Wilkins, C.J.
This is an appeal by the State Tax Commission from a decision of the Appellate Tax Board granting abatements to Sears Roebuck and Company, a corporation of New York, from the Massachusetts corporate excise tax for the fiscal years ending January 31,1956, and January 31, 1957. The appeal is pursuant to G. L. c. 58A, § 13 (as amended through St. 1957, c. 522), which provides that the decision shall be reviewed in accordance with the standards of review set forth in the State Administrative Proce[472]*472dure Act. G. L. c. 30A, § 14 (8). The stenographic report of the proceedings before the board and the exhibits are part of the record on appeal.
The proceedings before the board were under the formal procedure. The taxpayer’s appeals were from the failure of the commission to grant abatements of $36,156.07 and of $20,121.94, respectively, for the fiscal years ending January 31,1956, and January 31,1957. The respective abatements granted by the board were $13,478.77 and $10,246.69, both with interest. The board made findings of fact and a written report and filed an opinion.
The taxpayer, as a foreign corporation qualified to transact business in this Commonwealth, is subject to the excise tax on foreign corporations under G. L. c. 63, § 39, as amended,1 imposed in part upon “the value of its corporate excess employed within the commonwealth.” To ascertain the value of the corporate excess, the form and instructions supplied and approved by the Commissioner of Corporations and Taxation required, for each of the two taxable years, that the taxpayer determine “the fair value of its capital stock” (G. L. c. 63, § 30 [4], as amended)2 on the basis of figures with respect to the net value of its assets minus liabilities and to its average earnings over the preceding five years. To obtain “the fair value of its capital stock,” the average earnings were required to be capitalized at 10%, and were given a weight of 1, the net worth [473]*473was given a weight of 2, and the sum of these figures was divided by 3. The taxpayer’s returns were on the commissioner’s approved forms and followed his instructions. Its figures for net worth and average earnings are not challenged. The additional taxes assessed by the commissioner were due to the use of a new formula for determining the fair value of the capital stock which differed from that prescribed for the taxpayer at the times of filing its returns. Thus the commissioner determined the fair value of the capital stock for each taxable year on the basis of net worth with a weight of 3, average earnings over the preceding five years capitalized at 10% with a weight of 2, and the market value of the stock on the last day of the taxable year with a weight of 1. The overall weight was 6. The total of the three items was divided by 6.
In summary, the taxpayer, in arriving at the fair value of the capital stock, used two factors: (1) the average net income, and (2) the net worth. The commissioner and the tax commission used three factors: (1) the average net earnings, (2) the net worth, and (3) the market value of the shares as determined by the commissioner; and at the same time increased the weight to be given to the first two factors. By the taxpayer’s formula the value of the capital stock as of January 31,1956, was $1,114,110,083, and by the commission’s formula it was $1,351,176,605. As of January 31,1957, the respective figures were $1,220,968,215 and $1,375,920,369.
By the final step in the computation a portion of the fair value of the capital stock was determined to be the “corporate excess employed within the commonwealth” (G. L. c. 63, § 39, as amended) by an allocation ratio not in dispute, and this corporate excess was taxed. “Upon a consideration of all the evidence,” the tax board found figures as to the value of the corporate excess which lay in between those of the taxpayer and the tax commission. While the board considered the market value of the stock a relevant factor, there is no indication what weight it gave to this factor. The varying results reached by the taxpayer, the commis[474]*474sioner and the commission, and the Appellate Tax Board appear in the margin.1
The commission argues that the commissioner’s determination of the value of the capital stock is reasonable and sound and represents its fair value in accordance with statutory requirements. The commission devotes a large part of its brief to the refutation of an argument which the taxpayer does not make in this court, namely, that the commissioner was required to follow the method of valuation set out in his tax form and instruction sheet. The board correctly ruled, in accordance with the commission’s fourth request, that the commissioner was not so required. G. L. c. 63, § 44 (as amended through St. 1955, c. 549, § l),2 and § 45 (as amended through St. 1955, c. 549, § 2).
The board also ruled at the request of the commission that the commissioner may determine the fair value of the capital stock by any method he deems appropriate, so long as his determination represents the fair value; that in determining fair value the commissioner may consider the market price of the stock if the shares are actively traded; that the Legislature left the method of determining fair value to the sound judgment and discretion of the commissioner, “subject only to the obligation to take into consideration every relevant fact” (see Ray Consol. Copper Co. v. United States, 268 U. S. 373, 377); that the burden rests with the taxpayer to show that the commissioner’s determination does not constitute the fair value of its capital stock; and that the burden rests with the taxpayer to show that any alternative value constitutes the fair value of its capital stock. The board denied the first request of the commission that upon the evidence there should be a decision for [475]*475the commission; and the second request that upon the evidence presented the taxpayer was not aggrieved by the refusal of the commission to grant the applications for abatement.
The commission argues that the findings of the board are not supported by substantial evidence, because there is a presumption that the commissioner, when he made the assessment, had before him proof which was sufficient to satisfy a just and fair-minded person that such assessment ought to be made, and before the assessment is disregarded the board should be convinced by additional evidence that the commissioner acted in a manner which was unjust and unwarranted by the facts. This argument overlooks the paramount position of the board under the statutes. If the tax on a return as determined by the commissioner is believed to be excessive, the corporation may apply to the commission for an abatement. “If after a hearing or otherwise the commission finds that the tax is excessive in amount . . . it shall abate it in whole or in part accordingly.” G. L. c. 63, § 51 (as amended through St. 1954, c. 515, § 2; see now St. 1958, c. 503, § 1). Appeals from the decision of the commission in this case were governed by G. L. c. 63, §71 (as amended by St. 1954, c. 515, § 7; see now St. 1958, c. 523, § 3, and St. 1961, c. 277), and by G. L. c. 58A, § 7 (as amended through St. 1953, c. 654, § 25). Section 71 provides, “Any overpayment of tax determined by decision of . . . [the] appellate tax board shall be reimbursed by the commonwealth with interest . .
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Wilkins, C.J.
This is an appeal by the State Tax Commission from a decision of the Appellate Tax Board granting abatements to Sears Roebuck and Company, a corporation of New York, from the Massachusetts corporate excise tax for the fiscal years ending January 31,1956, and January 31, 1957. The appeal is pursuant to G. L. c. 58A, § 13 (as amended through St. 1957, c. 522), which provides that the decision shall be reviewed in accordance with the standards of review set forth in the State Administrative Proce[472]*472dure Act. G. L. c. 30A, § 14 (8). The stenographic report of the proceedings before the board and the exhibits are part of the record on appeal.
The proceedings before the board were under the formal procedure. The taxpayer’s appeals were from the failure of the commission to grant abatements of $36,156.07 and of $20,121.94, respectively, for the fiscal years ending January 31,1956, and January 31,1957. The respective abatements granted by the board were $13,478.77 and $10,246.69, both with interest. The board made findings of fact and a written report and filed an opinion.
The taxpayer, as a foreign corporation qualified to transact business in this Commonwealth, is subject to the excise tax on foreign corporations under G. L. c. 63, § 39, as amended,1 imposed in part upon “the value of its corporate excess employed within the commonwealth.” To ascertain the value of the corporate excess, the form and instructions supplied and approved by the Commissioner of Corporations and Taxation required, for each of the two taxable years, that the taxpayer determine “the fair value of its capital stock” (G. L. c. 63, § 30 [4], as amended)2 on the basis of figures with respect to the net value of its assets minus liabilities and to its average earnings over the preceding five years. To obtain “the fair value of its capital stock,” the average earnings were required to be capitalized at 10%, and were given a weight of 1, the net worth [473]*473was given a weight of 2, and the sum of these figures was divided by 3. The taxpayer’s returns were on the commissioner’s approved forms and followed his instructions. Its figures for net worth and average earnings are not challenged. The additional taxes assessed by the commissioner were due to the use of a new formula for determining the fair value of the capital stock which differed from that prescribed for the taxpayer at the times of filing its returns. Thus the commissioner determined the fair value of the capital stock for each taxable year on the basis of net worth with a weight of 3, average earnings over the preceding five years capitalized at 10% with a weight of 2, and the market value of the stock on the last day of the taxable year with a weight of 1. The overall weight was 6. The total of the three items was divided by 6.
In summary, the taxpayer, in arriving at the fair value of the capital stock, used two factors: (1) the average net income, and (2) the net worth. The commissioner and the tax commission used three factors: (1) the average net earnings, (2) the net worth, and (3) the market value of the shares as determined by the commissioner; and at the same time increased the weight to be given to the first two factors. By the taxpayer’s formula the value of the capital stock as of January 31,1956, was $1,114,110,083, and by the commission’s formula it was $1,351,176,605. As of January 31,1957, the respective figures were $1,220,968,215 and $1,375,920,369.
By the final step in the computation a portion of the fair value of the capital stock was determined to be the “corporate excess employed within the commonwealth” (G. L. c. 63, § 39, as amended) by an allocation ratio not in dispute, and this corporate excess was taxed. “Upon a consideration of all the evidence,” the tax board found figures as to the value of the corporate excess which lay in between those of the taxpayer and the tax commission. While the board considered the market value of the stock a relevant factor, there is no indication what weight it gave to this factor. The varying results reached by the taxpayer, the commis[474]*474sioner and the commission, and the Appellate Tax Board appear in the margin.1
The commission argues that the commissioner’s determination of the value of the capital stock is reasonable and sound and represents its fair value in accordance with statutory requirements. The commission devotes a large part of its brief to the refutation of an argument which the taxpayer does not make in this court, namely, that the commissioner was required to follow the method of valuation set out in his tax form and instruction sheet. The board correctly ruled, in accordance with the commission’s fourth request, that the commissioner was not so required. G. L. c. 63, § 44 (as amended through St. 1955, c. 549, § l),2 and § 45 (as amended through St. 1955, c. 549, § 2).
The board also ruled at the request of the commission that the commissioner may determine the fair value of the capital stock by any method he deems appropriate, so long as his determination represents the fair value; that in determining fair value the commissioner may consider the market price of the stock if the shares are actively traded; that the Legislature left the method of determining fair value to the sound judgment and discretion of the commissioner, “subject only to the obligation to take into consideration every relevant fact” (see Ray Consol. Copper Co. v. United States, 268 U. S. 373, 377); that the burden rests with the taxpayer to show that the commissioner’s determination does not constitute the fair value of its capital stock; and that the burden rests with the taxpayer to show that any alternative value constitutes the fair value of its capital stock. The board denied the first request of the commission that upon the evidence there should be a decision for [475]*475the commission; and the second request that upon the evidence presented the taxpayer was not aggrieved by the refusal of the commission to grant the applications for abatement.
The commission argues that the findings of the board are not supported by substantial evidence, because there is a presumption that the commissioner, when he made the assessment, had before him proof which was sufficient to satisfy a just and fair-minded person that such assessment ought to be made, and before the assessment is disregarded the board should be convinced by additional evidence that the commissioner acted in a manner which was unjust and unwarranted by the facts. This argument overlooks the paramount position of the board under the statutes. If the tax on a return as determined by the commissioner is believed to be excessive, the corporation may apply to the commission for an abatement. “If after a hearing or otherwise the commission finds that the tax is excessive in amount . . . it shall abate it in whole or in part accordingly.” G. L. c. 63, § 51 (as amended through St. 1954, c. 515, § 2; see now St. 1958, c. 503, § 1). Appeals from the decision of the commission in this case were governed by G. L. c. 63, §71 (as amended by St. 1954, c. 515, § 7; see now St. 1958, c. 523, § 3, and St. 1961, c. 277), and by G. L. c. 58A, § 7 (as amended through St. 1953, c. 654, § 25). Section 71 provides, “Any overpayment of tax determined by decision of . . . [the] appellate tax board shall be reimbursed by the commonwealth with interest . . ..” If the commissioner’s determination has been given the prima facie effect contended for by the commission, we should expect to find this stated in one of the statutes. Instead, it is apparent that the appeal to the board is the final step in the administrative process, and it is the decision of the board which it is our duty to review under G. L. c. 58A, § 13, and G. L. c. 30A, § 14 (8).
This is also the effect of our decisions. In Commissioner of Corps. & Taxn. v. J. G. McCrory Co. 280 Mass. 273, 277, it was said that an appeal to the board means a full new [476]*476trial or an entire rehearing upon all matters of fact and questions of law.” See Commissioner of Corps. & Taxn. v. Ford Motor Co. 308 Mass. 558, 570-572; O’Brien v. State Tax Commn. 339 Mass. 56, 59-60. In sustaining an appeal by the commissioner from a board decision in Commissioner of Corps. & Taxn. v. Assessors of Boston, 321 Mass. 90, there was no intimation that the board owed deference to the commissioner’s finding.
We, accordingly, are of opinion that in the state of the evidence the Appellate Tax Board was not obliged to accept the fair value of the capital stock as determined by the commissioner, or the weight accorded to market value by him. In considering whether the board’s own determination was supported by substantial evidence, we recite certain subsidiary findings by the board. During each of the tax years there were approximately 75,000,000 shares outstanding. A very substantial portion was held under a “plan of control” and was not available for trading on the stock market. Approximately 57% of the outstanding stock was available for such trading. The balance of approximately 43% was held by a profit sharing fund, by employees under contract stock agreements, and by investment corporations and trusts. The stock of the fund is in its name and not in the names of the employees, and can be obtained only by withdrawing from the plan. As to contract stock, employees are from time to time given an option to purchase at a price lower than the market value. An employee cannot dispose of contract stock while in the employ of the company. As of January 31, 1956, there were 102,984 stockholders, and as of January 31,1957, there were 126,389. In 1957 about 3,500,000 shares, or approximately 4.4% of the outstanding stock, were traded on the market. Of this, 2.2% was purchased by the profit sharing fund. In 1955 approximately 3.68% of the average number of shares outstanding changed hands, and in 1956 approximately 3.11%. The market quotations were 33 for January 31, 1956, and 27% for January 31, 1957. One of the commission’s experts testified that the values were $24 and $26, [477]*477respectively, and another testified that the prices quoted on the stock exchange reflected the fair value of the stock.
The board had before it all the relevant facts, including the corporate assets, the earnings, the capital stock situations, and the market value. On all these facts it was open to the board to determine what most fairly reflected the value of the capital stock and the value of the corporate excess in accordance with principles and methods consistent with the statutes and with a reasonable uniformity in their application, provided its conclusion was supported by substantial evidence. The board was not required to accept the identical formula for determining the weight to be given market value of the stock which was adopted by the commissioner even if it was reasonable. That it may have been reasonable does not mean it was exclusively so, nor would that circumstance preclude the board’s determination from being reasonable or being supported by substantial evidence.
There was no error in denying the commission’s first and second requests. There was no inconsistency between so ruling and in granting the commission’s other requests.
Decision affirmed.