedule prepared by the property valuation department. Physical equipment on leases was assessed at a figure computed by multiplying cost by sixty percent and the result by thirty percent or a net figure of eighteen percent of cost, as to physical equipment. Leaseholder productions and reserves were assessed at $800 times the daily average barrels of oil produced, with no deduction made for operators’ expense or a decline factor. The resulting figure was accepted as thirty percent of justifiable value of an average well.
For some time prior to 1965, the oil industry, including plaintiffs, requested modifications of the schedule so that more flexible valuations could result. The 1964 schedule was attacked on the grounds [286]*286that an average well valuation tend to overvalue poor wells (low production) and undervalue good wells (high production).
In response to requests of the industry, and pursuant to his authority under K. S. A. 74-2441 (b), the director of property valuation, in the fall of 1964, convened a hearing in Wichita, attended by county assessors and various representatives of the oil industry for the purpose of working out a modification of the schedule which would result in a more flexible application. The result was the 1965 schedule, with which we are concerned.
Dr. Charles F. Weinaug, a professor of petroleum engineering at the University of Kansas, has represented the property valuation department as a consultant for six years. Dr. Weinaug reviewed the 1965 schedule and recommended some modifications, which were accepted.
The evidence discloses the 1965 schedule was again modified in 1966. The 1965 schedule followed prior schedules and was essentially readopted in 1966 as to valuation of equipment, except that some reductions were made for changing prices and the aging of oil lease equipment in the state. Reserves or production was computed as a value varying between $325 and $1,100 per daily average barrels reduced by schedule allowances for operators’ expenses, transportation charges, and secondary recovery. The valuation tables projected the life of a well from less than one year to a maximum of five years and contained a precomputed decline factor of five percent per year and a precomputed ten percent discount factor for use of money.
The 1965 schedule adopted some, but not all, of the features of the schedule previously proposed by Weinaug in 1962. Weinaug was retained by Haskell County to evaluate the leases in question and to testify for defendants at the trial.
The variance between the testimony of Weinaug and that of Yates gives rise to the first contention of plaintiff on appeal.
The evidence discloses that both Weinaug and Yates are highly qualified petroleum engineers with many years of experience in valuing oil and gas leaseholds in Kansas and other states. Both testified that oil leases are difficult to value by any method because of a great number of unknown quantities and judgment factors involved.
Weinaug testified that he considered all the factors considered by engineers in making an analytical engineering valuation, includ[287]*287ing the statutory factors and he made a valuation as of January 1, 1965. He further testified that in making his evaluation he considered availability of money, rate of production, and the statutory factors of K. S. A. 79-331 — age of wells, quality of oil or gas, nearness of wells to market, cost of operation, character, intent and permanency of the market, the probable life of the well, the quantity of oil or gas produced, the number of wells being operated, and special water problems. He testified that there were no particular water problems in the leases involved in this litigation.
Yates testified that he used “analytical engineering valuation” in arriving at a valuation of reserves. His testimony as to his formula is narrated as follows:
“He values the leasehold by determining the total future reserves, projecting them on an annual basis and the oil revenue therefrom, deducts therefrom the operating costs on an annual basis to get the annual net operating income schedule by years throughout the future life of the property. He then discounts these figures at a current going back rate just for the cost of money. He used 6% as of January 1, 1967. This determines the present or future net cash realization expressed in present value dollars. . . .”
The record also discloses a considerable variance in the testimony of the two witnesses with respect to the values placed on equipment. Weinaug used the schedules prepared by the property valuation department resulting in an equipment valuation equal to eighteen percent of cost. Yates, on the other hand, valued equipment as salvage, at the time the lease will be abandoned, discounted back to the present day worth, after deducting cost of salvaging and deducting some of the inventory of pipe and any casing left in the well.
The opposing methods of equipment valuation result in considerable differences. Valuing the physical equipment under the state schedule, as applied by Weinaug, produced a thirty percent assessment of $72,925, as compared to $19,990, for physical equipment, arrived at by the method proposed by Yates. The method used by defendants in valuing physical equipment, as described by Weinaug, is aimed at valuation for equipment on a statutory basis for justifiable value as of January 1, 1965, not at some theoretically salvage date discounted back as proposed by Yates.
Plaintiffs also called as a witness Charles C. Rodd, a Vice-President of the Fourth National Bank and Trust Company, of Wichita, Kansas, who holds a degree in petroleum engineering and [288]*288has had many years of experience in judging engineering appraisals on oil and gas properties for loan purposes. He testified that Yates’ method of valuation is accepted in the petroleum engineering field, and that the conclusions reached by Yates are reasonable. The witness admitted that there will always be some variations on valuation work in the field.
Defendants also called the manager of the ad valorem tax department of Cities Service Oil Company who introduced an exhibit showing the sale price received for other leases sold in Western Kansas in 1965. The trial court found that such sale prices were not sufficiently supported by lease and geographical data upon which to base a comparison with properties involved herein.
In summary the evidence discloses that total sums intended to produce assessments at thirty percent of justifiable value are as follows: Haskell County Clerk and Assessor $666,220; Kansas Roard of Tax Appeals $629,600; Dr. Weinaug $551,280, and Mr. Yates $221,760.
The first position asserted by plaintiffs is that the valuation arrived at by the 1965 schedule is excessive to the extent that constructive fraud was practiced on them. To support their position plaintiffs’ principal arguments are that their witness, Mr. Yates, is better qualified than Weinaug, and that the method of valuation used by Yates is the most acceptable, since it was accepted by the oil industry and used in valuing for loan purposes according to the testimony of Rodd. We are not persuaded by either argument. A careful examination of the testimony of Weinaug and Yates, as to their education, training and experience, clearly reveals that Weinaug is equally, or better, qualified as an expert in the field.
As we have stated, the valuing of producing oil leases in compliance with K. S. A. 79-331, setting out eight factors, which must be considered as well as any other factors known by the assessor to affect the valuation of the property, is an extremely difficult operation. Most of the items set out in the statute are judgment factors and may easily result in great variations, although applied by expert petroleum engineers, as in this case. As may be seen by the thirty percent valuation figures enumerated the leaseholds, with which we are concerned, are very valuable. A slight difference of opinion as to the application of any of the statutory factors, in particular the probable life of the wells or rate of decline of future production, could cause wide variations in valuations.
[289]*289The trial court heard the lengthy and detailed testimony of the witnesses as to their respective methods of valuations, as well as the testimony of Weinaug, as to the background and promulgation of the state’s schedule, and concluded the application of the state’s schedules, in assessing plaintiffs’ leaseholds, did not amount to constructive fraud.
Generally, the credibility of witnesses and the weight and force of their testimony are matters for the determination of the trier of facts. (State v. Chuning, 201 Kan. 784, 443 P. 2d 248, State v. Scott, 199 Kan. 203, 428 P. 2d 458, and Carter v. Carter, 187 Kan. 74, 353 P. 2d 499.)
We find no error in the trial court’s rejection of the values proposed by plaintiffs’ witness Yates.
It appears the variance in valuations in this case basically stems from difference of opinion. There is no evidence that the assessment was arrived at fraudulently, arbitrarily or capriciously and in the absence thereof a difference of opinion as to value or an error in judgment by assessing officers is no reason for interference by a court. (Salt Co. v. Ellsworth County, 82 Kan. 203, 107 Pac. 640; Finney County v. Bullard, 77 Kan. 349, 94 Pac. 129.)
Generally, the function of a court in such matters of assessment is to make certain that a taxpayer has the benefit of the honest judgment of the assessing officers and unless the assessment is so out of proportion as to give reasonable assurance that officers could not have been honest in fixing the valuation; interference by courts is not justified. Courts will not substitute their judgment for that of the assessing authority in the absence of fraud, or conduct so oppressive, arbitrary or capricious as to amount to constructive fraud.
An exhaustive delineation of the limited authority of courts with respect to assessment processes may be found in the recent cases of Harshberger v. Board of County Commissioners, 201 Kan. 592, 442 P. 2d 5; Mobil Oil Corporation v. McHenry, 200 Kan. 211, 436 P. 2d 982; and Board of County Commissioners v. Brookover, 198 Kan. 70, 422 P. 2d 906. Reiteration of what was said and held in those cases need not be repeated.
Plaintiffs’ second position is that constructive fraud was practiced on them by defendants in that all other property in Haskell County was assessed at twelve percent of justifiable value. Plaintiffs argue that such lack of uniformity amounts to constructive fraud under the rule laid down by this court in Addington v. Board of County [290]*290Commissioners, 191 Kan. 528, 382 P. 2d 315. The record does not support the position taken by plaintiffs in this regard. The trial court found as follows:
“The plaintiffs failed to show any lack of uniformity in valuation and assessment between their property and all tire other oil leases and equipment in Haskell County. The only proof offered shows uniformity.
“The plaintiffs failed to show a lack of uniformity in valuation and assessment as between their properties and other personal properties. The exhibits when compared with assessments of personal property items with which I am familiar would tend to show a discrepancy in favor of the plaintiffs.”
The testimony of the county clerk-assessor that all personal property in Haskell County was assessed at thirty percent of justifiable value was unrefuted. As a result, plaintiffs’ claim of discrimination with respect to “all” other property in Haskell County clearly falls. In fact the evidence as to personal property, including oil and gas properties, proves uniformity rather than lack of it.
With respect to the establishment of discrimination by the real estate assessment ratio study, the trial court found as follows:
“The plaintiffs’ testimony offered to support their claim for a tax refund in the sum of $23,268.32 is based upon the applicable tax rate as applied to the difference between the approved value set by the State Board of Equalization and the 1964 Kansas real estate assessment ratio study manual of 12% (applied to Haskell County), which the plaintiffs contend is 12% of the justifiable value of Haskell County real estate.
“The ratio study manual considers and includes only part of one of the eleven factors (being section (i) which is the sale value on open market) set out in K. S. A. 79-503 as the factors to be considered in determining justifiable value. Said ratio study concerns less than one percent of the Haskell County real estate. This seems insufficient upon which to base a comparison for the purpose of determining a valuation and assessment'to be so arbitrary, oppressive, capricious and discriminatory as to amount to and constitute constructive fraud.”
We believe the findings of the trial court quoted are supported by the evidence. An exhibit prepared by the county clerk shows that in 1965 there were thirty-five sales in the county, amounting to .98 percent of a total of 3566 parcels of real estate, and in 1964 there were only forty sales, amounting to 1.12 percent.
The only other evidence as to assessment ratio is an exhibit in the form of an extract of the assessment ratio study for Haskell County for the years 1951 through 1965. As the trial court indicated, there was no foundation evidence offered as to the validity of the ratio study, as a basis for comparison, in determining the degree [291]*291of lack of uniformity, if any, between assessment of plaintiffs’ properties and real estate in Haskell County.
Plaintiffs rely chiefly on Addington v. Board of County Commissioners, supra, to support their position in this regard. At the outset, it must be noted that Addington was decided in 1961, several years prior to the enactment of the legislation heretofore referred to. In Addington we find the following statement:
“. . . In the instant case the rate of assessment fixed by the county clerk-assessor at more than thirty percent of the true value of plaintiff’s property, as compared to the rate of assessment of twelve percent of the market value of all other property located in the county and subject to the same tax levy, was so arbitrary, oppressive and grossly discriminatory that it constituted constructive fraud on the rights of the plaintiff as a taxpayer and destroyed uniformity and equality in the manner of fixing the assessed valuations; also, it was illegal, thereby entitling the plaintiff to the relief sought as to the illegal portion of the tax paid under protest.” (p.533.) (Emphasis supplied.)
In Addington the property involved was a grain elevator assessed under the personal property assessment schedule for 1961. It appears from a reading of the opinion in that case that the elevator property in question was singled out of all other properties, real and personal, and assessed at thirty percent justifiable value while all other properties in the county (Stevens) were assessed at twelve percent. Apparently, in Addington the assessment ratio study was taken to be adequate for comparison purposes in determining uniformity and no attack thereon was made as in the instant case.
In 1961 all property, real and personal, was valued at its actual value in money pursuant to G. S. 1949, 79-1406 (amended in 1963, now K. S. A. 79-1406), under the rules set out for specific determination of true value in money as provided in G. S. 1949, 79-501 (amended in 1963, now K. S. A. 79-501.)
In 1963, pursuant to K. S. A. 79-411 and K. S. A. 79-501, real property was to be assessed at thirty percent of its justifiable value in money and in addition to sale price eleven other factors were enumerated in K. S. A. 79-503 (amended in 1965, now K. S. A. 1967 Supp. 79-503) and consideration thereof required in determining the justifiable value of real property.
The force and effect of many of the 1963 enactments were considered and discussed in Board of County Commissioners v. Brookover, supra, where it was held that ratio studies provided for by K. S. A. 79-1436 may properly be considered in determining the necessity for reappraisal to arrive at justifiable value as provided by
[292]*292K. S. A. 79-1439. It was further held that the sale prices of real estate given by willing purchasers to willing sellers is substantial evidence of value for appraisal purposes, although consideration of other factors mentioned in K. S. A. 79-503 may be proper. In other words, the holding in Brookover indicates that a ratio study, based on sales, is admissible and may be substantial evidence of justifiable value, but the holding therein cannot be construed to mean that such evidence is conclusive.
Under the showing here, the trial court chose not to find the ratio study, based on sales of less than one percent of real estate parcels, standing alone, unsupported by any other evidence, as to actual percentage of justifiable value, to be a proper basis of comparison in establishing the assessment of plaintiffs’ properties as constructive fraud. Under the facts related, we believe the trial court’s finding is justified.
While Harshberger v. Board of County Commissioners, supra, was an injunction action, brought under the provisions of K. S. A. 60-907 (a), the problem involved is analogous in many respects to that under consideration here. The controversy in Harshberger stems from the fact that Ford county had completed its reappraisal of real estate and was on a thirty percent assessment ratio to the justifiable value, while none of the other counties bordering Ford county had completed their appraisal and none was using new valuations and assessments of thirty percent justifiable values; specifically five of such counties were applying a nineteen percent assessment ratio.
Plaintiffs in Harshberger were owners of taxable property situated in two hospital districts and five school districts, located partially in Ford county, and partially in other counties. They asked for injunctive relief because assessment ratios within the overlapping school and hospital districts differed according to the county within which the particular property was situated. We held the district court was without jurisdiction to grant the relief sought. While the instant action under K. S. A. 79-2005 is presented in a different framework, much of what is said in Harshberger is applicable here. The Ford County officials, as those in Haskell County in the instant case, were acting under legislative fiat and at the direction of the state board of equalization. In Harshberger we said:
“The courts have no difficulty with their power and authority where taxing bodies are attempting to proceed without statutory authority or contrary to [293]*293statute (City Rly. Co. v. Roberts, 45 Kan 360, 25 Pac. 854) or where taxing authorities are proceeding against property outside their jurisdiction (Sherwood Const. Co. v. Board of County Commrs., 167 Kan. 421, 207 P. 2d 409). These are matters rightly within the province of the judiciary. However, when courts are confronted with purely administrative acts relating to taxation their jurisdiction becomes quite limited.
“The courts cannot fix the value of property for the purpose of taxation. Matters of taxation, especially assessments, are administrative in their character and should remain free of judicial interference in the absence of fraud, corruption and conduct so oppressive, arbitrary or capricious as to amount to fraud.” (pp. 594, 595.)
In the case at bar, defendants have acted under legislative fiat in assessing plaintiffs’ properties at thirty percent justifiable value pursuant to K. S. A. 79-501 and 1439. The leases were assessed by valuing both equipment and oil (K.S. A. 79-330), as personal property, pursuant to K. S. A. 79-329, after consideration of all the factors enumerated in K. S. A. 79-331. The property valuation director properly furnished schedules pursuant to K. S. A. 74-2441. The county clerk-assessor conformed to the values in such schedules pursuant to K.S.A. 79-1412a, Seventh (amended in 1965, now K. S. A. 1967 Supp. 79-1412a, Seventh).
It is to be further noted that plaintiffs have presented their claims to the Haskell County Board of Equalization and the State Board of Tax Appeals, sitting as the State Board of Equalization, while the latter made some adjustments favorable to plaintiffs, neither board found lack of uniformity as claimed by plaintiffs.
If there is any discrepancy in Haskell County between real estate assessment ratios and the thirty percent of justifiable value required by law, it is to be promptly remedied by the county officials; since a reappraisal had been completed at the time of trial except for hearings thereon; according to the testimony of the county clerk-assessor. Since the law now requires that all property be assessed at thirty percent of justifiable value, reappraisal is the proper method of correcting inequalities with respect to real estate assessments. (See K. S. A. 79-1413a and Board of County Commissioners v. Brookover, supra.)
There is no indication in this record that, at any stage of the proceedings, the defendants attempted to proceed without statutory authority or in conflict with any statute. We find no indicia of bad faith, arbitrary or oppressive action or systematic discrimination resulting in a fraud upon plaintiffs’ rights by arbitrary distinction made [294]*294between their properties and other property in the county, as we found in Addington. This is not to say that inequality or lack of uniformity in assessment if knowingly, intentionally or fraudulently made, will not entitle a taxpayer to relief under the provisions of K. S. A. 79-2005.
However, where the only evidence of excessiveness is in dispute and evidence offered to establish a base for comparison in attempting to show lack of uniformity is found to be inadequate and insufficient by the trier of facts, an assessment, made within statutory confines, will not be invalidated by judicial intervention.
One other point requires attention. While the matter does not appear to have been raised by plaintiffs in the court below, it is specified in their points on appeal. They now claim that even though the valuations of Yates are rejected, the values of Weinaug should be substituted for the valuations of the board of tax appeals. Plaintiffs argue there was no other evidence before the court as to values except those testified to by Yates and Weinaug. The contention is not supported by the record.
Plaintiffs’ action was an attack on the valuations of the board of tax appeals, sitting as the state board of equalization, rather than on valuations of Weinaug whose testimony was offered by defendants to rebut that of plaintiffs’ witness Yates. The 1965 schedules were in evidence before the court. The schedules show on their face that factors to be considered in the assessment of oil and gas leases, as enumerated in K. S. A. 79-331, were in fact considered in the preparation of the schedules.
Dr. Weinaug testified that the framework of the 1965 schedule was veiy similar to that proposed by the committee of the oil industry and that he was called upon by the property valuation department to review this schedule after its adoption and that a part, but not all, of his recommendations were incorporated which explains the variance. In summation Weinaug’s testimony is narrated:
“. . . Based on his knowledge of the 1965 schedule and his analytical engineering valuation he made of the leases owned by the Plaintiff, he feels the valuations placed thereon by the county clerk for the year 1965 were fair and reasonable values.”
While uniformity of taxation does not permit a systematic, arbitrary or intentional valuation of the property of one taxpayer at a substantially higher valuation than that placed on other property within the same taxing district, the undisputed evidence here shows [295]*295that plaintiffs’ property is valued uniformly with all other personal property and the evidence is insufficient to establish a systematic, arbitrary or intentional discrimination against plaintiffs’ property with respect to the justifiable value of real estate in the county.
The evidence in this case fails to establish conduct by the defendants so arbitrary, oppressive and grossly discriminatory that it constituted constructive fraud on the rights of plaintiffs; therefore the judgment is affirmed.