This is an appeal under the formal procedure from the refusal of the appellee to abate a real estate tax assessed for fiscal year 1981 pursuant to G.L. c. 59, s. 38. These findings of fact and report are made pursuant to a request by the appellant under the provision of G.L. c. 58A, s. 13, as amended, and Rule 32 of the Rules of Practice and Procedure of the Appellate Tax Board.

FINDINGS OF FACT AND REPORT

The appellee valued the appellant’s residence at $54,200 and assessed a tax at the rate of $27.28 per $1000 in ihe amount of $1,478.58. On April 17,1981, within 30 days after the tax bill was sent, the appellant filed an application for abatement which was denied May 4, 1981 from which denial the appellant filed an appeal with this board on July 16, 1981.

The appellant presented evidence directed toward proving that the valuation of his house had been increased at a much larger percentage than other *148homes within the town and that his house had been assessed much higher than comparable property.

A rural town located in Western Massachusetts, Peru is approximately 18 miles from Pittsfield. With only a small amount of tillable land, the town ,is principally rugged terrain and there are approximately 660 parcels within the town, only two of which are farmed. Taking up large areas of the town are the Peru State Forest, the Peru Wildlife Management Area, Peru state Hunting Grounds and the Dorothy Frances Rice Wildlife Refuge. Without significant commercial activity there is virtually no .employment within the town and most of its working residents commute to nearby towns for occupations. The population of the town increased from 250 persons to 650 persons between 1970 and 1980.

Located in the so-called “BEALS DEVELOPMENT” the appellant’s lot is subject to deed restrictions. The town itself has very liberal zoning rules by which under special permit a business use is allowed everywhere and it is one of only two towns out of 34 municipalities in the county which permit mobile homes.

In contrast to the liberal zoning, lots in the BEALS DEVELOPMENT must be used for single family residential purposes, a structure less than 1-1/2 stories in height must have at least 864 square feet in the foundation excluding porches, a structure with more than 1-1/2 stories must have a minimum square footage of 764 square feet, garages must be attached to the dwelling, only one ancillary structure is permitted provided its design is in keeping with the house design, no modular or pre-engineered houses are allowed, adjacent houses must have different architectural design, no ancillary structure including tents may be used as a residence either temporarily or permanently, only domestic pets are permitted, vehicles must be stored behind screening.

This contrasts somewhat sharply with many of the other improvements in the town where mobile home, camps and an assortment of architecturally designed structures may be found.

Built in 1974 and occupied originally by the developer himself, the appellant’s home is a ranch style house with a first floor containing 1104 square feet, a deck with 460 square feet, an attached garage with 728 squpre feet and another garage with 576 square feet. The house, without a full basement, had a gable-type roof with asphalt shingles while the interior was of dry wall construction, carpeted floors and electric heat. With two bedrooms and one bath, the house was in very good condition and was located on a comer lot containing 3 acres on Andes Road. Typical of the area as to its topography, the landscaping was outstandingly attractive.

For the most part, houses in this particular development sold at considerably higher prices over many residences in the town where there was a minimum lot size of 2 acres.

Claiming considerable experience in property appraisal because of his occupation as a farm program specialist for the Farmer’s Home Loan Administration, U.S. Department of Agriculture the appellant, a magna ctirn laude graduate of the University of Massachusetts, was a certified “Farmer’s Home Administration” single family and farm real estate appraiser, and had training in real estate appraisal. An instructor for farm real estate properties valuations for the “Farmer’s Home Administration,” he had appraised between 250 to 300 single family residences for the “Farmer’s Home Administration. ’ ’

In developing his valuation for his home, he had prepared a chart showing the percentage of increase in assessments of homes in the town to make the point that his home had increased in assessment on a percentage basis greater than other homes in the town. He also prepared a list of what he considered comparable homes, their assessments, sales prices and descriptions. However, it is to be noted that the appellant made no claim of *149disproportionate assessment. He made a point of comparing the amount allocated to his land as compared to amounts allocated to the land of other taxpayers all as noted on assessors’ records and he likewise compared the square footage and other characteristics of other homes compared to his.

He gave an opinion of value of $36,000 as compared to the $54,200 at which his house had been assessed.

However, he purchased the property on September 26, 1980 for $67,000 which is $31,000 more than what he testified was the fair cash value of the property as of January 1, 1980. He attempted to explain this discrepancy by the assertion that he was not exactly a willing buyer due to family circumstances at the time and the need to locate near his job and a baby sitter whom he had been using as.well as the fact that he had recently experienced a very substantial capital gain on the recent sale of a house which gain he sought to make use for income tax purposes in this. acquisition.

Only a few of the many comparables shown the board were sufficiently similar to be of help in reaching a value by comparing assessments. Any apparent discrepancies between his assessment and other assessments were either not sufficiently significant or could be explained by rather obvious features characterizing the properties and warranting a difference in valuation.

On the evidence as a whole and on our findings in particular, it could not be said that the assessors were discriminating against the appellant in his particular assessment.

This conclusion reached by the board was supported by the testimony of appellee’s expert witness.

This witness was the regional manager for Western Massachusetts of McGee and Magane, Inc., a well-known appraisal firm, had appraised approximately 50,000 parcels of property in* his career and had qualified as an expert at this board before. He demonstrated a full knowledge of the area, the town and the details and characteristics of the property on appeal. His appraisal report, Exhibit A, is in evidence. On the basis of his study and analysis of sales of property in the town outside the Beals Development as compared to sales in the Beals Development, the board, concluded that the property in the development generally sold at much higher prices. After examining and evaluating the significance of the deed restrictions, studying detailed characteristics, such as the size, type of structure, location, etc., of appellant’s property as compared to residences in the town as a whole, he concluded that the appellant’s property was not overvalued at a figure of $54,200, and the board agreed that his study and conclusions were valid.

Thus, theboard rendered a decision for the appellee.

OPINION

The only issue in this appeal is that of overvaluation, since the question of disproportionate assessment raised in the petition was waived by the appellant.

The criteria for determining “fair cash value” has been set forth in many of our cases, notably Boston Gas Company v. Assessors of Boston, 334 Mass. 549, 556 (1955). Fair cash value is the price an owner, willing but under no compulsion to sell, ought to receive from one willing, but not under compulsion to buy the property in question, each party having full knowledge of all relevant facts.

The fact that appellant’s assessment may have increased at a percentage greater than the percentage increase in the assessments of other houses is not determinative of the issue. It could be that prior assessments and the institution of revaluation procedures reveáled that his former assessment was unduly low. The test is fair cash value or market value.

The market value of any real estate can not be determined with mathematical certainty but must ultimately rest in the realm of opinion, estimate and judgment, and need not coincide with the valuation given by any witness but must be based on *150substantial evidence: Assessors of Quincy v. Boston Consolidated Gas Co., 309 Mass. 60 (1941). The decision of the board is final as to findings of fact. G.L. c. 58A, s. 13. This board is not required to specify the exact manner in which it arrives at its fair cash value figures. Jordan Marsh Company v. Assessors of Malden, 359 Mass., 106 (1971).

.Being “in thebest position to determine the weight and credibility of the evidence”, the determination of these matters is for theboard unless the board’s decision is based on testimony which “cannot reasonably form the basis of impartial, reasoned judgment.” Oberg v. Burke, 345 Mass. 596, 598; New Boston Garden Corp. v. Board of Assessors of Boston, 1981 ad. sh. 1023, 1035.

“The burden of proof is upon the petitioner to make out its right as a matter of law to abatement of the tax. Nq intendment as to evidence can be made in its favor beyond what is shown on the record.” Judson Freight Forwarding Co. v. Commonwealth, 242 Mass. 47, 55 (1922). William Rodman & Sons v. State Tax Commission, 373 Mass. 606, 610 (1977).

On the basis of a careful analysis and evaluation of all the evidence and the board’s findings and applying the principles of law above set forth, the board was of the opinion that the appellant in .this appeal failed to sustain his burden of proof that the fair cash value of his property was less than $54,200.

Our decision for the appellee, was promulgated February 18, 1982. .

A True Copy,