SPALDING, J.

This is a bill in equity under G.L.c. 40A, § 21, inserted by St. 1954, c. 368, § 2, by way of appeal from a decision of the board of appeals of Northampton refusing to grant to the plaintiffs a variance for a commercial use in an area zoned for residential purposes. Edward T. Pendergast, whose property abutted the plaintiffs', was permitted to intervene. The court ordered the board to grant a variance, and the board and the intervener appealed. The judge made a report of material facts. The evidence is not reported.

We summarize the findings of the judge as follows: The plaintiffs, husband and wife, are the owners of two virtually contiguous parcels of land in the village of Florence in Northampton. One, the Homestead lot, so called, fronts upon Meadow Street. The other parcel, which is called the Shop lot, is separated from the Homestead lot by Meadow Avenue, a private way. The Shop lot is located in a residence B district. Prior to 1952, the plaintiff Anthony Ferrante had conducted a cabinet making business on the Homestead lot. Expanding his business in 1952, he caused to be erected a concrete block building, twenty-five feet by forty feet, on the Shop lot. This building, which cost $12,000, was erected pursuant to a building permit issued by "the appropriate . . . [city] official." "Since then he has continuously conducted his woodworking business from the Shop lot building." He employs several persons in this business and carries it on "in the ordinary manner with regard to the nature of the business." The judge, who took a view, found that the Shop lot was located in an area which "although zoned for residence can hardly be characterized as such." The only land, other than the Shop and Homestead lots, which fronts on Meadow Avenue, is a parcel owned by the intervener, Pendergast, and a parcel owned by one Bean. The intervener conducts a coal and ice business on his land, and Bean carries on an auctioneering business in a building which is in many respects "similar to those inexpensive metal buildings called `Quonset Huts.'" No "other property is near enough to be in any way affected." On the far side of the Bean property there is a "rather large cemetery." The area in which the Shop lot is located is "but a short distance from a main street which is highly commercial."

Under the heading, "Hardship," the judge found that the building erected by the plaintiffs could not be converted into a building for residential use, and that the "denial of a variance would not only end the . . . [plaintiffs'] business but would render this special purpose building incapable of occupancy and useless."

Under a heading entitled, "No substantial detriment to the public," the judge found that the "only persons who would be affected by the granting of the variance for the continued operation of the . . . [plaintiffs'] business would be the operator of the coal and ice business and the operator of the auctioneering business," and the latter did not object.

Under the caption, "No derogation from the intent of the zoning laws of the City of Northampton," the judge found as follows: "The subject property is located between two operating businesses and its general location . . . compels the conclusion that it could not reasonably be held to be appropriate for residential use."

After finding the foregoing facts, the judge ruled: "Although the doctrine of estoppel was not squarely advanced by the . . . [plaintiffs], the circumstances of the duly authorized . . . [city] official having issued the building permit (and the building having been built and the business operating . . .) taken together with all of the facts as set out above compel the conclusion that the . . . Board acted unreasonably and arbitrarily and thus in excess of its authority. . . ."

It is settled that, before a variance may be granted, all the requirements of G.L.c. 40A, § 15, must be met. Blackman v. Board of Appeals of Barnstable, 334 Mass. 446, 450. Atherton v. Board of Appeals of Bourne, 334 Mass. 451, 454. Shacka v. Board of Appeals of Chelmsford, 341 Mass. 593, 595. Sullivan v. Board of Appeals of Canton, ante, 117. One of the provisions of § 15 is that a variance may be granted only where, "owing to conditions especially affecting such parcel or such building but not affecting generally the zoning district in which it is located, a literal enforcement of the provisions of the ordinance or by-law would involve substantial hardship, financial or otherwise to the appellant." The judge failed to find specifically that the variance should be granted "owing to conditions especially affecting such parcel," and the decree, therefore, is defective. Shacka v. Board of Appeals of Chelmsford, 341 Mass. 593. Barnhart v. Board of Appeals of Scituate, 343 Mass. 455, 458. Coolidge v. Zoning Bd. of Appeals of Framingham, 343 Mass. 742, 744-745. Since the case comes here on a statutory report of the material facts without the evidence, the report must "contain every fact necessary to support the decree, from the entry of which no fact not expressly found may be implied." Carilli Constr. Co. v. John Basile Co. Inc. 317 Mass. 726, 727. The fact that the plaintiffs constructed a building in 1952 in contravention of the applicable zoning ordinance does not constitute a condition "especially affecting such parcel." Colabufalo v. Public Bldgs. Commr. of Newton, 336 Mass. 205, 211. A use which exceeds zoning limitations "cannot be made a fulcrum to lift those limitations." Cary v. Board of Appeals of Worcester, 340 Mass. 748, 750. Nor do the facts that there are other nonconforming buildings in the area and that the plaintiffs expended a substantial amount of money justify the granting of a variance. Bicknell Realty Co. v. Board of Appeal of Boston, 330 Mass. 676, 680. Bruzzese v. Board of Appeals of Hingham, 343 Mass. 421, 423-424.

Rarely can a court order the granting of a variance when the board has denied the petition. No person has a legal right to a variance. "If a case should come to us in which an owner had been denied a variance solely upon a legally untenable ground and the board should indicate that except for that ground the variance would have been granted, perhaps the court could give relief." Pendergast v. Board of Appeals of Barnstable, 331 Mass. 555, 559. The board's decision suggests no such untenable ground. Nor does it appear to have been reached by whim or caprice. See Pendergast v. Board of Appeals of Barnstable, supra, page 560. The plaintiffs argue that the board failed to state any ground for its decision other than that the variance is not one which "the Board has authority to grant." But this court has ruled that detailed findings are not required when the board refuses to grant a variance. Cefalo v. Board of Appeal of Boston, 332 Mass. 178, 181. Conceivably a decision of a board might be held to be arbitrary when all the facts presented compelled a finding that each requirement of § 15 had been satisfied, and the board failed to make any findings to support its exercise of discretion in denying the variance. Such a case is not before us.

Cases cited by the plaintiffs where the court has ordered the board to grant a building permit are inapposite. The board has no discretion to deny a building permit on zoning grounds when an applicant has complied with all the applicable zoning by-laws or ordinances. These cases usually arise when the board has misinterpreted the relevant by-law or ordinance. See D'Ambra v. Zoning Bd. of Appeal of Attleboro, 324 Mass. 61.

The trial judge seems to have rested his decision to some extent on estoppel by reason of the fact that the plaintiffs had been granted a building permit by the "appropriate . . . [city] official." This court has held that the doctrine of estoppel cannot stay the hand of a municipality in enforcing its zoning laws. Cochran v. Roemer, 287 Mass. 500, 510. Building Commr. of Medford v. C. H. Co. 319 Mass. 273, 283. Manchester v. Phillips, 343 Mass. 591, 597. And this is the prevailing view elsewhere. See Rathkopf, The Law of Zoning and Planning, c. 67, and cases collected in 119 A.L.R. 1509 et seq. The reasons for the inapplicability of estoppel in cases of this sort have been well stated by the Supreme Court of New Jersey in Zahodiakin Engr. Co. v. Zoning Bd. of Adjustment, 8 N.J. 386, where it was said at page 396, "The want of fundamental power cannot be indirectly supplied by the application of the doctrine of estoppel in pais. The elements of estoppel are wanting. The governmental zoning power may not be forfeited by the action of local officers in disregard of the statute and the ordinance. The public has an interest in zoning that cannot thus be set at naught. The plaintiff landowner is presumed to have known of the invalidity of the exception and to have acted at his peril." This language is pertinent to the case at hand. It follows that the issuance of a building permit and the erection of a building not authorized by the zoning ordinance did not entitle the plaintiffs to a variance by reason of estoppel.

The final decree is reversed and a decree is to be entered stating that the decision of the board did not exceed its authority, that no modification of its decision is required, and that the clerk of the court within thirty days after the entry of the decree send an attested copy thereof to the board.

So ordered.