GILLERMAN, J.

When Michael Corrao (Corrao) died on February 13, 1985, he owned fifty percent of the outstanding capital stock (the stock) of Norwell Mfg. Co., Inc., a Massachusetts corporation (the company); the remaining fifty percent was owned by Cambridge Street Metal Company, Inc. (Cambridge). Harry Indursky (Indursky) was the president and controlling stockholder of Cambridge. On June 25, 1965, twenty years before his death, Corrao had entered into a stock purchase agreement (the agreement) with Cambridge and Indursky which bound Corrao's legal representative, within ten days after her appointment and qualification, to offer to sell to the company all of Corrao's stock in the company, and, within sixty days of receipt of the offer, the agreement bound the company to purchase and pay for Corrao's stock at a price determined by the company's public accountant. When the required offer was not made following Corrao's death, the company and Indursky brought an action for declaratory and injunctive relief to enforce the agreement, including the price of the stock as determined by the accountant. Partial summary judgment was entered establishing the finality of the payment established by the accountant.

The material facts, which are set out in the verified complaint and affidavits, are not in dispute. The agreement provides that the purchase price for Corrao's stock shall be "determined by the [company's] accountant applying the formula set forth in subparagraph (b) of paragraph #3 of this agreement. . . ."

Subparagraph (b) of paragraph #3 provides that the "purchase price per share shall be payable in cash . . . and shall be determined in accordance with the formula below and to be applied by . . . the Certified Public Accountant then employed by Norwell, whose decision as to the purchase price per share shall be conclusive and binding on the parties." The formula then follows:

"1. The purchase price shall be determined by said accountant as of the [date of the death of Corrao]. . . .

"2. Inventory shall be valued at lower of cost or market.

"3. Real estate shall be taken at market value (said value as determined by said accountant to be conclusive and binding).

"4. All other assets at Book Value.

"5. No value shall be given or applied to goodwill.

"6. All liabilities shall be taken at Book Value and without limiting the generality of the foregoing, shall include all liens and encumbrances affecting any of the real estate or equipment.

"7. The Total of subdivision (6) shall be deducted from the sum of the total of matters contained in subdivision (2), (3), and (4) and said figure obtained shall then be divided by the number of shares of stock of Norwell then issued and outstanding and the result shall constitute the purchase price per share."

The formula also excludes from assets the value of life insurance on the life of Corrao.

In spite of the plain terms of the agreement, the stock owned by Corrao at his death was not, as we have said, offered to the company, and on March 27, 1985, suit was brought against Josephine Corrao individually and as executrix of Corrao's estate seeking a declaration of the rights of the parties under the agreement and specific enforcement of its terms. Mrs. Corrao answered the complaint and asserted a variety of counterclaims alleging wrongdoings by the company and Indursky and that the purchase price for the stock had been calculated incorrectly by the accountant.

On June 1, 1985, Laventhol Horwath, the company's public accountant, submitted its "special-purpose statement of assets, liabilities and shareholders' equity of Norwell Mfg. Co., Inc., and the related computation of purchase price per share as of February 13, 1985." The report of the accountant (the special report), which is more fully described below, determined that shareholders' equity was $3,142,639, that 200 shares were issued and outstanding, and that the purchase price per share, therefore, was $15,713.20.

Approximately one year later the parties agreed on a stipulation under the terms of which Corrao's stock was transferred to the company, Mrs. Corrao was paid $1,571,320, the amount determined to be due by the accountant, and Mrs. Corrao waived all her counterclaims against the plaintiffs except that she reserved the counterclaims that (i) the accountant "undervalued the stock under the formula" set forth in the agreement, and (ii) interest is due and payable on all amounts finally determined to be due her.

On September 29, 1986, the plaintiffs moved for partial summary judgment seeking a declaration that the payment established by the accountant was "conclusive and binding" and for dismissal of the reserved counterclaims of the defendant. A judge of the Probate Court, sitting in the Superior Court under statutory authority, allowed the motion on November 3, 1986. The memorandum accompanying the judge's order states that the "parties, in effect, agreed on a method of arbitration to determine the value of this stock. . . . In the absence of fraud or bad faith, neither of which is suggested here, the valuation by the CPA is binding and conclusive on the parties." On October 28, 1988, a judge of the Superior Court, finding no just reason for delay, and as a result of the allowance of plaintiffs' motion for summary judgment, ordered the entry of a final judgment for the plaintiffs on their claims (except the claim for damages) and dismissed the counterclaims of Mrs. Corrao.

In support of their motion for partial summary judgment, the plaintiffs had filed an affidavit of the accountant responsible for the preparation of the special report. The accountant stated that in his opinion the computation of the price per share for the stock, as stated in the special report, was "presented fairly on the basis of the accounting methods described in par. 3(b) of the Stock Purchase Agreement."

The defendant's opposition to the motion was supported principally by an affidavit of her public accountant. He stated that he had been retained by the defendant and that he had reviewed the stock purchase agreement as well as the work papers of the accountant which were prepared in connection with the special report. He concluded that the company's accountant had not followed the formula in three respects. First, the work in process inventory was incorrectly calculated. Second, the value of the real estate was "outrageously low. . . ." Third, the formula required liabilities to be stated at book value, but the company's accountant had, incorrectly, included a liability for a deferred income tax which was not on the books of the company on February 13, 1985.

The plaintiffs respond by arguing that the agreement makes the accountant's determination of price "conclusive and binding" on the parties. In the absence of a showing of fraud or bad faith, the argument continues, asserted errors in the application of the formula are legally irrelevant. Although the first two points made by the defendant's accountant are without merit, we think the third point is justified. Accordingly we modify the partial judgment entered for the plaintiffs.

1. The agreement of June, 1965. As long ago as Palmer v. Clark, 106 Mass. 373 (1871), the Supreme Judicial Court made it clear that a reference to a third person (the appraiser) "to make an appraisement of property and the like" is not a submission to arbitration. Id. at 389. See Eliot v. Coulter, 322 Mass. 86, 89 (1947) (describing Palmer v. Clark, as the "leading case" and pointing out that there is no arbitration when there is "no existing claim to be arbitrated. There [is no arbitration when there is] . . . only a valuation to be made that would in the future prevent a resort to the courts or to technical arbitration"). Where there is no existing claim or controversy, and therefore nothing to be arbitrated, the provisions of G.L.c. 251, §§ 1 et seq. (Uniform Arbitration Act for Commercial Disputes), are inapplicable.

Nevertheless, there are similarities between a submission to an arbitrator and a submission to an appraiser. In the absence of fraud, neither errors of fact nor errors of law are sufficient to set aside the award of an arbitrator. Plymouth-Carver Regional Sch. Dist. v. J. Farmer Co., 407 Mass. 1006, 1007 (1990). Substantially the same rule applies to the award of an appraiser. Ordinarily the judgment of an appraiser "cannot be impeached for mistake arising from error in the judgment of the referee, or in drawing conclusions from evidence and observation. To avoid it, the mistake must be one which shows that he was misled, and so far misapprehended the case that he failed to exercise his judgment upon it. . . ." Palmer v. Clark, supra at 389. More recently the Supreme Judicial Court has said, in a case where the submission to the appraiser was unqualified, that "the correctness of the principles and methods of valuation adopted by the appraisers cannot be inquired into by the courts, in the absence of fraud, corruption, dishonesty or bad faith. . . ." Eliot v. Coulter, 322 Mass. at 91.

But just as an arbitrator may exceed his authority by granting relief which is beyond the scope of the arbitration agreement, Plymouth-Carver Regional Sch. Dist. v. J. Farmer Co., supra at 1007, so too an appraiser can exceed his authority by making an award which is not within the limits of the submission to him. The issue turns on the agreement of the parties. See, as to appraisers, Dynan v. Fritz, 400 Mass. 230, 240 n. 14 (1987). Moreover, it is for the court, not the appraiser, to decide the scope of the submission where that question is in dispute. Ibid.

Appraisers, as we have noted, do not settle disputes; they make factual determinations requiring a special skill or competence ordinarily beyond the abilities of the contracting parties. So, for example, architects and engineers are commonly selected to make judgments on matters within their special training and expertise. See, e.g., Audette v. L'Union St. Joseph, 178 Mass. 113, 115 (1901) (engineer); Acmat Corp. v. Daniel O'Connell's Sons, Inc., 17 Mass. App. Ct. 44, 49 (1983) (architect). Here the parties agreed to rely on the accountant in the calculation of book value, but that reliance, and the submission, were not unqualified. It is clear to us that the contracting parties never intended to be bound by the decision of the appraiser regardless of how he reached his decision. See Dynan v. Fritz, supra at 240 n. 14 ("The agreement . . . certainly does not delegate to the accountant an unreviewable authority to determine the legal consequences of a significant ambiguity in the buy-back agreement"). Compare Grobet File Co. of America, Inc. v. RTC Sys., Inc., 26 Mass. App. Ct. 132, 134 (1988) (suggesting that an arbitrator could not award $100,000 in damages when the contract limited allowable damages to $50,000).

Subparagraph (b) of paragraph 3 provides without ambiguity that the "purchase price per share . . . shall be determined [by the accountant] in accordance with the formula. . . ." It is only a determination which has been arrived at by applying the formula that is entitled to be "conclusive and binding on the parties." The plaintiffs' argument that the decision of the accountant should be enforced because it is "in effect, a binding arbitration," misses the central point that this is an appraisal, not an arbitration, that the parties defined the subject of the submission and that the accountant was not free to depart from that definition. The formula provides, for example, that no value shall be given to good will; had the accountant added value for good will it certainly would have deviated impermissibly from the agreed terms of the submission and thus exceeded its authority. Application of the formula to the determination of price per share is made expressly obligatory on the accountant; adherence to the formula was the understanding that provided the basis for the agreement that the decision of the accountant would be conclusive and binding, and the failure to follow those instructions may call into question the calculation.

2. Claims that the formula was not followed. Mrs. Corrao claims, as we have said, that the company's accountant failed to follow the formula in three respects. First, the affidavit of the accountant for Mrs. Corrao, Andrew P. Donellon, challenged the calculation by the company's accountant of the value of the work-in-process component of inventory which, under the formula, was to be taken at the lower of cost or market. To the agreed work-in-process material cost of $417,897, Donellon added an item he called "estimated labor and overhead" having a value of $250,000, and yielding a total of $667,897. The affidavit also describes the work in process calculation by the accountant for the company; from the item "Retail, per Norwell listing — $417,897," the company accountant deducted 62% for "cost to retail."

The affidavit fails to provide either an explanation of the different accounting treatments, or a statement of reasons why the method employed by the company's accountant may be incorrect. Perhaps Donellon concluded that the accountant erroneously failed to include an appropriate amount of labor and material in arriving at the total value of work in process, but that is speculative and in any event is irrelevant. There is no showing whatsoever that the company's accountant did not follow the formula in this respect. At most the affidavit suggests a disagreement as to the "correct" accounting method of calculating the value of work in process. That, however, is precisely what was entrusted to the judgment of the company's accountant. On this first point, Eliot v. Coulter, 322 Mass. at 91, controls ("the correctness . . . and methods of valuation adopted by the appraisers cannot be inquired into by the courts"). The affidavit has no probative value, and we conclude that this claim has not been adequately supported.

Second, Donellon's affidavit asserts that the "value of the real estate was outrageously low . . . [and] discovery will establish, we believe, that opinion relies [ sic] on a company unfamiliar with the area. . . ." This is not a claim that the formula — which called for the accountant's "conclusive and binding" determination of the market value of real estate — was not followed. It is a more assertion that with a different appraisal the result would be more favorable to Mrs. Corrao. Accordingly there is no merit to this second claim.

The third claim is more complex. The claim is that the company's accountant included a liability for deferred income taxes — $199,555 — which was not otherwise on the books of the company on that date. This was incorrect, Donellon says, because the formula calls for all liabilities to be taken at "book value."

The opinion section of the special report reveals what the accountant did. It states that the special report was prepared "on the basis of accounting practices specified in the Stock Purchase Agreement" (that is, the formula), which "differ in some respects from generally accepted accounting principles. . . ." The upward adjustment of real estate to appraised value is one such deviation, and, the special report says, the "gain resulting from the excess of appraised values over the carrying values [of the real estate] . . . gives rise to a corresponding deferred tax liability." Note 7 to the special report shows the excess of appraised value of land and buildings over carrying value at $561,527, from which the accountant deducted the deferred income tax of $199,555 on the unrealized appreciation, with the difference constituting an increase in shareholders' equity attributable to the appraised value of real estate as required by the formula. The final paragraph of the opinion portion states that the resulting statement of shareholders' equity and the related computation of the purchase price per share "are presented fairly on the basis of accounting [methods] described in . . . [the formula]."

The company's accountant was in error. The required calculation of the purchase price per share (shareholders' equity — assets less liabilities — divided by the number of shares issued and outstanding) is an abstraction; it draws from information contained in the company's books and records (recorded assets and liabilities) and makes only those adjustments called for by the formula. One need only ask: what adjustments? The agreed adjustments were: (i) real estate must be taken at market value; (ii) no value may be assigned to good will (whether or not there is a value for good will for the company); (iii) proceeds of life insurance on the life of Corrao are excluded from assets. The formula does not call for any adjustment to recorded liabilities in order to give effect to a deferred tax liability possibly arising from the write-up of real estate.

It may be that generally accepted accounting principles call for the provision of a deferred tax liability when the write-up of an asset is expected to create taxable income at some future date, see Afterman and Willis, GAAP Practice Manual, § 21.6 (1988), but that is beside the point: the formula does not call for the application of generally accepted accounting principles to the calculation of the price per share, nor does it call for any adjustment to liabilities which might result from the write-up of real estate. Given the clear instruction in the formula to value real estate at market, not historic cost, an adjustment for deferred taxes was foreseeable, and its omission from the formula confirms the intention of the parties to give the Corrao estate the undiminished benefit of the market value of the company's real estate. It is, as we have said, the mutual intent of the parties that controls the outcome; we find no basis for concluding that the parties understood and agreed upon the provision for a deferred tax liability. Compare First Fed. Sav. Loan Assn. of Boston v. State Tax Commn., 372 Mass. 478, 483 (1977) ("We see no basis . . . for assuming that the Legislature intended to import accounting practice into its statutory language. . . .").

As this was an action for declaratory relief, the parties are entitled to a declaration of rights. See Boston v. Keene Corp., 406 Mass. 301, 314 (1989). The judgment below in effect declared that "the valuation by the [company's accountant] is binding and conclusive on the parties." Our decision requires that the judgment be modified to declare that the defendant shall receive from the plaintiff Norwell Mfg. Co., Inc., the amount of $99,777.50, representing fifty percent of the erroneously eliminated sum of $199,555. The defendant is entitled to interest on $99,777.50 at the rate of twelve per cent per annum from July 2, 1986, the date of her stipulation when she first offered the stock to the company and demanded the purchase price. See G.L.c. 231, § 6C. In all other respects the valuation by the company's accountant is binding and conclusive on the parties.

So ordered.