Nolan, J.

The plaintiffs, former minority shareholders of the defendant corporation, appeal from a judgment entered against them after a trial before a judge of the Superior Court. Their suit challenged actions taken by the five majority shareholders, who also were named as defendants, which resulted in the forced redemption of all minority stock. On appeal, the plaintiffs argue that (1) the trial judge erred in ruling that the five majority shareholders, who also constituted the entire board of directors of Hycor, Inc., did not violate their fiduciary duty of loyalty to the minority shareholders when they effectuated a “recapitalization” of the corporation; and (2) the trial judge erred in ruling that the five dollar per share price, paid to former minority shareholders for their stock, was “consistent with various indicia used to determine the value of closely-held stock.” For the reasons set forth below, we reverse and remand the case for further consideration of the price issue.

The relevant facts may be summarized as follows. Hycor, Inc. (Hycor), is a Massachusetts corporation that was organized in 1967 by the five individual defendants (the majority shareholders). Each of the majority shareholders has been a member of Hycor’s board of directors, and an employee of the corporation, since its organization. Hycor’s business primarily involves general scientific research and development in the field of military defense. Hycor specializes in the design and manufacture of electronic radar and optical countermeasure systems.

The majority shareholders and their family members owned all of Hycor’s stock from May, 1967, when the corporation was organized, until February, 1969. At that time, Hycor made *217 a public offering of 75,000 shares of stock, at four dollars a share, in an effort to raise capital. After the public offering, there were 525,000 shares of stock issued and outstanding. The majority shareholders and their families owned approximately 440,000 shares, or eighty-five percent, of the outstanding stock. The stock owned by the majority shareholders was not registered under the Federal Securities Act of 1933, and therefore, sale of this stock was restricted. A notation to this effect appeared on the stock certificates owned by the majority shareholders.

Between 1967 and 1980, Hycor was profitable in every fiscal year except one, 1971. In June of 1979, discussions took place between some of the majority shareholders and Hycor’s corporate counsel. These discussions concerned the possibility of the defendants’ acquiring 100 per cent ownership of the Hycor stock. On February 4, 1980, the majority shareholders, acting as directors of Hycor, mailed a written “Notice of Special Meeting of Stockholders” to be held at Hycor’s offices on February 13, 1980. The notice stated that the purpose of the meeting was to vote on a recapitalization proposal. Under the terms of this proposal, Hycor’s articles of organization would be amended to reduce the authorized capital stock from two million shares with a par value of one cent, to five hundred shares, with a par value of forty dollars. In effect, each “old” share would be reduced to 1/4,000 of a “new” share. Furthermore, no fractional shares of Hycor stock would be recognized after the recapitalization. Each holder of a fractional share would receive five dollars upon surrender of each “old” share certificate.

A letter from defendant Hyman, as president of Hycor, accompanied this notice. Hyman stated the reasons for the proposed recapitalization to be “the somewhat disappointing market history of the stock” and that “dividends . . . have not represented a significant return on a $4.00 investment.” He indicated that the board of directors had no plans to increase dividends. Hyman also noted that there had been very limited trading in the stock.

*218 On February 13, 1980, there were 517,000 shares of Hycor stock issued and outstanding. Approximately 81 per cent of these shares were owned by the majority shareholders and their families. The remaining shares were owned by 331 shareholders (the minority shareholders). Each minority shareholder owned less than 4,000 shares of stock. The special meeting of shareholders was held on this date. The four plaintiffs and one other minority shareholder appeared at the meeting and objected to the recapitalization proposal and the offer price of five dollars per share. Each of the named plaintiffs voted against the proposed recapitalization. The majority shareholders voted in favor of the plan; therefore, the change in the articles of organization was approved.

On April 24, 1980, the minority shareholders commenced this action. They alleged that the defendants had acted fraudulently, and had misrepresented the basis for the proposed amendment to the articles of organization in order to induce the plaintiffs to approve the change. The plaintiffs also alleged that the actions of the defendants constituted a breach of the fiduciary duty that the defendants owed to the corporation’s minority shareholders, and that the defendants failed to give proper notice to the minority shareholders as required by G. L. c. 156B, § 87. The plaintiffs sought an appraisal of the fair market value of their shares in Hycor on the date that the amendments to the Articles of Organization became effective. They asked that damages be awarded to reflect accurately this value. Alternatively, the plaintiffs asked that the vote of the shareholders be declared a nullity and set aside, arguing that the actions of the majority constituted a breach of fiduciary duty and, furthermore, lacked a fundamental corporate purpose. The plaintiffs also asked the court to award punitive damages, costs, interest, and reasonable attorneys’ fees.

The plaintiffs filed a motion under Mass. R. Civ. P. 23, 365 Mass. 767 (1974), to have their suit certified as a class action. The defendants opposed the class action certification and moved"for dismissal of the action under Mass. R. Civ. P. 9 (b), 365 Mass. 751 (1974), and 37, as amended, 390 Mass. 1208 (1984), or, alternatively, summary judgment pursuant to *219 Mass. R. Civ. P. 56, 365 Mass. 824 (1974). A judge of the Superior Court denied the defendants’ motion to dismiss and motion for summary judgment. He granted the plaintiffs’ motion for class action certification, except as to the count in the plaintiffs’ complaint seeking an independent appraisal of the stock’s value under G. L. c. 156B. He noted that only those stockholders who did not vote in favor of the proposal would be proper plaintiffs in such an action. He stated that this number was too small to warrant certification on this count. One of the minority shareholders, Albert A. Carr, was designated as class representative and the case proceeded as a class action under the counts for fraud and breach of fiduciary duty.

After trial, the judge ordered judgment entered for the defendants. He refused to find that “[tjhere was no legitimate business purpose for the recapitalization,” characterizing the plaintiffs’ assertions to this effect as “[ujnsubstantiated by the evidence.” The judge denied the plaintiffs’ request for findings that the procedure used by the majority shareholders to effectuate the recapitalization was “unfair and a clear abuse of corporate power and control.” Furthermore, he was not persuaded that “[ajny arguable business purpose for the recapitalization could have been achieved by less drastic alternatives.” Finally, he ruled that the five dollars per share price offered to the minority shareholders “was fair and reasonable and consistent with various indicia used to determine the value of closely held stock.”

1. Validity of the recapitalization. The plaintiffs claim that the judge implicitly ruled that, as a matter of law, the recapitalization was fair and not an abuse of corporate power. They challenge this ruling, arguing that it constituted judicial approval of patently wrongful conduct by the majority shareholders, who violated their fiduciary duty of loyalty to the minority shareholders. Additionally, the plaintiffs argue that the ruling implies that the recapitalization was not a “freezing-out” of minority interests. The plaintiffs conclude that the judge’s ruling was “manifest error.”

A. Statutory basis for recapitalization. The minority shareholders characterize the actions of the majority sharehold *220 ers as a “freeze out” of minority shareholders which lacked a legitimate business purpose. We turn first to the statutory provisions cited by the majority shareholders as authorizing the transaction at issue. General Laws c. 156B, § 71, as appearing in St. 1981, c. 298, § 1, provides, in relevant part, that “[a] corporation may . . . authorize, at a meeting duly called for the purpose, by vote of two-thirds of each class of stock outstanding and entitled to vote thereon or, if the articles of organization so provide, by vote of a lesser proportion but not less than a majority of each class of stock outstanding and entitled to vote thereon, any amendment of its articles of organization; provided, only, that any provision added to or changes made in its articles of organization by such amendment could have been included in, and any provision deleted thereby could have been omitted from, original articles of organization filed at the time of such meeting.” Section 28 of that chapter permits a corporation to issue fractional shares of stock. The statute also authorizes the payment of cash in lieu of fractional share interests.

Pursuant to these statutory provisions, the majority shareholders amended the corporation’s articles of organization, effectuating a recapitalization of Hycor and authorizing the payment of cash in exchange for fractional shares. This type of transaction, commonly described as a “reverse stock split,” is one method employed by majority shareholders to eliminate public ownership in a company. See Note, Going Private: An Analysis of Federal and State Remedies, 44 Fordham L. Rev. 796, 798-799 (1976).

The defendants argue that they proceeded in accordance with the applicable corporate statutes in their attempt to return Hycor to private status. In Teschner v. Chicago Title & Trust Co., 59 Ill. 2d 452, 457 (1974), appeal dismissed, 422 U.S. 1002 (1975), the Hlinois Supreme Court considered whether the defendants had proceeded under the provisions of the Illinois Business Corporation Act in amending its articles of incorporation and reclassifying stock for the purpose of eliminating fractional shares. That court accepted the defendants’ interpretation of the relevant statutory provisions as authorizing their *221 actions. The court stated that “[a]t common law the unanimous consent of the stockholders of a corporation was required to make fundamental changes in the corporation. To provide needed flexibility and to remove what was in effect a power of veto held by a dissenting minority, legislatures authorized the making of corporate changes by majority vote.” Id. at 456. The court concluded that as a general rule, absent fraud, “interests of minority shareholders can be terminated” under Illinois law. Id. We agree with the rationale underlying this conclusion. Setting aside the issues of fairness of price and lack of corporate purpose, which we discuss below, we decide that the majority shareholders acted in compliance with the relevant portions of the Massachusetts corporation law when they effectuated the transaction at issue.

B. Judicial review of the transaction. Having decided that the transaction, on its face, was permissible under the provisions of the statute governing Massachusetts corporations, we turn to the plaintiffs’ claims of breach of fiduciary duty and unfairness. Despite apparent compliance with statutory requirements, a transaction such as the one at issue is still subject to judicial scrutiny on these grounds. Cf. Clark v. Pattern Analysis & Recognition Corp., 87 Mise. 2d 385, 390 (N.Y. Sup. Ct. 1976). At this point, however, it is not enough for those challenging such a transaction merely to label it a “freeze-out.” See Tanzer Economic Assocs. v. Universal Food Specialties, Inc., 87Mise. 2d 167,175 (N.Y. Sup. Ct. 1976). “Freeze-outs, by definition, are coercive: minority shareholders are bound by majority rule to accept cash or debt in exchange for their common shares, even though the price they receive may be less than the value they assign to these shares. But this alone does not render freezeouts objectionable.” Brudney and Chirelstein, A Restatement of Corporate Freezeouts, 87 Yale L.J. 1354, 1357 (1978). At the same time, however, we recognize that courts must avoid an “automatic stamp of approval of that which is manifestly inequitable.” Tanzer, supra.

We begin our analysis by considering the nature of the duty that the defendants owed to the plaintiffs under these circumstances. The plaintiffs contend that Hycor was a close corporation, and thus the defendants, as directors and majority *222 shareholders, owed the plaintiffs a duty of “utmost good faith and loyalty.” Donahue v. Rodd Electrotype Co. of New England, Inc., 367 Mass. 578, 593 (1975). The defendants argue that Hycor was not a close corporation, and suggest that the defendants, as directors and stockholders of Hycor, were required to act in good faith and with inherent fairness. The defendants further state, however, that even if Hycor were a close corporation, the defendants met their burden of proving that they acted with the utmost good faith and loyalty.

In ruling on the fairness of the price that the defendants offered to the plaintiffs in exchange for their shares of stock, the judge referred to “indicia used to determine the value of closely held stock.” It appears, therefore, that he considered Hycor to be a close corporation. We need not decide this issue.

In Donahue v. Rodd Electrotype Co. of New England, Inc., supra at 593, we held that stockholders in a close corporation owe one another a duty of “utmost good faith and loyalty.” The test to be applied when minority shareholders in a close corporation bring suit against the majority alleging a breach of the strict faith duty owed to them by the majority is “whether the controlling group can demonstrate a legitimate business purpose for its action.” Wilkes v. Springside Nursing Home, Inc., 370 Mass. 842, 851 (1976). Once the majority advances such a purpose, it is incumbent upon the minority shareholders to establish that the majority could have achieved the same legitimate objective through an alternative course of action less harmful to the minority’s interest. Id. at 851-852. In Wilkes, however, we expressed our concern that “untempered application of the strict good faith standard enunciated in Donahue [in some instances] will result in the imposition of limitations on legitimate action by the controlling group in a close corporation which will unduly hamper its effectiveness in managing the corporation in the best interests of all concerned.” Id. at 850.

In the case before us, the judge ruled that the evidence fell short of substantiating the plaintiffs’ claim that the recapitalization was not designed to achieve a legitimate business purpose. We find no error in this ruling. The evidence presented by the defendants on this issue included the testimony of *223 Hycor’s president, Hyman, and its corporate counsel, Mr. Butterworth. Hyman testified that the main reason behind the recapitalization was not to eliminate all the public stockholders, but was related to the “dreadful market history of the stock.” He stated that, while Hycor had the responsibilities of a public company, it did not enjoy the benefits of such status. Specifically, he noted the lack of a ready market for Hycor stock. Mr. Butterworth’s testimony supported these assertions. We are satisfied that, based upon the evidence before him, the judge’s decision was proper.

In the judge’s opinion, the plaintiffs failed to establish that “[a]ny arguable business purpose for the recapitalization could have been achieved by less drastic alternatives.” On appeal, the plaintiffs suggest that the “business purpose” at issue was avoiding the annoyance of telephone calls directed to the company’s president concerning the purchase and sale of Hycor stock. They argue that less drastic means existed to eliminate this problem. However, the plaintiffs’ argument ignores evidence that Hycor’s status as a public company required the company to comply with various statutory duties, yet the company did not enjoy a ready market for its stock. We agree that the plaintiffs failed to cony their burden of establishing that less drastic alternatives were available to effectuate the defendants’ legitimate business purpose.

2. Fairness of price. The plaintiffs challenge the judge’s finding that the five dollars per share price offered to minority shareholders was “consistent with various indicia used to determine the value of closely held stock.” They argue that the stock valuation method employed by the defendants’ expert witness, whose testimony the judge apparently accepted, is obsolete.

We recognize that “[vjaluation is a question of fact calling for the considered judgment of the trier of fact whose determination should not be disturbed unless clearly erroneous.” Northern Natural Gas Co. v. United States, 470 F.2d 1107,1110 (8th Cir.), cert. denied, 412 U.S. 939 (1973). In the present case, however, the judge did not describe the facts supporting his conclusion that the price was fair, nor did he indicate what test he employed in making this decision. In the absence of any indication of the basis of the judge’s finding, we are unable to determine whether it was erroneous.

*224 Massachusetts Rule of Civil Procedure 52(a), 365 Mass. 816 (1974), provides that “[i]n all actions tried upon the facts without a jury, the court shall find the facts specially and state separately its conclusions of law thereon.” The rule “does not require extensive detail, but does impose on the judge an independent duty to articulate the essential grounds of his decision.” Schrottman v. Barnicle, 386 Mass. 627, 638 (1982). “The nature and exactness of the findings required depends on the circumstances of the particular case.” Kelley v. Everglades Drainage Dist., 319 U.S. 415, 419 (1943) (construing parallel Federal rule). After reviewing the record before us, we deem it necessary to remand this case so that the judge may explicate the grounds for his conclusion that the price offered by the defendants was fair and reasonable. We are unable, on this record, to ascertain the basis for the judge’s conclusion.

Because the issue of the continuing validity of “Delaware block method” of stock valuation is likely to arise on remand, we express our opinion on this matter. We do not agree that the “Delaware block method” for valuing closely held stock, as set forth in our decision in Piemonte v. New Boston Garden Corp., 377 Mass. 719 (1979), is outmoded. Citing Weinberger v. UOP, Inc., 457 A.2d 701 (Del. 1983), the plaintiffs contend that the Delaware Supreme Court has rejected this valuation method. The Weinberger court stated this method is outmoded “to the extent it excludes other generally accepted techniques used in the financial community and the courts” and that it would no longer “exclusively control such proceedings” (emphasis added). Weinberger, supra at 712-713. We need not accept judicial interpretations of Delaware law made subsequent to our Legislature’s adoption of c. 156B. Id. at 723. In any event, we have never held that the Delaware block method is the only approach that a judge may employ in valuing stock. In Piemonte, we stated that a judge “might appropriately follow” this general approach. Id. at 723-724.

We remand the case, solely with respect to the fairness of the price, for proceedings consistent with this opinion.

So ordered.