Opinion

Both the taxpayer, Chase Brass & Copper Co., Inc. (hereafter Chase) and the state Franchise Tax Board (hereafter Board) appeal from a 1975 judgment in the total amount of $57,578.77 for the recovery of corporate franchise taxes, plus interest,, for the years 1954, 1955 and 1956. The 1975 judgment was entered after retrial and recomputation pursuant to the limited remand of this court (Div. Four) in Chase Brass & Copper Co. v. Franchise Tax Bd., 10 Cal.App.3d 496 [95 Cal.Rptr. 805] (hereafter Chase I). We have concluded that: 1) the court below acted within the scope of the remand; 2) as to the Board, the doctrine of the law of the case was properly applied as to the “other metals” and prevents redetermination of that issue here; 3) the Board did not abuse its discretion in using a three-factor formula of sales, property and payroll to determine the allocation of Chase’s income to California and in using cost rather than fair market value for the property factor; and 4) the method of recomputation used by the Board was not arbitrary or erroneous, and was fairly calculated to assign to California that portion of the net income of the unitary business reasonably attributable to the business done in this state.

In view of the posture of this appeal, we first restate the pertinent facts and issues determined in Chase I. On that appeal, as in the instant one, the facts were stipulated; accordingly, only questions of law were determined. Chase, a Connecticut corporation, is a wholly owned subsidiary of Kennecott Copper Corporation (hereafter Kennecott), the nation’s largest producer of copper, a New York corporation. Kennecott does no business in California; it mines, smelts and refines copper, gold, silver and molybdenite and other metals. The copper and other metals are mined in Utah, Nevada, Arizona and New Mexico. Metals other than copper are sold in operations completely unrelated to Chase. Copper is not fabricated by Kennecott, but is sold through a subsidiary of Kennecott, Kennecott Sales Corporation (hereafter Kennecott Sales). Chase I also involved the question of whether two other out-of-state Kennecott subsidiary corporations, Braden Copper Company (hereafter Braden) and Bear Creek Mining Company (hereafter Bear Creek), were part of the unitary business, as well as a goods-in-transit issue settled by the parties after Montgomery Ward & Co. v. Franchise Tax Bd., 6 Cal.App.3d 149 [ 85 Cal.Rptr. 890 ],

Kennecott Wire and Cable Co. (hereafter Kennecott Wire), a Rhode Island corporation owned by Kennecott, manufactures copper rod, wire and cable for transmission of electricity. Kennecott Wire uses refined primary copper, all of which it buys from Kennecott through Kennecott Sales; Kennecott Wire’s sales operation in California is largely through Chase. Kennecott Wire did not do business in California in 1954, 1955 and 1956.

Chase, like Kennecott Wire, is a manufacturer. Chase’s products are brass (made from copper and zinc), bronze (copper and alloys, mostly tin), and copper rod, sheet, wire and tube. The manufacture is done entirely outside California. Chase buys 80-84 percent of its needed copper supply from Kennecott Sales, derived from Kennecott and Braden. In California, Chase warehouses and sells its products and those of Kennecott Wire.

The issues to be determined under the California Franchise Tax Law were summarized in Chase I, as follows, at pages 501 and 502: “When a corporation engages in multistate business, including business in California, and the business is unitary, there must be an allocation of income by formula. Separate accounting is not allowable, although it is usable for a corporation which, by operating here and elsewhere, conducts a nonunitary business. In the case of Chase itself, it was always recognized by the company that its own business is unitary, wherefore its own computation of the franchise tax was done according to formula. But the Board contends that the geographic unitary character of Chase is not all that is to be considered; there must also be taken into account the whole intercorporate parentage and affiliation of the Kennecott family. Mainly, it is the vertical aspect which is put before us: the relationship of Chase to Kennecott Sales, to Braden and to Kennecott. Secondarily, there is to be considered the horizontal relationship of Chase to Kennecott Wire.

“Intercorporate unitary character of business, in which the activities of the parent are considered, under an appropriate factual situation, is a valid concept for taxing purposes. (Edison Cal. Stores, Inc. v. McColgan, 30 Cal.2d 472 [ 183 P.2d 16 ].) This holding of the Edison Stores case was but a logical sequence of the holding in Butler Bros. v. McColgan, 17 Cal.2d 664 [ 111 P.2d 334 ], in which a single company had operated through wholly controlled branches. In both cases, there were strong and embracing central controls. The general test which we are to apply is this: ‘If the operation of the portion of the business done within the state is dependent upon or contributes to the operation of the business without the state, the operations are unitary.’ (Edison Cal. Stores v. McColgan, supra, at p. 481; Superior Oil Co. v. Franchise Tax Board, 60 Cal.2d 406, 412 . . ..)” (Italics added.)

After applying the three particulars of the test, Justice Devine in Chase I, at page 506, disagreed with a portion of the lower court’s holding, and held that the business of Kennecott, Kennecott Sales, Kennecott Wire and Chase was unitary and, therefore, subject to an allocation of income by formula. This resulted in an assessment of Chase’s corporate franchise tax at a much higher figure as a result of the application of the “unitary business” theory. At the same time, Justice Devine agreed with two of the parts of the lower court’s holding, namely, that: 1) Chase’s business was not unitary with two other foreign Kennecott subsidiary corporations, Braden and Bear Creek; and 2) “Kennecott’s sales of gold, silver and molybdenite metals, which are not bought by Chase or Kennecott Wire, are not part of the unitary business.” (Chase I, p. 506.)

In addition, as the Board conceded that there was an error in the application of the property factor as the result of the intervening decision of McDonnell Douglas Corp. v. Franchise Tax Bd., 69 Cal.2d 506 [ 72 Cal.Rptr. 465 , 446 P.2d 313 ], Justice Devine noted at page 506 that “the case must be remanded in any event. Our decision requires further revisions of the formula.” The judgment was reversed with directions to proceed in accordance with the Chase I opinion. On denial of the petition for rehearing, this court added the further rulings and explanations, set forth below, so far as pertinent, at pages 506 and 507. Subsequently, the state Supreme Court denied Chase’s petition for hearing (June 24, 1970) and the U.S. Supreme Court dismissed Chase’s petition for lack of jurisdiction ( 400 U.S. 961 [ 27 L.Ed.2d 381 , 91 S.Ct. 365 ]). In both of these further review proceedings, the Board did not challenge the portion of the Chase I judgment holding that Kennecott’s sales of the metals other than copper were not a part of the unitary business.

Preliminarily, we turn to the issues pertaining to the scope of review on this appeal. At the retrial, the court, on the basis of the law of the case, prohibited the introduction of new evidence as to the net income from the metals other than copper to be used in recomputing the unitary net income; the court used the figures contained in finding 2(h) of the Chase I trial court decision, which had been challenged on the Chase I appeal. However, in its first conclusion of law, the court after the retrial stated that the use of these figures for “the net income from the sales of metals other than copper is erroneous and produces the ludicrous result that the depletion allowances and other expenses attributable to metals other than copper are allowed as expenses of the copper business, thus understating the amount of unitary net income of the copper business. This Court would like to remedy this error but feels that it does not have the authority to do so within the scope of the remand.”

On this appeal, the Board first maintains that the lower court’s limited interpretation of the scope of the remand on the retrial constituted reversible error. The Board argues that a finding of fact, as distinct from a conclusion of law, cannot be the basis for the application of the doctrine of the law of the case and, in any event, the rule is only a procedural one that does not go to the power of the court and should not be adhered to where its application will result in an unjust decision (People v. Scott, 16 Cal.3d 242, 246 [ 128 Cal.Rptr. 39 , 546 P.2d 327 ], reiterating People v. Shuey, 13 Cal.3d 835, 845 [ 120 Cal.Rptr. 83 , 533 P.2d 211 ]).

We, however, agree with Chase’s contention that in the instant case, the determination that Kennecott’s “other metals” business was not a part of the unitary business, was one of law. As clearly indicated in Chase I, at page 502, the facts were stipulated or uncontroverted and the only issues before the court were questions of law. Nor do we think that under the particular circumstances of this case there was demonstrated such a “manifest misapplication of existing principles resulting in substantial injustice” (People v. Shuey, supra, p. 846 ) as to permit us to disregard the legal determination made on the “other metals” issue in Chase I.

In any event, as indicated above, the Board did not challenge this portion of the ruling, including the use of the 2(h) finding on the appeal of Chase I or during the further review of Chase I. Thus, as to the Board, the determination excluding the net income from the other metals is the law of the case (Gore v. Bingaman, 20 Cal.2d 118, 122-124 [ 124 P.2d 17 ]; Pillsbury v. Superior Court, 8 Cal.2d 469, 471-472 [ 66 P.2d 149 ]), and the Board is precluded from raising the matter here as to the three tax years in issue. Even assuming an error, as did the court below, the other metals issue was tried and resolved on the basis of uncontroverted evidence and determined in the first appeal; accordingly, that portion of the Chase I judgment is binding and conclusive. We see no fundamental error or injustice that requires a reexamination of the issue reached on the first appeal (Gore v. Bingaman, supra, p. 123 ). We merely hold here that in our view, the instant case is not a proper one for the application of any of the exceptions to the doctrine of the law of the case.

Chase, in turn, attempts to relitigate the portion of the Chase I judgment determining that its income was unitary with Kennecott and Kennecott Sales. For this contention, Chase relies on Kennecott Copper Corp. v. State Tax Com’n., 27 Utah 2d 119 [ 493 P.2d 632 ], appeal dismissed 409 U.S. 973 [ 34 L.Ed.2d 237 , 93 S.Ct. 323 ], decided by the Supreme Court of Utah after Chase Í. We recognize that an intervening or contemporaneous change in the law or the establishment of a new precedent by controlling authority is one of the recognized exceptions to the rule of the law of the case (Ryan v. Mike-Ron Corp., 259 Cal.App.2d 91, 97 [ 66 Cal.Rptr. 224 ]). However, the Utah decision is not controlling as to this court; also, it is based on the application of separate accounting principles to the unitary business, which are contrary to the law of this state, as set forth in Superior Oil Co. v. Franchise Tax Bd., 60 Cal.2d 406, 416 [ 34 Cal.Rptr. 545 , 386 P.2d 33 ], and Honolulu Oil Corp. v. Franchise Tax Bd., 60 Cal.2d 417, 425 [ 34 Cal.Rptr. 552 , 386 P.2d 40 ].

Chase’s reliance on intervening decisions of the State Board of Equalization is equally inapposite. Nor is there any merit to Chase’s additional contention that the unitaiy income determination of Chase I is not the law of the case before us because of Chase’s federal constitutional objections to the validity of the allocation formula devised on remand. People v. Scott, 16 Cal.3d 242 [ 128 Cal.Rptr. 39 , 546 P.2d 327 ], and People v. Shuey, 13 Cal.3d 835 [ 120 Cal.Rptr. 83 , 533 P.2d 211 ], clearly indicate that the presence of federal constitutional questions does not eliminate the rule of the law of the case. As the California Supreme Court denied Chase’s petition for a hearing, the unitary business determination of Chase I is the law of the case on this appeal.

We turn, therefore, to the main issues presented on this appeal pertaining to the Board’s use of: 1) the three-factor formula,' 2) Chase’s book value for the property factor, and 3) the method of recomputation of Chase’s tax liability. We note that as to each of these matters, the court below, after the remand, concluded that the Board’s action was fair and consistent with due process and Revenue and Taxation Code section 25101.

At the time of the tax years here in issue, former Revenue and Taxation Code section 25101 provided, so far as pertinent: “When the income of a taxpayer subject to the tax imposed under this part is derived from or attributable to sources both within and without the State, the tax shall be measured by the net income derived from or attributable to sources within this State. Such income shall be determined by an allocation upon the basis of sales, purchases, expenses of manufacture, pay roll, value and situs of tangible property or by reference to any of these or other factors or by such other method of allocation as is fairly calculated to determine the net income derived from or attributable to sources within this State; provided, however, that any such factors or other method of allocation shall take into account as income derived from or attributable to sources without the State, income derived from or attributable to transportation by sea or air without the State, whether or not such transportation is located in or subject to the jurisdiction of any other state, the United States or any foreign country.” (Italics supplied.)

Pursuant to the statute, the Board applied the traditional three-factor property-payroll-sales formula, computed as described in the footnote below. (See Wahrhaftig, Allocation Factors in Use in California, 12 Hastings L.J., 65 , 73-76.)

Chase argues that since the statute permitted the use of other additional factors, the Board should have used a fourth “expenses of manufacture” factor. However, the Board’s discretion to use the three-factor formula has been upheld by an unbroken series of California decisions. In Edison California Stores v. McColgan, 30 Cal.2d 472 [ 183 P.2d 16 ], our Supreme Court declared (at p. 479) that the overall fairness of the three-factor property, payroll and sales formula was settled. John Deere Plow Co. v. Franchise Tax Bd., 38 Cal.2d 214, 222 [ 238 P.2d 569 ], appeal dismissed 343 U.S. 939 [ 96 L.Ed. 1345 , 72 S.Ct. 1036 ], held the same for the vertically integrated manufacturing and selling business there involved. In El Dorado Oil Works v. McColgan, 34 Cal.2d 731 [ 215 P.2d 4 ], appeal dismissed 340 U.S. 801 [ 95 L.Ed. 589 , 71 S.Ct. 52 ], the taxpayer argued that a five-factor formula was necessary. In rejecting this contention, our Supreme Court construed the predecessor of former Revenue and Taxation Code section 25101, and said at page 737: “On the contrary, the broad language of the section indicates that the factors therein designated are suggestive, but not mandatory or exclusive, and that the commissioner is empowered in his discretion to choose such tax base for his formula allocation as will cariy out the act’s purpose to achieve a proper apportionment of business done within and without the state, and at the same time avoid double taxation.” (Italics added.)

In McDonnell Douglas Corp. v. Franchise Tax Bd., 69 Cal.2d 506 [ 72 Cal.Rptr. 465 , 446 P.2d 313 ], our Supreme Court emphasized, at page 515, that it was not empowered to select the factors. More recently, the applicable rules were summarized by this court (Div. One) in Montgomery Ward & Co. v. Franchise Tax Bd., 6 Cal.App.3d 149, at page 155 [ 85 Cal.Rptr. 890 ], as follows: “ ‘Discretion as to the factors to be used was placed in the commissioner and his successor, the Franchise Tax Board. As stated in RKO Teleradio Pictures, Inc. v. Franchise Tax Board, 246 Cal.App.2d 812 , at page 819 . ..: “The Franchise Tax Board is given discretion in the selection of [the] factors to be utilized in a tax formula (El Dorado Oil Works v. McColgan [supra] 34 Cal.2d 731 , 736 . . .) and where, as here, the taxpayer contends that the formula is arbitrary and reaches an unreasonable result, the burden is on the taxpayer to establish such facts by clear and convincing evidence.” (see Butler Bros. v. McColgan, supra, 315 U.S. 501, 507 [ 86 L.Ed. 991, 996 ], . .)’ ( 69 Cal.2d at p. 512 , fn. omitted.)” In Gen. Motors v. District of Columbia, 380 U.S. 553 , at page 559 [ 14 L.Ed.2d 68 , at page 72, 85 S.Ct. 1156 ], the United States Supreme Court approved the use of the three-factor formula; by the great majority of states.

Chase here has not met its burden of establishing by clear and convincing evidence that the three-factor formula used is arbitrary and reaches an unreasonable result. It merely argues that the formula is intrinsically unfair. As our Supreme Court noted in El Dorado Oil Works v. McColgan, 34 Cal.2d 731 , at page 739 [ 215 P.2d 4 ]: “. . . it necessarily must be concluded that defendant’s application of the three-factor formula as a preferred general practice is not open to objection as an unauthorized exercise of power so long as it produces the desired proportionate result directed by the statute and at the same time avoids subjecting the taxpayer to double taxation.”

Chase’s additional contention that by the use of the .three-factor formula more income has been allocated to California than the California portion of the unitary business could possibly earn, is equally without merit. This contention is based on treating Chase as a separate and independent entity with a separate accounting system. As indicated by the quotation from John Deere Plow Co. v. Franchise Tax Bd., 38 Cal.2d 214, 223 [ 238 P.2d 569 ], quoted below at pages 472 and 473, this argument disregards the basic concept of a unitary income—namely, that the unitary income is the result of the function of the entire unitary business to which each element contributes. As stated in Chase I at page 507, separate accounting is not permitted for the unitary business of the corporations, and the contention therefor has been repeatedly rejected (John Deere, supra, p. 229; Edison California Stores, Inc. v. McColgan, 30 Cal.2d 472 , at pp. 479 and 482 [ 183 P.2d 16 ], citing Butler Brothers v. McColgan, 17 Cal.2d 664 [ 111 P.2d 334 ], and Household Finance Corp. v. Franchise Tax Board, 230 Cal.App.2d 926, 929 [ 41 Cal.Rptr. 565 ]).

The United States Supreme Court in affirming the unitary assessment against Butler Brothers , said at 315 U.S. pages 507-508 [86 L.Ed. page 996]: “It is true that appellant’s separate accounting system for its San Francisco branch attributed no net income to California. But we need not impeach the integrity of that accounting system to say that it does not prove appellant’s assertion that extraterritorial values are being taxed. Accounting practices for income statements may vary considerably according to the problem at hand. Sanders, Hatfield & Moore, A Statement of Accounting Principles (1938), p. 26. A particular accounting system, though useful or necessary as a business aid, may not fit the different requirements when a State seeks to tax values created by business within its borders. Cf. Hamilton, Cost as a Standard for Price, 4 Law & Contemporary Problems 321. That may be due to the fact, as stated by Mr. Justice Brandéis in Underwood Typewriter Co. v. Chamberlain, 254 U.S. 113, 121 , that a State in attempting to place upon a business extending into several States ‘its fair share of the burden of taxation’ is ‘faced with the impossibility of allocating specifically the profits earned by the processes conducted within its borders.’ Furthermore, the particular system used may not reveal the facts basic to the State’s determination. Bass, Ratcliff & Gretton, Ltd. v. Tax Commission, supra, p. 283. In either aspect of the matter, the results of the accounting system employed by appellant do not impeach the validity or propriety of the formula which California has applied here.”

We conclude that the Board properly used the three-factor formula and turn to Chase’s contentions as to the purported unfairness of each factor as computed on remand.

As to the property factor, Chase contends that the Board erred in using actual original cost, rather than fair market value, for its mining properties. The parties agree that during the tax years here in issue, the Board computed the property factor by including all property at the tax basis of the taxpayer. As Kennecott’s mining properties were subject to percentage depletion, their tax basis was zero. While Chase I was pending, the state Supreme Court held in McDonnell Douglas Corp. v. Franchise Tax Bd., 69 Cal.2d 506 [ 72 Cal.Rptr. 465 , 446 P.2d 313 ], that all property used in producing the income subject to apportionment had to be reflected in the property factor. Accordingly, the Board agreed that its original method of computing the property factor was wrong. In making the recomputafion, the Board included the mining properties at original cost, jthe very same value used by Kennecott for its own balance sheet. The parties further stipulated that the term “mining properties” included land and ore bodies in the land but excluded milling and smelting plant and machinery. Chase’s proposed fair market value calculation of the mining properties, however, included the value of the plants and equipment. On this appeal, Chase also argues, contrary to the record, that the book value used by the Board contains no element of cost or other value for the ore bodies.

Chase also argues that the term “value” as used in former Revenue and Taxation Code section 25101 can only be construed as fair market value. However, the term “value” has never been defined by the applicable statutes and is clearly not defined as “fair market value” in the Uniform Division of Income for Tax Purposes Act (Rev. & Tax. Code, §§ 25120-25139), adopted for use in this state for the income years beginning January 1, 1967. (Stats. 1966, ch. 2.)

Revenue and Taxation .Code section 25130 now provides: “Property owned by the taxpayer is valued at its original cost. Property rented by the taxpayer is valued at eight times the net annual rental rate. Net annual rental rate is the annual rental rate paid by the taxpayer less any annual rental rate received by the taxpayer from subrentals.” (Italics added.)

Thus, the statute equates “value” and “cost” rather than value and fair market value. Here, the Board’s inclusion of Chase’s mining properties at cost was a logical and reasonable approach to the three tax years here in issue that predated the present statute and met the “rough approximation” standard articulated as follows in McDonnell Douglas Corp. v. Franchise Tax Bd., supra, at page 511, quoting from El Dorado Oil Works v. McColgan, supra, at page 741: “ ‘No method of allocation can precisely determine the amount of income attributable either to any given geographic area or to any given part of a series of business transactions culminating in the realization of a profit, and “any effort” in that regard “must be more or less arbitrary and fictitious” (Gorham Mfg. Co. v. Travis, 274 F. 975, 978 ) as a matter of practical tax administration. In short, as was recently said by the Supreme Court of the United States in sustaining the validity of a franchise tax assessment, the “practical impossibility of a state’s achieving a perfect apportionment of expansive, complex business activities . . . [makes] ‘rough approximation rather than precision’'. .. sufficient” in the formula allocation of income from a unitary business. (International Harvester Co. v. Evatt, 329 U.S. 416, 422 [ 91 L.Ed. 390, 395 , 67 S.Ct. 444 ].)’ ”

Chase’s determination of fair market value based on Hoskold’s Formula used by its witness, is necessarily also only a rough approximation as its own witnesses indicated. The Hoskold Formula used long range estimates into the next century of matters such as amount of production, sales income and costs of production. At the 1966 hearing, Chase’s witness indicated that mines were “rarely actually transferred by buying or selling.” At the 1972 hearing, Chase’s witness Ward indicated that Kennecott’s mining properties were chiefly acquired by tax free stock exchanges over a period of many years, and were carried over to Kennecott’s books at the same cost as they had appeared on the books of the prior owner. The witness opined that as a result of this method of acquisition, the market value could not be determined. The same witness also indicated that the acquisition cost of a mine had no relationship to its profitability which depended on productivity and that the book value figures had to be adjusted upwards each year as more additional claims around the perimeter of existing mines were acquired to accommodate the inverted cone mining method used.

We conclude that the Board’s adjustment of the value of Chase’s mining properties was in accord with McDonnell Douglas, and not arbitrary or unfair to Chase.

We turn next to Chase’s contentions concerning the payroll and sales factors. The record indicates that the Board computed the payroll factor by the standard method of comparing the salaries paid to California employees with the salaries paid to all employees of the unitary business.

Chase contends that this method was arbitrary and unfair as it did not take into account the fact that Kennecott’s mining employees are more productive than Chase’s fabrication ana sales employees. We note that there is no factual evidence in the record to sustain this contention and that Chase’s argument ignores the necessarily subjective determinations that underlie it.

In any event, where a unitary business operates across state lines, the profitability or productivity of one group of employees as against another, based on separate accounting in each state, is not relevant to the apportionment formula used for unitaiy business. In rejecting a substantially similar contention (namely, that income from the California portion of the business should not be computed by the apportionment formula as the California operations were not as profitable as the out-of-state ones), our Supreme Court said in John Deere Plow Co. v. Franchise Tax Bd., 38 Cal.2d 214 , at pages 223 and 224 [ 238 P.2d 569 ]: “But in so arguing plaintiff fails to take into account the underlying concept of formula apportionment in the allocation of income from a unitary business: that the unitary income is derived from the functioning of the business as a whole, to which the activities in the various states contribute; and that by reason of such interrelated activities in the integrated overall enterprise, the business done within the state is not truly separate and distinct from the business done without the state so as reasonably to permit of a segregation of income under the separate accounting method rather than use of the formula method in assigning to the taxing state its fair share of taxable values. [Citations.] As above stated, here the overall organization of Deere and Company was a manufacturing and selling business having its operations extending into a number of different states and providing an example of a typical unitary business subject to formula allocation as a reasonable method of apportionment for franchise tax purposes. [Citations.] The fact that the taxpayer may show that according to a separate accounting system, the activities in the taxing state were less profitable than those without the state, or even resulted in a loss, does not preclude use of a formula as a method of apportionment of the unitary income.”

Contrary to Chase’s contention, Household Finance Corp. v. Franchise Tax Board, 230 Cal.App.2d 926 [ 41 Cal.Rptr. 565 ], does not support its arguments. In Household Finance at page 930, the court, on the authority of John Deere, supra, rejected the taxpayers’ similar argument that its costs in California were higher than elsewhere because of the higher salaries paid here. Generally, Chase’s contentions overlook the fact that a unitary business is one in which all parts contribute to the total profits in unmeasurable amounts. Thus, if the profits of any portion of the unitary business are separated from the rest, the base is necessarily inaccurate as the profits from any segment cannot be determined with certainty.

As to the sales factor, the record indicates that the Board excluded sales from one member of the unitary group to'another, as no net income is realized as a result of the internal sales. Thus, the sales factor only included sales to outside purchasers. Chase argues that the sales factor as so computed erroneously distorts Kennecott’s sales outside of California. These contentions ignore the fact that while gross sales are used to compute the sales factor, only net income is subject to the franchise tax. Since no net income is produced by the internal sales, it was not required that they be included in the computation. We think the above described methods used by the Board were fairly calculated to assign to California only that portion of the net income reasonably attributable to the business done in this state, and conclude that the Board properly computed the payroll and sales factors.

Finally, we turn to Chase’s argument that on remand, the court below abused its discretion in approving the Board’s use of allegedly erroneous figures in making the required adjustments to the property, payroll and sales factors of the allocation formula to reflect the Chase I holding that the “other metals business” was not a part of the unitary business. We note that as one commentator indicated, Chase I did not explain how this was to be done, “but it would certainly involve methods which are equivalent to formulary apportionment, and which have the same inherent inaccuracy.” (Boren, Separate Accounting In California and Uniformity in Apportioning Corporate Income, 18 UCLA L.Rev. 478, at p. 532.)

The record indicates that in the initial Chase I assessment, the Board, on the basis of its determination that the “other metals” activities were part of the unitary business, included in the respective denominators of the property, payroll and sales factors, the part of Kennecott’s property, payroll and sales attributable to the “other metals” activities. After the remand, the Board first determined the percentage relationship between the sales of other metals and total sales for each year; then it applied this percentage to the payroll and property factors and subtracted the resulting amounts from the total payroll and total property factors to obtain the final denominator for each factor.

Chase objects primarily to the Board’s use of the relative sales value in making these adjustments. Pursuant to this approach, the Board used the sales value of copper and the other metals in order to apportion the plants and payroll in computing these factors. Chase argues that the Board’s method is contrary to the holding of Chase I indicating that the other metals are separate businesses from the unitary copper business and that its by-products accounting method as to the other metals calls for different results. However, as admitted by Chase, all of the other metals came from the same ore as the copper. The other metals are separated from the copper at various stages of the process. Up to the point where the other metals are separated out, the same property and same payroll are involved in the process. Thus, it makes no sense for the purposes of the payroll and property factors to attribute 100 percent of the payroll and property only to the copper business or only to the other metals business. The joint-products approach used by the Board was reasonable and in accord with the holding of Chase I.

Chase also argues that the Board should have apportioned the payroll and property, not on the basis of sales value, but on the basis of the weight of copper and the other metals. This contention, as the Board points out, fails to recognize that the factors chosen for the apportionment formula are based on their income-producing element (Montgomery Ward & Co. v. Franchise Tax Bd., 6 Cal.App.3d 149, 159 [ 85 Cal.Rptr. 890 ]; John Deere Plow Co. v. Franchise Tax Bd., 38 Cal.2d 214, 224 [ 238 P.2d 569 ]). The payroll factor also is to reflect the personal services of individuals in the earning of income (Wahrhaftig, Allocation Factors in Use in California, 12 Hastings L.J. 65 , 73). Here, although Kennecott recovered about 16 pounds of copper per ton of ore, the sales price of the copper was about $.36 per avoirdupois (16 oz.) pound. Although only minute quantities of some of the other metals were recovered per ton, the most valuable of these other metals, silver and gold, were sold to the federal government at the fixed prices of $10.86 and $420 per troy (12 oz.) pound, respectively. The allocation by weight proposed by Kennecott would treat a 16-ounce avoirdupois pound of copper as being equally capable of producing income as a 12-ounce troy pound of gold. For this reason, the Board’s use of sales value rather than weight to apportion the payroll and properties between copper and other metals was reasonable under the circumstances and not in conflict with the holding of Chase I. Chase has not explained how this particular practice has resulted in an unfair determination of its taxable California net income.

In conclusion, we can only reiterate that all authorities recognize there is an inherent inaccuracy in any use of the unitary business allocation formulas. The Board’s methods and calculations here in issue must be viewed within the context of these limitations. In view of the many complex computations and unprecedented recomputations required here after Chase I, we think the trial court properly concluded that the Board’s methods were fair and within its statutory mandate.

Affirmed. Each party to bear its own costs on appeal.

Kane, J., and Rouse, J., concurred.

Petitions for a rehearing were denied July 7, 1977, and the opinion was modified to read as printed above. Petitions of both parties for a hearing by the Supreme Court were denied August 11, 1977, Bird, C. J., did not participate therein.

Although the Board’s notice of appeal is from the entire judgment, the major issues are the trial court’s deletion of income from metals other than copper and the doctrine of the law of the case. Chase’s cross-appeal is also from the entire judgment but is concerned primarily with the factors of the allocation formula and the Board’s method of recomputation. Chase’s initial appeal was dismissed. The judgment allowed the following amount for each tax year in issue: 1954- $ 6,519.41 1955- $ 23,146.83 1956- $ 27,912.53. In the absence of the application of the unitary theory, Chase would have been permitted to recover $231,257.32 (Chase /, p. 499). Although the Chase l opinion specifically referred only to gold, silver and molybdenite, the parties agree that several other metals, selenium and platinum, are also involved. Accordingly, we use the collective term of “other metals.” “1. The formulary taxation procedure is not in itself a simultaneous process of taxing and of disregarding the separate entity of the taxed corporation. (Edison California Stores v. McColgan, 30 Cal.2d 472, 481 [ 183 P.2d 16 ].) “2. We do not regard the case of Norfolk & Western Ry. Co. v. Missouri State Tax Com., 390 U.S. 317 [ 19 L.Ed.2d 1201 , 88 S.Ct. 995 ], to be decisive or even relevant to the case at hand. In the Norfolk case, the railroad was able to show, by actual count of its rolling stock on the lien date, that the number of units within Missouri was substantially less than that which had been assumed by the taxing authorities, and that a certain ‘enhanced value’ theory proposed by the taxing authorities would require a challenge to a total value figure which had been agreed _upon. The case is far removed from the present one, wherein the operations of the corporations are unitary and separate accounting is not permitted. “3. Since the formula must be recomputed, the special issues relating thereto, which our opinion has not resolved, are to be" presented to and tried by the trial court (the subject of the gold, silver and molybdenum operations, however, has been decided by our opinion)." (Italics added.) “In the years in question, Braden had net profit on molybenite [j/c] arid Kennecott had net profit on metals other than copper, principally gold, silver and molybdenite, in the following amounts: 1954 1955 1956 Braden $ 1,786,328.29 $ 2,633,771.88 $ 2,611,516.06 Kennecott 30,321,857.61 32,743,300.57 34,835,182,66 $32,108,185.90 $35,377.072.45 $37,446,698.72 “For purposes of this finding, ‘net profit’ means gross sales price less direct expenses incurred after the particular metal has been separated from the copper. ‘Net profit’ does not take into consideration any indirect expenses, such as overhead, or any direct expenses incurred in the mining, concentrating or smelting of the ore prior to the time the copper bearing material is separated from the material containing these other metals; for internal accounting purposes, Kennecott treats all such direct expenses and indirect expenses as costs of producing copper.’’ In essence, the doctrine provides that when an appellate court has rendered a decision, that rule is to be followed in all subsequent proceedings in the same action [People v. Scott, supra, at p. 246 , citing People v. Shuey, supra, pp. 840-848 ). The record indicates that finding of fact 2(h) was based on Chase’s exhibit that was not controverted by the Board. There was no other evidence before the court on this issue. The Board objected to the introduction of the exhibit but did so solely on grounds of relevancy; this ground, of course, does not go to the truth of the matter. Thus, we do not deal with the Board’s contentions that Revenue and Taxation Code section 24425 requires that some of the common expenses allocable to the “other metals,” including depletion, must be deducted and that new evidence adduced at the retrial indicated that there was, in fact, no separate “other metals” business. Although the Utah court held that Kennecott was unitary with Chase and its other subsidiaries, and thus consistent with Chase /, both Chase and the Board agree that the Utah case was wrongly decided and joined in the appeal to the United States Supreme Court. We take judicial notice of these decisions pursuant to Evidence Code section 453, only for the purpose of disposing of Chase’s argument. The record thus indicates that the Board of Equalization’s first decision in Appeal of Harbison-Walker Refractories Company, California-Tax Reports, 204-294, was rendered several days after Chase I. Thereafter, the Board of Equalization decided to rehear the matter for two reasons: Chase I, and doubts as to whether the facts, had been fully developed by the parties. At the rehearing, new facts supporting a unitary holding were developed and the Board of Equalization, on a consideration of all of the facts, held that the unitary business tests had been satisfied, and cited Butler Brothers v. McColgan, 17 Cal.2d 664 [ 111 P.2d 334 ], affirmed 315 U.S. 501 [ 86 L.Ed. 991 , 62 S.Ct. 701 ], and Edison California Stores v. McColgan, 30 Cal.2d 472 [ 183 P.2d 16 ]. “The percentage of the firm’s total real property and tangible personal property in California is computed; the percentage of the firm’s total payroll of wages, salaries and commissions paid to employees in California is computed; the percentage of the firm’s gross sales, less returns and allowances, in California is computed. The three percentage figures are totaled and the resulting sum is then divided by three. The final figure applied to total business income represents the percentage of the total net business income of a firm which can be allocated'to California.” Chase has never explained how the denominator of the expenses of manufacture factor would be computed as the unitary business did no manufacturing in California. Thus, the numerator of the manufacture formula would be zero and the total of the property, sales and payroll factors would be divided by four, resulting in a lower allocation percentage. Culligan Water Conditioning v. State Bd. of Equalization, 17 Cal.3d 86, 92 [ 130 Cal.Rptr. 321 , 550 P.2d 593 ], cited by Chase, is clearly distinguishable from the instant situation where the courts have long approved and recognized the grant of discretionary power to the taxing body in the selection of the allocation factors. The Chase I stipulation indicates that Kennecott’s mining properties were initially included in the property factor at an amount of $46 million for each of the three tax years here in issue. Contrary to Chase’s argument, McDonnell, supra, did not prescribe the use of fair market value for the property factor. In that case, the Board had followed its practice of including property at the tax basis of the taxpayer; thus, the property owned by the federal government and used by McDonnell Douglas, rent free was not included in the property factor. The court held that since both the owned and nonowned property contributed to the production of income, the federally owned property could not be excluded. Subsequently, the Board recomputed the property factor and included the federally owned property by giving it a hypothetical tax base, i.e., its depreciated net book value to which McDonnell Douglas stipulated. The Board indicated that since inventories and land are not depreciable, their amount was computed at cost. Chase’s machinery and equipment in California were assessed at the same figure as the federal tax basis or net book value, i.e., cost less depreciation. As a result of the recomputation, the mining properties were included in the property factor at more than $106 million and for each of the three years here in issue, an upward adjustment of more than $60 million annually. . As a result of this conclusion, it is not necessary for us to reach the constitutional arguments made by Chase (cf. Montgomery Ward & Co. v. Franchise Tax Bd., 6 Cal.App.3d 149, 158 [ 85 Cal.Rptr. 890 ]). As all of these “other metals” activities occurred outside California, the numerator of each factor as originally computed has no components attributable to “other metals.” This is a general summary of the method used by the Board. The detailed calculations and figures are described in the stipulations of the parties on remand. The figures used in the Board’s revised schedules were derived from the figures and tax returns at the first trial and from Kennecott’s federal tax returns, which were introduced without objection as exhibits B, C and D at the 1972 hearing of the second trial. The Board’s revised schedules were a part of the Board’s exhibit A;.Chase’s objection to only the net income figures in exhibit A was sustained; exhibit A was marked but never admitted into evidence. After the mined ore is concentrated, molybdenite is removed. During the ensuing smelting and refining stages, copper and the other metals are still together. Only in the final refining stage are all the gold, silver and other metals separated from the copper.