
119 Ariz. 111 (1978)
579 P.2d 1081
PIMA COUNTY, a body politic, and Arizona Department of Revenue, Appellants,
v.
CYPRUS-PIMA MINING COMPANY, a corporation, Appellee.
No. 13182.
Supreme Court of Arizona, In Banc.
April 10, 1978.
Rehearing Denied May 9, 1978.
*112 Bruce E. Babbitt, former Atty. Gen. by James Powers, Sp. Asst. Atty. Gen., Phoenix, for appellants.
Bilby, Shoenhair, Warnock & Dolph by David W. Richter, Michael A. Lacagnina, Tucson, for appellee.
STRUCKMEYER, Vice Chief Justice.
By this appeal, the Arizona Department of Revenue and Pima County seek to set aside the valuation for tax purposes fixed on the open pit copper mine of Cyprus-Pima Mining Company by the Superior Court for the year 1975. The judgment of the Superior Court is reversed with directions to enter judgment in favor of appellants, reinstating the valuation of appellee's mine at $67,300,000, the amount fixed by the State Board of Tax Appeals.
This case presents the same basic question as was presented in Mohave County v. Duval Corporation, 119 Ariz. 105, 579 P.2d 1075 (1978) (opinion filed this date); namely, whether the valuation of the Cyprus-Pima Mine as fixed by the State Board of Tax Appeals is lawful under A.R.S. § 42-201(4). The Cyprus-Pima Mining Company *113 appealed its property tax valuation to the State Board of Tax Appeals. The State Board fixed the value of 60.86% of the mine at $67,300,000.[1] The mining company was still not satisfied and petitioned the Superior Court for a reduction pursuant to A.R.S. §§ 42-146, 42-151 and 42-152. As in Duval, the Superior Court ordered the valuation reduced. Here the reduction was from $67,300,000 to $39,600,000.
The Arizona Department of Revenue and Pima County did not cross-appeal from the State Board's valuation; but in their answer to Cyprus-Pima's appeal, they asked the Superior Court to increase the valuation. The Superior Court was, however, of the view that because of the failure to present this issue to the State Board of Tax Appeals and to file a timely appeal or cross-appeal, the only issues were whether the valuation of the State Board was excessive and, if so, how much.
The first question we consider then is whether Cyprus-Pima's valuation for tax purposes may be increased without directly appealing from the valuation of the State Board. We think not.
By statute A.R.S. § 42-123(B)(6), the Department of Revenue may contest valuations of property before the State Board of Tax Appeals. If the decision of the State Board is, in the opinion of the Director of the Department of Revenue, erroneous, he may "appeal" such decision to the Superior Court in the manner provided in A.R.S. § 42-151. By § 42-151, an appeal is commenced by filing a notice of appeal. The Department of Revenue did not file a notice of appeal. Rather, as stated, it sought affirmative relief in its answer to the appeal of Cyprus-Pima. The procedure used by the Department to test the decision of the Board of Tax Appeals does not comply with the statute. The right to appeal is statutory and the method provided by the Legislature is exclusive. County of Pima v. State Dept. of Revenue, 114 Ariz. 275, 560 P.2d 793 (1977); Williams v. Bankers Nat. Ins. Co., 80 Ariz. 294, 297 P.2d 344 (1956). We therefore hold that the valuation fixed by the State Board may not be raised except and in the manner provided by law; that is, by direct appeal. We do not hold, however, that evidence of valuation in amounts greater than the State Board's finding may not be shown to support its valuation. We only hold that where there is no appeal or cross-appeal, a valuation may not be set greater than that fixed by the State Board.
Appellants question the failure of the Superior Court to dismiss Cyprus-Pima's appeal because Cyprus-Pima did not file a receipt for the payment of its taxes as required by statute.
A.R.S. § 42-151(E) provides:
"All taxes levied and assessed against property on which an appeal has been filed by the owner thereof shall be paid under protest prior to the date the tax becomes delinquent. A receipt shall be given for the amount of such tax paid, and within forty-five days a copy of the receipt shall be filed by the owner with the clerk of the court in which the appeal is docketed. If such taxes are not paid prior to becoming delinquent, or if a copy of the receipt for payment is not so filed, the court shall dismiss the appeal."
It is appellants' position that because Cyprus-Pima did not file a copy of the receipt for payment of taxes within 45 days, the Superior Court should have dismissed the appeal. We think, however, the circumstances of this case did not require the dismissal of Cyprus-Pima's appeal to the Superior Court.
Cyprus-Pima timely paid all the taxes assessed against it for the year 1975. The first half of the 1975 taxes was due on November 3, 1975 and it was paid on that date. On November 5, 1975, Cyprus-Pima filed with the Clerk of the Superior Court a receipt which indicated payment of the first half of *114 the 1975 taxes. The second half of the 1975 taxes was not due until May 3, 1976. These taxes were paid April 28, 1976, the day the trial of the action was concluded in the Superior Court. Cyprus-Pima did not file a receipt showing payment of the second half of taxes within 45 days. However, prior to entry of judgment, Cyprus-Pima filed with the clerk of the court a post office receipt for certified mail indicating delivery of its check to the county treasurer on April 28, 1976.
The plain purpose of the statute in requiring the payment of taxes before they become delinquent is to insure the continued fiscal soundness of the government. In this we think the statute is mandatory. The purpose of the requirement that a receipt be filed with the Clerk of the Superior Court is to notify the court that the taxpayer has complied with the law. Where, as here, the taxpayer timely pays its taxes and satisfactorily makes known to the court that its taxes had been paid before the court orders the appeal dismissed, we think the spirit of the law is satisfied. A statute should be given a sensible construction. Sanders v. Folsom, 104 Ariz. 283, 451 P.2d 612 (1969). We hold that there was sufficient compliance with the provision of § 42-151(E).
Before examining the basis for the Superior Court's action in reducing the valuation of the Cyprus-Pima Mine, certain points should be emphasized.
First, the Legislature requires for tax purposes that the valuation of property shall be at its "market value." A.R.S. § 42-201(4).[2] More will be said later about the determination of the market value of the Cyprus-Pima Mine.
Second, the term "cash flow" as used in the evidence means the total of all revenues minus all costs  net income after taxes. The cash flow (net income after taxes) and the full cash value for 60.86% of the Cyprus-Pima Mine for the five years preceding 1975 were:


            CASH FLOW             FULL CASH VALUE
    1970     $13,333,000             $21,544,000
    1971       9,034,000              21,179,000
    1972      11,414,000              36,698,000
    1973      20,231,000              34,568,000
    1974      21,330,000              28,604,000

It is obvious from the above that the full cash value of the Cyprus-Pima Mine was not adequately reflecting market value. The figures show that the mine was consistently being valued at less than three times earnings or, in some cases, at less than two times earnings and that, therefore, the value of the mine was being recovered long before its ore body was expected to be exhausted. Consequently, in 1975 the decision was made to evaluate by a method which would produce a more realistic result.
Both parties rested their cases on the testimony of two expert appraisal witnesses. For the mine, Alfred Petrick, Jr. testified to a valuation of $35,900,000 for 60.86% of the mine, and Fredrick C. Kruger testified to a valuation of $39,682,000. The Arizona Department of Revenue's two witnesses, Jack W. Still and Ernest K. Lehmann, testified, respectively, to valuations of $93,666,099 and $79,000,000.
Before examining the evidence supporting Cyprus-Pima's valuations, we note the Superior Court's findings of facts 8 and 9. In number 8, the Superior Court found that "the valuation * * * of $67,300,000 as found by the State Board of Tax Appeals is excessive." In finding 9, the court found that the testimony and valuation of Fredrick C. Kruger "were more persuasive than those of any other expert witness and the Court therefore substantially adopts Dr. Kruger's valuation." The Superior Court did not give any reason why the testimony of Kruger was "more persuasive." Nor did the Superior Court find that the witnesses for the State did not use standard appraisal methods or techniques. Hence, the court's findings of fact provide us with little, if any, basis as to why the court found the State's valuation to be excessive.
*115 We have said that a mere difference of opinion as to the method to be used in computing valuation does not justify judicial intervention in the area of taxation. Mohave County v. Duval Corp., supra; Navajo County v. Four Corners Pipe Line Company, 106 Ariz. 511, 479 P.2d 174 (1970), rehearing denied, 107 Ariz. 296, 486 P.2d 778 (1971). And see County of Yuma v. Tongeland, 15 Ariz. App. 237, 488 P.2d 51 (1971). If a difference of opinion as to the method of computation does not justify judicial intervention, then clearly a difference in result arrived at by use of a different method cannot alone justify intervention. The burden of proof to establish error in the State's valuation is not satisfied by pointing to a finding of fact that the trial judge simply preferred one witness over others. Consequently, the difference in results alone does not justify judicial intervention. However, in order that there be no misconception as to our views of Cyprus-Pima's case, we think an explanation of why its experts' valuations are unsound and do not therefor reflect the requirements of the Arizona Statute § 42-201(4) is appropriate.
By statute, A.R.S. § 42-124, the State Department of Revenue is charged with the duty of valuing mines within the State on or before the first Monday in June of each year. Accordingly, the Department of Revenue valued the Cyprus-Pima Mine for the year 1975 early in that year. All of the expert witnesses who testified in the Superior Court capitalized income. They attempted to arrive at the market value of Cyprus-Pima for 1975 by projecting costs forward from the year 1974 through the estimated life of the mine, the year 1986, and subtracting these costs from anticipated projected revenues for the same period, thereby obtaining a cash flow for each of the remaining years of the life of the mine. The cash flow was then discounted to present value to obtain full cash value or market value.
While the testimony of the witness for Cyprus-Pima, Alfred Petrick, Jr., was not accepted by the court, nevertheless we have examined it and summarily dismissed it with the following brief comments. In arriving at a range of future prices for copper, Petrick used only the past history of domestic copper prices. The evidence is undisputed that Cyprus-Pima sold a substantial part (assertedly 60%) of its production on the international market. The price on the international market (London Exchange) ranged at times up to nearly twice that of the domestic market. Petrick's valuation is therefore based on wholly fictitious values which Cyprus-Pima had received in the past for the price of copper. By this means, future cash flows derived therefrom were unrealistically reduced or lessened.
Fredrick C. Kruger's valuation, which the trial court found was "more persuasive," is so fraught with infirmities as to be totally useless as a means by which a lawful valuation can be made. Kruger used the same basic method as all the expert witnesses in that he projected a future cash flow for each of the remaining years of the life of the mine which he then discounted to present value. In arriving at future cash flows he attempted to arrive at future costs of production and future receipts from the sale of metals. Unlike the witness Petrick, Kruger took into account the fact that the copper produced by the Cyprus-Pima Mine was sold on both the domestic and foreign markets and that the foreign market was on the whole substantially higher than the domestic market. He examined the history of both markets from 1963 through 1974 and summarized the result in the form of a graph, page 13 of Appellee's Exhibit 23 (see Appendix 1).[3] Concerning this exhibit, Kruger testified on direct examination:
"I think it might be of interest to go now to Page 13. Page 13 is entitled, `Price Per Pound of Copper in 1975 Dollars.' *116 It is plotted from 1963 to 1975. And the lower line indicated here is the actual average quote for the year for domestic copper. This upper line is the average quote for each year for foreign copper. And I have calculated the trend line, and that trend line averages domestic and foreign is this line that comes out here."
The line Kruger calculated as a trend line is the broken line commencing at the year 1979 and running through the year 1985 to the end of the life of the mine. He then repeated on cross-examination:
"The way I arrived at this curve was to plot the domestic and foreign copper prices for the period 1973  1963 to 1975. Then I calculated a trend line, which is this line, here."
He testified concerning that part of the broken line shown on the exhibit as commencing in the year 1975 and running through 1978:
"However, I must take cognizance of the fact that at the time of this valuation, in 1975, the average price of copper was indeed way down at this point, here. Then following the concensus of the marketplace, the futures, I projected the price out here. But in arriving back at what I call the average trend, I have followed this period, here. So I am predicting that we will get back to this average trend sometime in the late '70's.
* * * * * *
But I have to face the fact that as of the late months in 1975 the price was way down here, and to ignore the fact that costs were up and prices were down would not be a smart valuation. So that is why, using the evidence from the futures, using the evidence from my own evaluation of the market, I projected this horizontally for something like two years. But I felt that we are going to get back to this trend line eventually. And what I have done is taken this periodicity swing and come back to my trend line at this point, here."
Kruger's testimony is, therefore, to the effect that he took the prices of domestic copper and foreign copper from 1963 to 1975 and averaged the two to obtain the price which Cyprus-Pima received for the copper it produced and from that average established a trend. He did not use the trend for the years 1975 through 1978, but commencing in 1979 he projected the trend forward in the form of a line on the graph to the end of the life of the mine. Kruger made it clear that he departed from his trend line for four years, 1975 through 1978, because he had to "face the fact" that in 1975 the price of copper was "way down."[4]
On cross-examination, Kruger explained that the trend line which he adopted and projected forward was an average of the domestic and foreign prices of copper through the years 1963-1974. He conceded that there is no line drawn on the exhibit indicating the average. He testified that if he had placed the average on the graph, this would be the line from which he derived his trend line. Neither did Kruger place the trend line for the years 1963-1978 on the exhibit which he says he established by using the average prices of copper, foreign and domestic.[5] He said that the trend line which he projected from 1979 to the termination of mining activities was a "least squares projection" of what would be the third line if it were on the exhibit. Kruger, when asked to explain what the *117 "least squares" method is, answered: "I can't explain it to you."[6] Kruger never explained his calculations or how he derived his trend line for the price of copper.
But irrespective of the inability of the Superior Court or an appellate court to verify the accuracy of Kruger's trend line, his graph and testimony clearly establish that he departed from the trend by using for future cash flow as the price for copper for 1975 its actual price for the month of October, 1975, his estimate of the price of copper for the year 1976, and an extrapolation for the years 1977 and 1978. Kruger therefore did not trend the average price of copper into the future. Rather, he took the price of October, 1975 and the anticipated low prices for 1976 through 1978 to establish cash flow. But he did not incorporate prices which might rise above the trend line after the year 1976[7]which would cause a rise in the cash flow through subsequent years to 1986.[8]
By using the actual price of copper for the month of October, 1975 for the year 1975 and its estimated price for the years 1976, 1977, and 1978, Kruger arrived at Cyprus-Pima's net income for those years. He then discounted this cash flow as shown in Appendix 2, which is a part of Appellee's Exhibit 23. However, if the trend line as placed by Kruger on his graph is projected backward to the year 1963  shown by the wavy line in Appendix 1  the full cash value of Cyprus-Pima comes to $77,756,000 instead of $39,682,000. See Appendix 3. It is to be emphasized that the only difference between Appendix 2 and Appendix 3 is that the cash flow was calculated in Appendix 3 on the basis of Dr. Kruger's own trend line rather than on the suppositious low prices for copper during the years 1975 through 1978.
The State's witness Ernest K. Lehmann testified to the obvious in response to this question:
"Q. * * * if in 1976, again, this mine had, for example, zero cash flow instead of $24 million, the effect on your valuation, because of the discount factor applying at a higher percentage to those figures, would reduce your valuation to something like $55 million. Is that correct?
A. Again, if you change the assumptions of the valuation, yes, it would. But there are corollary assumptions since you are going on an averaging basis that there will be years where these revenues will be exceeded and there will be years when the revenues will fall short."
The foregoing alone is dispositive of this case, but Kruger made even a more serious error completely invalidating his final evaluation. Kruger inflated the cost of producing *118 copper from the Cyprus-Pima Mine at 3.48% per year, but he did not inflate the price of copper. He was asked these questions on cross-examination and gave these answers:
"Q. * * * And then you indicated that you escalated those costs at 3.48% per year on the basis of an index with which I am not familiar. Would you explain it to me, please? Implicit price deflators.
A. If you go back to pre-1900, the wholesale price index was used. Then the consumer price index was used. About 1958, because we were changing from a materials economy to a service economy, the implicit price deflator was a new series put out by the Department of Labor. And that is the series that I have used.
Q. And apparently this index shows a figure of 3.48% per year for some year. What year was it?
A. For the period of 1963-1975. The last line."
Kruger testified that he used the historic trend to obtain the future price of copper for the years 1979 through 1986. The historic trend showed that the price of copper in relationship to a constant valued dollar was rising at the rate of 1.5¢ per pound per year. But he did not correspondingly inflate the price of copper. By failing to consider that the price of copper must eventually inflate, the results derived through comparing the price received for copper with the cost of its production when projected forward to the future years results in an unrealistically low cash flow (net income) for the Cyprus-Pima Mine.
The State in rebuttal testimony asked its witness Ernest K. Lehmann, consulting geologist, these questions, to which he gave these answers:
"Q. * * *
At my request did you plot on a copy of Page 13 of Dr. Kruger's report a line which would indicate what would happen to the price of copper if it was inflated in the same way as the costs?
A. Yes, sir, I did.
Q. And do those two dotted lines drawn on that Exhibit reflect the results of your computations?
A. Yes, sir. The dot-dash line, which is the middle line, reflects an inflation of the price  the dot-dash line reflects the inflation of the price by the 3.48% per year of his base price. That is 83  well, if you project his line back to 1975, you start out with 77.5 cents per pound, and the middle line reflects purely inflating that by the inflation index he used. The upper line represents the combination of inflation plus his 1 1/2 cents per pound increase in real price per year. So the upper line really is the inflation of his line.
* * * * * *
Q. Now, Mr. Lehmann, I want to avoid confusion about terminology here; whether we are talking about increasing price or whether we are talking about inflating price. Now, it is true, is it not, that Dr. Kruger predicted increased prices? Is that correct?
A. This is the way I understand the graph that is in front of me. He has taken the period 19  is it 1963 to 1975, foreign and domestic copper prices, and brought them up to constant 1975 dollars. And then he has calculated a trend line predicting a price from 1979 on, the smooth part of the curve, there, which increases in real dollars, 1975 dollars, at the rate of 1 1/2 cents per pound of copper per year.
Q. But which does not reflect future inflationary effect on those dollars?
A. That's right."
It is true that Kruger's projected trend line of copper prices is upward, but merely indicating an increase expressed in terms of constant value dollars on a graph is not recognizing inflation. It is a recognition that based on past history the real value of copper has been increasing in comparison with the average of all other goods and services. Kruger's projection of costs has the inflated factor of 3.48% per year compounded annually to the end of the life of *119 the mine. Such is unequivocally established by this testimony of Kruger:
"Q. That's right. So that in projecting costs of producing this copper, you took into account inflation, whereas in projecting the prices of copper, you took inflation out. Is that right?
A. I used the historic background, yes, sir.
Q. And then the answer to my question is yes.
A. Yes."
The principle is settled that there must be a finding by the trial court supported by competent evidence that the valuation fixed by the Department of Revenue or the Board of Tax Appeals was excessive. Mohave County v. Duval Corp., supra; Graham County v. Graham County Electric Coop., 109 Ariz. 468, 512 P.2d 11 (1973); Navajo County v. Four Corners Pipe Line, supra. The approach which the witness Kruger used to determine market value, while ostensibly that of capitalization of income, in departing from the projected trend price of copper for the years 1975 through 1978 and failing to adjust for inflation compels the conclusion that appellee did not establish by competent evidence the mine's full cash value different from that fixed by the Board of Tax Appeals.
Accordingly, the judgment of the Superior Court is ordered reversed. The determination of the Board of Tax Appeals fixing the full cash value of 60.86% of the Cyprus-Pima Mine for the year 1975 at $67,300,000 is affirmed for the reason that appellee failed to sustain its burden of proof in the Superior Court.
The judgment of the Superior Court is reversed and the valuation as fixed by the Board of Tax Appeals is affirmed.
CAMERON, C.J., HAYS and HOLOHAN, JJ., and HENRY S. STEVENS, Court of Appeals Judge, Retired, concur.
GORDON, J., did not participate in the determination of this matter. Hon. HENRY S. STEVENS, Court of Appeals Judge, Retired, was called to sit in his stead.


*120 APPENDIX



*121 APPENDIX 2


                                           PRESENT VALUE
                       CASH FLOW          DISCOUNTED @ 18%
1975                 $ 2,459,000           $ 2,084,000
   6                     442,000               317,000
   7                   4,515,000             2,748,000
   8                  14,609,000             7,535,000
   9                  26,709,000            11,675,000
1980                  16,742,000             6,202,000
   1                  33,839,000            10,623,000
   2                  31,776,000             8,454,000
   3                  29,919,000             6,745,000
   4                  26,421,000             5,048,000
   5                  11,340,000             1,884,000
   6                   1,636,000               224,000
Ore Reserve Mined Out                            -
Total                                       63,539,000
Percent on Federal Land                          .6086
                                            38,670,000
Salvage                8,700,000             1,012,000
Full Cash Value                            $39,682,000


APPENDIX 3


                                           PRESENT VALUE
                       CASH FLOW          DISCOUNTED AT 18%
1975                 $28,347,000           $24,023,000
   6                  28,463,000            20,442,000
   7                  27,817,000            16,930,000
   8                  26,946,000            13,898,000
   9                  26,709,000            11,675,000
1980                  16,742,000             6,202,000
   1                  33,839,000            10,623,000
   2                  31,776,000             8,454,000
   3                  29,919,000             6,745,000
   4                  26,421,000             5,048,000
   5                  11,340,000             1,836,000[*]
   6                   1,636,000               224,000
Ore Reserve Mined Out                            -
Total                                      126,100,000
Percent on Federal Land                          .6086
                                            76,744,000
Salvage                8,700,000             1,012,000
Full Cash Value                             77,756,000

NOTES
[1]  39.14% of the mine is on State lease land which was not taxed by the Arizona Department of Revenue.
[2]  A.R.S. § 42-201(4) provides:

"`Full cash value' for property tax purposes is synonymous with market value which means that estimate of value that is derived annually by the use of standard appraisal methods and techniques."
[3]  Appendix 1 is page 13 of Cyprus-Pima's Exhibit 23, except that the dotted and dot-dash lines have been superimposed by appellants to form a part of their Exhibit 40, and the wavy line has been placed upon the exhibit by this Court for purposes of demonstrating the extension of Kruger's trend line. The explanations on Appendix 1 are provided by this Court.
[4]  The date of Kruger's testimony at the trial in the Superior Court was April 27, 1976. His exhibit 13 was dated November 29, 1975. He used hindsight in fixing the price of copper for the year 1975 because he used the actual price of copper for the month of October, 1975 rather than his trend line of the average of prices projected forward into the future from the year 1974. Neither does he calculate the effect of 1975 prices on the trend line and thereby construct and project forward a new line with which to average the price of copper in the future.
[5]  Since Kruger's graph does not show the basic data or the calculations he used to arrive at the average between domestic and foreign prices or the computation by which he derived the trend line, it is impossible to verify the accuracy of Kruger's graph or testimony in this important respect.
[6]  M. Blair, Elementary Statistics, 243 (1949), defines least squares in this manner:

"By `least squares' is meant a regression line which is drawn through the paired items of the data so that the vertical distances between the points and the regression line when squared and summed make the smallest total possible. It is a line which on the average comes nearest to all the points or items of data. There is but one possible location for such a line." (Emphasis added.)
For a further explanation and one of the formulas by which the "least squares" method is derived, see B.F. Goodrich Co. v. Department of Transportation, 541 F.2d 1178, 1201 (6th Cir.1976).
[7]  The trend line was derived from the average of foreign and domestic prices.
[8]  How Kruger derived the future price for copper which he used to determine cash flow is important because Cyprus-Pima argues in its brief that Kruger inflated the price of copper more than he inflated costs. Its argument is that from 1975 to 1980 "he inflated the price $.239, while he only inflated the costs by $.092." Kruger, by establishing a trend line for the average price of copper from 1963 to 1975, established a basis for anticipating the price of copper which the company would receive in the future. However, instead of using the trend line which presumably his own calculations indicated as appropriate, Kruger substituted arbitrary values which were well below the values on his trend line for the years 1975-1978. For 1975 and 1976 he kept his projection nearly level. Then in order to return to his trend line in 1979, he had to necessarily increase the price for the years 1977 and 1978. The result was that between 1975 and 1980 Kruger did increase price more than cost, but the increase was due to the necessity to compensate for his departure from his trend line beginning in 1975.
[*]  Kruger's figures mistakenly indicate the present value to be $1,884,000. See Appendix 2 for the year 1985.
