The board of assessors of the city of Peabody (assessors) appeals, pursuant to G. L. c. 58A, § 13, from a decision of the Appellate Tax Board (board), granting Alstores Realty Corporation (Alstores) abatements of real estate taxes of $765,301.84 for fiscal 1979, and $646,060.30 for fiscal 1980. On appeal, the assessors claim error in the board’s determination to allow certain operating expenses, in the board’s choice of a capitalization rate, in the board’s determination of fair economic rent for Jordan Marsh Company, a corporate affiliate of Alstores, and in its failure to take into account the real estate taxes paid to Alstores by other tenants. The assessors also complain that the board left out of its gross income figure rental income from kiosks. We conclude that there is no error in the board’s allowance of Alstores’ operating expenses, and in its choice of a capitalization rate. However, the board’s use of Jordan Marsh’s actual rent was error. Further, the board did not add tax payments by tenants to gross income or alternatively reduce the tax factor to reflect the taxes paid to Alstores by tenants. The board also did not add income from kiosks in its gross income figure. We, therefore, reverse and remand for further proceedings.
We summarize the facts found by the board.1 North Shore Shopping Center is located at the junction of Route 114 (Andover Street) and Route 128 in Peabody. The subject parcel includes an enclosed mall with access to fifteen buildings and over seventy rental outlets. It also includes a gas station, an automotive center, and a pump house. Fourteen buildings were constructed in 1957-1958. Additional buildings and the mall enclosure were built in 1977-1978. The “anchor” stores, that is, those which are thought to draw the greatest number of customers to the mall, are *62Jordan Marsh and Sears, Roebuck.2 The mall is regarded as one of the best in New England.
Both Alstores and the assessors offered testimony by expert appraisers. The board adopted the assessors’ expert’s property residual technique of capitalization of income3 as the “best determinative” of the value of the property. The board, however, rejected the assessors’ income figures as “too speculative” and accepted in their entirety Alstores’ expert’s figures for gross income, operating expenses, and net income. To compute net income, Alstores’ expert added actual rental income paid by tenants to Alstores to an imputed rent for the Sears building,4 and then subtracted actual expenses incurred in operating the property, a sum for the use of furniture, equipment and rolling stock, “which serves to develop the income,” and “charges on the land.” He compensated for his failure to include tax payments by tenants as part of gross income by reducing the tax factor.
The board rejected both the assessors’ and Alstores’ capitalization rate computations. Instead, the board used net income figures “capitalized at rates which included a return of the investment, a depreciation factor and an appropriate tax factor.”5 The board derived its tax factor from the tax rate, adjusted for disproportionate assessment. The board then divided the capitalization rate into the net income *63figure to ascertain fair cash value.6 The tax rate was adjusted to compensate for disproportionate assessment,7 and the board calculated the tax and issued its abatement decisions.8
1. Computation of operating expenses. The assessors claim that the board, in adopting Alstores’ expert’s figures for net operating income, erred by permitting expense deductions outside the range testified to by the experts and by including expenses not related to the operation of land or *64improvements. The short answer to these claims is that the board, based on expert testimony, found that “the actual expenses were reasonable and were in line with other shopping centers.” The board then adopted Alstores’ expert’s figures for net operating income. There is no error.
The assessors claim that the board deducted from gross income promotional expenses and certain administrative expenses (dues, membership, and travel) not related to the operation of land or improvements. The board considered insurance, administration, promotion, special jobs, water and sewer, landlord maintenance, common area maintenance, heating, and air conditioning to be operating expenses.9 There was expert testimony that these expenses were related to the operation of a shopping mall.
Alstores’ expert admitted that Alstores’ expenses were higher than average10 but claimed that the expenses were reasonably related to operating the shopping mall, which the board found to be one of New England’s best shopping malls.11 It was within the board’s expertise to accept this *65testimony. “The weight to give to the testimony of a witness, after the disclosure by cross-examination of possible but not fatal weaknesses in that testimony, is clearly for the trier of fact, in this case the board.” Assessors of Lynnfield v. New England Oyster House, Inc., 362 Mass. 696, 702 (1972).
The assessors, in effect, are asking us to create a list of specific expenses which can be considered operating expenses. This we decline to do. Operating expenses of property owners will vary with the use of the land and the nature of the improvements. The issue of what expenses may be considered in any particular piece of property is for the board. “The board could select the various elements of value as shown by the record and from them form, as it properly did, its own independent judgment.” Assessors of Quincy v. Boston Consol. Gas Co., 309 Mass. 60, 72 (1941).
2. Computation of the capitalization rate. The assessors claim that the board erroneously excluded documentary evidence of comparable sales that would show, if accepted, a lower ratio of net income to sale price, and thus justify a lower capitalization rate than the one the board chose to adopt.
The assessors’ expert submitted evidence of five sales that he claimed were comparable. The assessors’ expert, however, admitted that two of the sales were not arm’s-length transactions, two were subject to mortgages, and the remaining sale should be given little evidentiary weight because it had taken place eight years earlier. A trier of fact could reject the sales as reported by the assessors’ expert as evidence of the appropriate capitalization rate because these sales were not comparable and therefore could not be used to determine a capitalization rate. Thus, the expert’s evidence was “too unreliable to be accepted as a correct test of value.” Peoples Sav. Bank v. Assessors of Chicopee, 384 Mass. 808, 809 (1981), quoting State v. Lincoln Memory Gardens, Inc., 242 Ind. 206, 213 (1961).12
*66The assessors also claim that the board’s capitalization rate was not based on substantial evidence. The board considered testimony by both experts and reached its own capitalization rate. “[T]he board [is] not required to indicate the capitalization of earnings rate which it in fact used. The board did not accept the actual computations of any witness and was not obliged to do so.” Assessors of Lynnfield v. New England Oyster House, Inc., 362 Mass. 696, 700 (1972). See Foxboro Assocs. v. Assessors of Foxborough, 385 Mass. 679, 689 (1982); New Boston Garden Corp. v. Assessors of Boston, 383 Mass. 456, 469 (1981). The fact is that the capitalization rate used by the board was more favorable to the assessors than that testified to by Alstores’ expert, although not as favorable as the capitalization rate urged by the assessors. The board’s determination was not erroneous simply because it did not accept one expert’s testimony completely. “The essential requirement is that the board exercise judgment.” New Boston Garden Corp. v. Assessors of Boston, supra at 473. The board’s rejection of both the assessors’ and Alstores’ capitalization rates belies the assessors’ claim that the board uncritically accepted the testimony of Alstores’ expert.
3. Computation of gross income. The assessors allege that the board erred in adopting Alstores’ expert’s gross income figures because those figures were based on actual rents rather than earning capacity, the board erred by failing to include tax payments by tenants as part of Alstores’ gross income, and the board erred by not including substantial income derived from kiosks in its gross income calculation.13 We agree.
*67(a) Use of actual rental income in gross income calculations. The assessors allege that the board erred in adopting Alstores’ expert’s gross income figures because those figures were based on actual rents rather than earning capacity. The assessors argue that the board failed to consider the “identity of interests” between Alstores, the lessor, and Jordan Marsh Company, one of the lessees, both of which are subsidiaries of Allied Stores Corporation. See Jordan Marsh Co. v. Assessors of Malden, 359 Mass. 106, 107 (1971); Me-serve v. Jordan Marsh Co., 340 Mass. 660, 664 (1960). The assessors contend that a lease from Alstores lacks an essential element of a market transaction, i.e., independence of economic actors. Thus, the actual rental income that Alstores derives from the Jordan Marsh lease is not substantial evidence of economic rent.
“Actual sales are . . . very strong evidence of fair market value, for they represent what a buyer has been willing to pay to a seller for a particular property.” First Natl Stores, Inc. v. Assessors of Somerville, 358 Mass. 554, 560 (1971). However, “the evidentiary value of such sales [or rentals] in less than arm’s-length transactions is diminished.” New Boston Garden Corp. v. Assessors of Boston, 383 Mass. 456, 469 (1981), citing Jordan Marsh Co. v. Assessors of Malden, 359 Mass. 106, 108 (1971). See Foxboro Assocs. v. Assessors of Foxborough, 385 Mass. 679, 682 (1982). See also Shawmut Inn v. Kennebunkport, 428 A.2d 384, 395 (Me. 1981) (little weight given to sale price “consummated between shareholders in a close corporation”); Ancel, Determining Fair Market Value of a Shopping Center for Purposes of Property Tax Assessment, 1965 U. Ill. L.F. 253, 260 n.28 (“In seeking to use such [sales] data [for computing a capitalization rate], one would have to make certain that . . . sales were demonstrable, arms length dealings”).
*68The same principles also apply to rental income. “[I]f examination discloses that rent has been arbitrarily set without regard to the market rental value . . . through self-dealing, as, for example, where a landlord and tenant are business affiliates . . . the rent arrangement will be of little, if any, guidance to sound appraisal.” Merrick Holding Corp. v. Assessors of the County of Nassau, 45 N.Y.2d 538, 543 (1978). See Supervisor of Assessments of Alleghany County v. Ort Children Trust Four, 294 Md. 195, 211 (1982) (where lease between parties is “arms length, bona fide transaction” and parties agree rent established at time of lease is economic rent, lease is valid evidence for assessment purposes); Matter of Marine Midland Properties Corp., 91 A.D.2d 824 (N.Y. 1982) (“The court erred ... in capitalizing the value of the property when it used the actual rents paid by the tenant to petitioner, a related corporation. . . . This sum, supposedly representing rent, had no relation to market rental . . . and had no probative value”). Because a lease between corporate affiliates does not necessarily reflect market conditions, we hold that such a lease, standing alone, is not substantial evidence of earning capacity.
The board decision, without reference to the relationship between Jordan Marsh and Alstores, states that “$2.70 per square foot... is deemed to be a fair economic rent.” Contrary to the assessors’ claim, this figure can be approximated from the record by adding Jordan Marsh’s actual rent to its payments toward real estate taxes and dividing by the number of square feet rented.14 The board, however, purported to derive the $2.70 figure by adding “real estate tax payments, percentage rent payments plus expenses” to Jordan’s base minimum rent of approximately $1.60 a square *69foot. The record reflects that Jordan Marsh paid no “percentage rent payments.”15
Further, the board did not use the $2.70 figure as the figure to determine fair economic rent. The board specifically adopted Alstores’ expert’s income figure which used Jordan’s actual rent (approximately $1.60 a square foot) in its gross income figure. The board found that “the actual amount paid by Jordan Marsh is a fair economic rent,” based on size and Jordan’s “anchor store” role.16 The “actual amount paid” is $1.60 a square foot.17 Because Jordan Marsh’s lease was a lease between corporate affiliates and not an arm’s-length transaction, the board erred in using Jordan Marsh’s actual rent as if it were “fair economic rent.”
(b) Tax payments by tenants. The assessors allege that the board erred in calculating gross income by not taking into consideration the tax payments made by tenants. The experts before the board indicated that these tax payments to Alstores could have been included in the fair market value by one of two methods: (1) adding the tax payments to the other components of gross income, or (2) adjusting the tax factor to take into account tax payments by tenants.18
*70The board specifically adopted Alstores’ expert’s gross income figures which did not include tax payments by the tenants. Therefore, the board had to adjust the tax factor19 to take into account tax payments by tenants, as well as dis-proportionality. The board, however, calculated its tax factor by proportionately reducing the tax rate by the forty-eight per cent disproportionate assessment figure stipulated by the parties for 1979 and by using the equalized tax rate ($48.70) found by the Department of Revenue for 1980. See Tregor v. Assessors of Boston, 377 Mass. 602 (1979). The tax factor was not reduced by the board to reflect tax payments by tenants in either year. The board adjusted the tax factor only for disproportionality. Because the board used actual rents and did not add the tax payments to gross income, the board erred when it did not reduce the tax factor to reflect tax payments by tenants.
(c) Income from kiosks. The assessors claim that the board did not include income from kiosks in gross income. The assessors cite Alstores’ expert as admitting that he did not include in the income computation rental income from kiosks. The board accepted Alstores’ expert’s gross income figures. There were at least one permanent kiosk and several temporary kiosks in operation during the fiscal period in ques*71tion. The board should have considered the evidence of gross income from these kiosks.
The board erred by using the actual rent paid by Jordan Marsh, by failing to consider taxes paid by tenants, and by failing to include income from kiosks. Therefore, on consideration of the whole record we conclude that the subsidiary facts found by the board and the reasons for its conclusions are not supported by substantial evidence. Although we have not required the board to break down its calculations, the board must be sufficiently specific as to the subsidiary facts it finds, its calculations, and the reasons for its conclusions so that appellate review is meaningful. See Foxboro Assocs. v. Assessors of Foxborough, supra at 689; New Boston Garden Corp. v. Assessors of Boston, supra at 472; Assessors of Lynnfield v. New England Oyster House, Inc., supra at 700. The decision of the board is reversed, and these matters are remanded to the board for further proceedings.
So ordered.
Additional evidence will be discussed in our analysis of the issues.
The Filene’s store located at North Shore Shopping Center is not included in the subject parcel.
The property residual technique of capitalization of income requires that land and buildings be capitalized as a single unit. Alstores’ expert used the building residual technique, in which the value of the land is calculated directly and the improvements are evaluated by capitalization of income.
Sears paid no rent on its building since it had built it. Thus, no actual rental figure existed for the Sears building. Sears did rent land from Al-stores, which rent was added to an imputed building rental sum of $700,000. The imputed rent, which totaled $757,000, was based on a comparison with the footage rental rate that Sears paid at Methuen Mall.
The board did not break down its capitalization rate into component parts and is not required to do so. Assessors of Lynnfield v. New England Oyster House, Inc., 362 Mass. 696, 700 (1972).
For 1979, the board divided a net income of $2,997,130 by a capitalization rate of .1545 and found that the fair cash value was $19,400,000. For 1980, the board divided a net income figure of $3,192,572 by a capitalization rate of .1687 to reach a fair cash value of $18,925,000.
For 1979, the board based taxation on forty-eight per cent of fair cash value ($9,312,000). The tax rate was $71.80 a thousand, which equaled a tax of $668,601.60. Since the assessors had assessed a tax of $1,433,903.44, the board ordered an abatement of $765,301.84.
For 1980, the board based taxation on the Department of Revenue’s equalized tax rate of $48.70. Based on a fair cash value of $18,925,000, the board calculated that the tax should be $921,647.50. Since the assessors had assessed a tax of $1,567,707.80, the abatement equaled $646,060.30.
Alstores’ expert computed the capitalization rate from three components: the return that the investors could hope to earn on an investment, a tax factor, and an amortization rate. He based the return on investment in part on the prevailing money market. In his calculations the tax factor was reduced by the percentage of taxes paid by tenants, thus presumably compensating for his decision not to include these tax payments in his net income computation. He concluded by dividing the net income figure by the capitalization rate and adding the quotient to the value of the land, thus arriving at the fair market value. Alstores’ expert did not adjust his tax factor downward to account for disproportionality.
The assessors’ expert based his computation of the capitalization rate on two discrete figures: a tax factor and a combined “return on investment and depreciation” figure. Because the assessors’ expert calculated gross income by a market analysis of the rental rates that the property should command, rather than on the basis of actual rental income, he did not add tax payments by tenants to gross income or reduce Alstores’ tax factor to compensate for tenant tax payments. The assessors’ expert adjusted the tax factor downward in accord with the disproportionality ratio. He based his estimate of return on investment on a ratio between net income and the selling price of five other properties. He then added the tax factor and the return on investment figure and arrived at a capitalization rate which was divided into the net income figure to ascertain fair cash value.
The dues, membership, and travel expenses that the assessors contest are insignificant amounts and would not affect the result. For example, these expenses totaled $2,686 for 1979. Total expenses for that year were $685,519. The contested expenses, therefore, equaled less than four-tenths of one per cent of the total expenses and added less than .073 of one per cent to the ratio of expenses to gross income. The record is not clear for 1980.
The assessor’s expert fixed expenses at ten per cent of effective gross income, stating this was “very consistent with the experience of like properties in the Essex County and New England area generally.” Alstores’ expert testified that average expenses were between fourteen and eighteen per cent, that one shopping center had expenses of thirty-two per cent, and that North Shore, at 18.6 per cent, was “a shade high.” He computed net operating income using actual expenses. The difference may be explained in part by the fact that the assessors’ expert used a larger effective net income figure.
There is no contention that these promotional expenses were not incurred. We note that “North Shore schedules special events almost every week of the year; some are charitable and civic, and some are simply entertainment. Many events have a direct commercial benefit for the tenants of the shopping center by attracting people to the shopping center; others benefit North Shore and its tenants by creating goodwill” (footnote omitted). Batchelder v. Allied Stores Intl, Inc., 388 Mass. 83, 86 (1983).
The board heard the evidence and then excluded it. The board could have disregarded the evidence as not relevant. Since the board heard *66the evidence, the fact that the board excluded it, rather than disregarding it, is not prejudicial to the assessors.
Exclusion of a sixth sale (Burlington Mall) was justified because the assessors’ expert, although including it in a list of sales, did not state that he had relied on it in calculating a capitalization rate. Further “[i]t was open to the board to accept the testimony of the taxpayer’s witness as the more convincing.” Assessors of Weymouth v. Tammy Brook Co., 368 Mass. 810, 811 (1975).
The assessors also allege that the board erred mathematically in accepting Alstores’ expert’s figure for the Sears rental because Sears’ rental *67area, when multiplied by $3.50 a square foot, does not equal $757,000. Alstores’ expert stated, however, that the $3.50 rental figure at Methuen Mall was a means of estimating the rent at North Shore, not a means of deriving a precise equivalent. No mathematical error is involved.
According to Alstores’ expense report, Jordan Marsh paid, in 1979, $603,707 in rent and $371,969.79 in real estate taxes for 369,432 square feet for its main store and basement store. This equals slightly more than $2.64 a square foot.
Rent in this mall generally consisted of a guaranteed minimum combined with a proportionate share of operating costs and taxes as well as “percentage rent payments.”
Percentage rent payments are rental payments in excess of minimum rents based on the square footage of the rental property and the gross sales income derived therefrom.
Alstores’ expert imputed a rental figure to the other anchor store of $3.50 a square foot.
If by “actual amount paid” the board meant $2.70 a square foot, the record as we read it indicates that the $2.70 figure was not used in the board’s calculations.
Alstores’ expert stated that “[i]n view of the fact that numerous tenants contribute taxes, the actual tax rate . . . should be reduced to reflect the portion of those taxes that it is reasonably prudent to assume will be paid by the tenants.” Thus, he reduced the tax factor to compensate for taxes paid by tenants.
The “tax factor” is a percentage added to the capitalization rate “to reflect the tax which will be payable on the assessed valuation produced by the formula.” Assessors of Lynn v. Shop-Lease Co., 364 Mass. 569, 573 (1974). “Logically, therefore, income should be capitalized before taxes ‘with the capitalization rate increased to yield the return the investor expects plus the amount of local taxes payable.’” Assessors of Lynnfieldv. New England Oyster House, Inc., 362 Mass. 696, 700 n.2 (1972), quoting New Brunswick v. New Jersey Div. of Tax Appeals, 39 N.J. 537, 546 (1963).
The reduction of the tax factor for disproportionality assures that the tax factor, and hence the capitalization rate, will reflect the actual taxes that will be paid by the taxpayer. The lower tax factor will result in a lower capitalization rate and therefore a higher fair cash value. The reduction of the tax factor for disproportionality and the reduction of the tax rate after the fair cash value has been calculated are independent reductions, both of which are required under the capitalization of income method used by the board. See Assessors of Lynn v. Shop-Lease Co., supra. See note 8, second par., supra.