The board of assessors of the town of Province-town (assessors) challenges a decision of the Appellate Tax Board (board) granting abatements of certain real estate taxes assessed against the plaintiffs (taxpayers). The assessments cover fiscal years 1982-1985. This court granted the assessors’ petition for direct appellate review. We affirm.
*729In 1977, two of the taxpayers purchased a 4.7 acre shorefront property in Provincetown. A resort complex, including three motel buildings, occupied a portion of the land. In 1979, these taxpayers converted the waterfront motel building situated on approximately 1.93 acres of the land into a condominium facility. See G. L. c. 183A, § 16. The new condominium was called The Royal Coachman Condominium (condominium). The condominium master deed provided that some or all of the units could be devoted to time-sharing use.2 All of the condominium units are currently time-share facilities.
From the time of purchase through fiscal year 1981, the assessors apparently valued the property as a motel complex. The taxpayers received one assessment on the entire property. For fiscal year 1982, the assessors increased the assessment on the property four-fold. In doing so, the assessors valued individually the condominium common areas and facilities. The individual condominium units, however, were not assessed separately. The assessors mailed one tax bill for the entire 4.7 acre parcel to certain of the taxpayers as individuals, and not to the trustees of the condominium trust.
The taxpayers sought declaratory relief in the Superior Court in Barnstable County. They claimed that record ownership of the condominium rested with the individual time-share unit owners. On August 5, 1983, a judge of that court found that the taxpayers had established a “de facto” condominium. The judge determined that the condominium, and the taxpayers as trustees but not as individuals, were the record owners for assessment purposes.3 See G. L. c, 59, § 11 (1986 ed.); G. L. c. 183A, § 14.
*730The tax bill for fiscal year 1983 was issued on July 28, 1983. That bill assessed the taxpayers, as individuals, on the property as a whole. On December 29, 1983, the assessors mailed tax bills for fiscal year 1984. Again, condominium units were not assessed separately. The bills were addressed to the taxpayers individually or as trustees of the condominium. The taxpayers filed a contempt complaint in the Superior Court. A second judge of that court issued a preliminary injunction on January 24, 1984, restraining the assessors from collecting the fiscal year 1984 bill. On February 2, 1984, the parties agreed to a permanent injunction against collection of the fiscal year 1984 bill, as issued in December, 1983. The agreement declared the bill null and void. On February 17, 1984, a third Superior Court judge enjoined the assessors from the collection of taxes not assessed on the condominium by individual unit. See G. L. c. 183A, § 14; G. L. c. 59, § 11. The judge further ordered that, within forty-five days, the assessors were to issue to the taxpayers, as trustees, separate tax bills on each condominium unit for fiscal years 1982 and 1983. No appeal was taken from these decisions.
Ten months later, on December 6,1984, the assessors issued, in proper form, bills for fiscal years 1982 and 1983. These bills, on which no interest was assessed, were paid in full within thirty days of issuance.4 On the assessors’ constructive denial of an application for abatement, the taxpayers appealed to the board.
On December 20,1984, the assessors issued a bill, in proper form, for fiscal year 1984. The taxpayers again paid the amount in full within thirty days. The assessors denied constructively *731the taxpayers’ application for abatement. A timely appeal to the board followed. A similar procedural history governed the assessment for fiscal year 1985, which was issued on August 13, 1985.
1. Jurisdiction of the board. The assessors challenge the board’s jurisdiction to hear the appeals for fiscal years 1982 and 1983. The assessors assert that the taxpayers failed to comply with statutory requisites to preserve their right to appeal. See G. L. c. 59, §§ 57 & 64 (1986 ed.). The assessors argue, first, that the taxpayers did not pay fully and in a timely manner the originally issued fiscal year 1982 and 1983 assessments. In the alternative, they assert deficient payment on the fiscal year 1982 and 1983 bills that were issued in December, 1984. We do not see the relevance of actions taken on the original bills for these years. The judgments of the Superior Court of August 5, 1983, and of February 17, 1984, make clear that these assessments were issued improperly. The Provincetown tax collector acknowledged before the board that these bills had been rescinded. Nor do we perceive a problem regarding the lawfully issued bills of December 6,1984. Again, the tax collector conceded that these bills had been paid on time and in full. See note 4, supra. The board properly determined that it had jurisdiction over these appeals for fiscal years 1984-1985.
2. Review of the board’s decision. “A decision of the board will only be disturbed if it was not supported by ‘substantial evidence,’ or was tainted by an error of law. ” Tenneco Inc. v. Commissioner of Revenue, 401 Mass. 380, 383 (1987), and cases cited. Substantial evidence is that which “ a reasonable mind might accept as adequate to support a conclusion. ” G. L. c. 30A, § 1 (6) (1986 ed.). In New Boston Garden Corp. v. Assessors of Boston, 383 Mass. 456, 466 (1981), quoting L.L. Jaffe, Judicial Control of Administrative Action 598 (1965), we stated that we shall consider the entire record to determine whether “the evidence points to no felt or appreciable probability of the conclusion or points to an overwhelming probability of the contrary.”
*732The board accepted the market data valuation approach of the taxpayers’ appraiser.5 This method used comparable sales of condominium units in two nearby locations — one practically next door to the condominium and the other approximately one-quarter mile away.6 Through this approach, a comparison of the values of the comparable properties, with necessary adjustments, was applied to units in the condominium. Further, the condominium’s square foot value was refined to distinguish ocean view units from poolside units. The board found, specifically, that this market data method valued the condominium properly, in accordance with accepted appraisal practices.
fil contrast, the board rejected the assessors’ proffered approach as “patently absurd . . . unreasonable [and] unsupportable.” The assessors urged adoption of an “aggregate of the time-share deeds” approach. Here, the actual or imputed7 sale prices of time-share intervals fór a particular unit were added together for the thirty-week period of availability.8 The unit was then valued at that aggregate price. No allowances were made for personal property in the units (furniture and appliances) or for marketing costs, unsold intervals, and other sundry expenses. Marketing costs alone were found by the board to be 45% to 55% of the gross sale prices which the assessors’ witnesses utilized.
*733Neither of the assessors’ witnesses produced any basis of support for his use of this methodology. The assessors’ valuation resulted in assessments up to six times greater than assessments on comparable units of superior quality. The assessors argued that the time-share provision made these condominium units more valuable than ordinary condominium units. As the board noted, however, it is possible that a condominium unit could be leased for weekly intervals.9 The board concluded that the assessors’ approach failed to produce a reasonable estimate of a fair market value for each unit.10
We have reviewed the record. The assessors offered an alternative valuation method. The board was not required to adopt a particular valuation method or to believe a particular witness’s testimony. New Boston Garden, supra at 469, and cases cited. The reasons militating against adoption of the assessors’ approach were detailed carefully in the board’s opinion. Further, the assessors took ample opportunity to explore fully with the taxpayers’ appraiser his reasons for choosing nontime-share condominiums as comparable properties. They offered no adequate evidence to require use of a market data valuation approach that included time-share properties. The record supports the board’s choice of a valuation approach. See id. at 470-471 (board must credit proponent’s evidence if *734“logically adequate, and . . . neither contradicted nor improbable”). We find no indication in the record of an “overwhelming probability” that the board’s conclusion was erroneous and unsupported by substantial evidence.
Decision of the Appellate Tax Board affirmed.
Time-sharing, or interval ownership, is the exclusive right to possess and use real property for set time periods.
The judge ruled that, under G.L. c. 183A (1986 ed.), time-share ownership is not an interest in real property. He declared invalid that portion of the master deed purporting to convey a property interest in time-share units. The judge made it clear, however, that he did not rule on the validity of the purchase and sale agreements between the trustees of the condominium and the purchasers of time-share interests. The decision of August 5, 1983, was not appealed and is not now before us.
We note the recent adoption of G. L. c. 183B (Supp. 1987), the Real *730Estate Time-Share Act. This law creates a real estate interest in time-share units, and provides for tax assessments to the individual time-share owners. G. L. c. 183B, § 3 (a) & (b). This law does not govern the case at bar.
The tax collector for the town of Provincetown testified before the board that the bills issued on December 6, 1984, for fiscal years 1982 and 1983, had been paid in full and on time. The board so found.
The tax collector, however, had refused to acknowledge receipt of payment until the taxpayers, under protest, paid retroactive interest of $58,460.10 on the prior bills for fiscal years 1982 and 1983.
The taxpayers’ appraiser testified regarding his reasons for not choosing either an income approach or a reproduction cost approach to valuation. The board concluded that the methodology used by this appraiser was both proper and consistent with the rulings of the Superior Court.
Neither of the other properties sold time-share intervals. We note, however, that the board took a view of the subject property and of the comparable properties. Whether the other properties were “comparable” was within the board’s sound discretion. See Alstores Realty Corp. v. Assessors of Peabody, 391 Mass. 60, 65-66 (1984).
For certain intervals, a value higher than the actual sale price was imputed. This occurred where a less desirable time interval was purchased at a reduced price in conjunction with the purchase of two or more units for a desirable period, or where intervals were unsold.
For a variety of reasons, the condominium units were usable only during thirty weeks of each year.
In reaching its decision, the board adopted the Superior Court judge’s ruling of August 5, 1983. See note 3, supra, and accompanying text. Specifically, the board emphasized that time-share intervals did not constitute a real property interest. The assessors claim that the board misinterpreted the Superior Court judge’s decision. Their interpretation limits the decision to a resolution of record ownership for assessment purposes.
The board’s broader reading of the decision was essentially correct. Nonetheless, at one point in its decision, the board mistakenly credited the Superior Court decision as a mandate that the units must be valued as a condominium, irrespective of time-share usage. Given the other grounds for the board’s conclusions, however, this assumption is not fatal to its decision.
“Fair cash value or fair market value is ‘the price an owner willing but not under compulsion to sell ought to receive from one willing but not under compulsion to buy.’ Boston Gas Co. v. Assessors of Boston, 334 Mass. 549, 566 (1956).” New Boston Garden, supra at 458 n.2.