The board of assessors of Lynn appeals from a decision of the Appellate Tax Board (the-board) granting abatements of 1970 and 1971 real estate taxes to Shop-Lease Co., Inc. (Shop-Lease). The parties stipulated before the board “that for purposes of this hearing only substantially all properties assessed by the Board of Assessors of the City of Lynn during the years . . . 1970 and 1971 were, as a matter of policy, assessed at 30 percent of the fair cash value of such properties.” The premises were leased by Shop-Lease to various tenants for office and retail uses.
The parties in their presentations before the board, and the board in its decision, used a capitalization of net earnings approach to arrive at the fair cash value of the property, and all agreed that the assessed value should be thirty per cent of the fair cash value. The board in its formula for capitalizing net earnings in order to arrive at the fair cash value of the property used a factor for local real estate taxes which assumed that Shop-Lease would have to pay local real estate taxes based on the fair cash value of the premises and not based on thirty per cent of the fair cash value. The sole issue on this appeal is whether the board committed an error of law in its selection of the tax factor to be used in its formula *571for the capitalization of earnings.1
The specific facts underlying this issue can be stated briefly. The premises were assessed for $216,700 in 1970 and $702,000 in 1971. The Lynn tax rate in 1970 was $200 for each thousand dollars of valuation and in 1971 was $207 for each thousand dollars of valuation.
The board determined that the net income from the premises before any allowance for depreciation, return on investment and local real estate taxes was $154,450. The board used “a 10% factor for return on investment and depreciation.” Based on the $200 1970 tax rate (disregarding, as do we in further discussion in this opinion, the slightly higher rate in 1971), the board “allowed a tax factor of 20%.” Although the board acknowledged the assessors’ argument that the factor should be six per cent (30% of 20%), the board rejected that argument without explanation. The board then arrived at a fair cash value in both years of $514,800 by dividing the net income ($154,450) before any allowance for depreciation, return on investment or taxes, by the combined factor for depreciation, return on investment and taxes (.10 + .20 = .30). This fair cash value was reduced by the board, “[ujsing the 30% ratio agreed to by both parties,” producing an assessed value of $154,440. Abatements were accordingly granted.2
The board’s decision in effect provides an allowance for local real estate taxes of $102,960 (20% of the fair cash value found by it [$514,800]). However, on the basis of the as*572sessed value established by the board’s decision ($154,440) the actual 1970 local real estate tax to be paid is only $30,888 (20% of $154,440). Thus that portion of the net income available for depreciation, return on investment and taxes which will be available for other than taxes will be approximately $123,500, rather than $51,480 (10% of the fair cash value found by the board). Such a return would support a higher fair cash value of the property than that found by the board.
The question whether the tax factor should be reflective of the effective tax rate, where it is different from the actual tax rate, has not been considered by this court previously and has been considered elsewhere in only one reported decision of which we are aware. See New Brunswick v. New Jersey Div. of Tax Appeals, 39 N. J. 537, 545-547 (1963). The issue should not, of course, arise in this Commonwealth. Assessors have a constitutional and statutory duty to tax property at its full and fair cash value. Bettigole v. Assessors of Springfield, 343 Mass. 223, 230-232 (1961). G. L. c. 59, §§ 38, 52. See Leto v. Assessors of Wilmington, 348 Mass. 144, 146 (1964); Shoppers World, Inc. v. Assessors of Framingham, 348 Mass. 366, 372 (1965). The effective tax rate should, therefore, always be the actual tax rate. Clearly the apparent general practice in Lynn in 1970 and 1971 to assess substantially all property at thirty per cent of its fair cash value was improper under the law of the Commonwealth.
Shop-Lease argues in part that the assessors should not be entitled to benefit from their misdeeds. If, however, the tax factor used by the board was erroneous as matter of law, the taxpayers of Lynn should not be compelled to suffer in effect a forfeiture to Shop-Lease of tax revenues to which the city is entitled. We wish to make it clear nevertheless that a board of assessors which has flagrantly failed to comply with its constitutional and statutory duty to assess all property at its full and fair cash value may expect to receive an unsympathetic reception in this court.
We believe the board committed an error of law in using a *573tax factor which failed to reflect the tax which would be payable as the result of its decision. The purpose of a tax factor, in a formula for capitalizing earnings, is to reflect the tax which will be payable on the assessed valuation produced by the formula. See Assessors of Lynnfield v. New England Oyster House, Inc. 362 Mass. 696, 700, fn. 2 (1972). Where the fair cash value determined by capitalization of earnings is to be reduced in arriving at the assessed valuation, the tax factor must be proportionately reduced. This is the practice indorsed in New Brunswick v. New Jersey Div. of Tax Appeals, 39 N. J. 537, 546-547 (1963). See to the same effect Ancel, Determining Fair Market Value of a Shopping Center for Purposes of Property Tax Assessment, U. of Ill. Law Forum, 253, 260 (1965); Keith, Property Tax Assessment Practices, 514 (1966); Nelson, Real Estate Taxes and Value, The Appraisal Journal, 41, 43 (January, 1966).
We decline to accept the argument of Shop-Lease that the stipulation concerning assessment practices in Lynn, on which Shop-Lease relied to establish its claim of disproportionality of assessments, is not sufficiently broad so as to establish that the effective 1970 tax rate in Lynn was not a rate of $200 for each thousand dollars of assessed valuation but only thirty per cent of that rate. In the face of the stipulation, and in the absence of any evidence to the contrary, the board would not have been warranted in concluding that persons buying and selling real estate in Lynn in 1970 and 1971 did so believing that the effective tax rate was $200 for each thousand dollars of assessed valuation.
We are not concerned here with the question whether there is substantial evidence supporting the board’s decision. Clearly Shop-Lease’s expert used in his formula the same tax factor (20%) which was adopted by the board in its decision. Here, however, the dispute concerning the proper tax factor is not one where expert testimony is decisive. The dispute involves the proper implementation, in a mathematical sense, of a principle on which there can be no reasonable disagreement, once it is established that the effective tax rate differs from the actual tax rate.
*574From what we have said, the appeals must be remanded to the board. We note, however, that there may have been determinations by the board adverse to Shop-Lease, and even more favorable to the assessors than indicated by the assessors’ own evidence, which might have been appealed by Shop-Lease if the board had not reached the decision it did concerning the tax factor. For example, without explanation, the board arrived at annual expenses of $20,550 to be deducted from the annual gross income from the property, although witnesses for both Shop-Lease and the assessors arrived at expenses in excess of $43,000. We believe it is appropriate for the board in its determination of the issues to reconsider all aspects of its decision.
The decision of the Appellate Tax Board is reversed. The case is remanded to the board for further proceedings in conformity with this opinion.
So ordered.
The assessors raised this question in various ways. They objected to the use by Shop-Lease’s expert of a tax factor which assumed taxes would be payable on the basis of 100% of the fair cash value, rather than 30% of that amount. They offered evidence that the formula should reflect what they called the effective tax rate (30% of the actual rate) rather than the stated tax rate. The assessors also raised the issue in requests for rulings which were refused by the board. One such request was the following: “5. Where both parties have stipulated that the appellee has assessed its taxable properties during the years in question, at 30% of fair market value (average assessment), then, as a matter of law, the tax factor to be used in computing the fair market value of the subject property by means of the capitalization of net income approach, must be the effective tax rate, namely, the actual tax rate multiplied by the stipulated percentage at which properties are assessed in relation to fair market value.”
The failure of the board to arrive at $154,450 (instead of $154,440) after first dividing, then multiplying, $154,450 by .3 we assume was a typographical error or was caused by roundings.