The plaintiffs were stockholders in Boston Garden Arena Corporation (Garden Arena), a Massachusetts corporation whose stockholders voted on July 19,1973, to merge with the defendant corporation in circumstances which entitled each plaintiff to "demand payment for his stock from the resulting or surviving corporation and an appraisal in accordance with the provisions of [G. L. c. 156B, §§ 86-98].” G. L. c. 156B, § 85, as amended by St. 1969, c. 392, § 22. The plaintiffs commenced this action under G. L. c. 156B, § 90, seeking a judicial determination of the "fair value” of their shares "as of the day preceding the date of the vote approving the proposed corporate action.” 2 G. L. c. 156B, § 92, inserted by *722 St. 1964, c. 723, § 1. Each party has appealed from a judgment determining the fair value of the plaintiffs’ stock. We granted the defendant’s application for direct appellate review.
On July 18, 1973, Garden Arena owned all the stock in a subsidiary corporation that owned both a franchise in the National Hockey League (NHL), known as the Boston Bruins, and a corporation that held a franchise in the American Hockey League (AHL), known as the Boston Braves. Garden Arena also owned and operated Boston Garden Sports Arena (Boston Garden), an indoor auditorium with facilities for the exhibition of sporting and other entertainment events, and a corporation that operated the food and beverage concession at the Boston Garden. A considerable volume of documentary material was introduced in evidence concerning the value of the stock of Garden Arena on July 18, 1973, the day before Garden Arena’s stockholders approved the merger. Each side presented expert testimony. The judge gave consideration to the market value of the Garden Arena stock, to the value of its stock based on its earnings, and to the net asset value of Garden Arena’s assets. Weighting these factors, the judge arrived at a total, per share value of $75.27. 3
Value Weight Result
Market Value: $ 26.50 X 10% = $ 2.65
Earnings Value: $ 52.60 X 40% = $21.04
Net Asset Value: $103.16 X 50% = $51.58
Total Value Per Share: $75.27
*723 In this appeal, the parties raise objections to certain of the judge’s conclusions. We shall expand on the facts as necessary when we consider each issue. We conclude that the judge followed acceptable procedures in valuing the Garden Arena stock; that his determinations were generally within the range of discretion accorded a fact finder; but that, in three instances, the judge’s treatment of the evidence was or may have been in error and, accordingly, the case should be remanded to him for further consideration of those three points.
General Principles of Law
The statutory provisions applicable to this case were enacted in 1964 as part of the Massachusetts Business Corporation Law. St. 1964, c. 723, § 1. The appraisal provisions (G. L. c. 156B, §§ 86-98) were based on a similar, but not identical, Delaware statute (Del. Code tit. 8, § 262). See Notes by Boston Bar Committee — 1964, M.G.L.A. c. 156B, §§ 86-92, 94-97. In these circumstances, consideration of the Delaware law, including judicial decisions, is appropriate, but in no sense should we feel compelled to adhere without question to that law, which has been in the process of development since our enactment of G. L. c. 156B in 1964. We do not perceive a legislative intent to adopt judicial determinations of Delaware law made prior to the enactment of G. L. c. 156B and certainly no such intent as to judicial interpretations made since that date. 4
The Delaware courts have adopted a general approach to the appraisal of stock which a Massachusetts judge *724 might appropriately follow, as did the judge in this case. The Delaware procedure, known as the "Delaware block approach,” calls for a determination of the market value, the earnings value, and the net asset value of the stock, followed by the assignment of a percentage weight to each of the elements of value. See generally, Note, Valuation of Dissenters’ Stock under Appraisal Statutes, 79 Harv. L. Rev. 1453, 1456-1471 (1966).
There have been no appellate decisions in this State concerning the appraisal of stock since the present appraisal statute was enacted, and there were few under the previously applicable, somewhat similar, statute.
5
See
Martignette
v.
Sagamore Mfg. Co.,
With these considerations in mind, we turn to the specific issues that have been argued on appeal, considering, in order, the judge’s determination of market value, earnings value and net asset value of the stock; his decision concerning the weighting of these components; the defendant’s objection to the consideration of certain evidence; and, finally, the judge’s decision on the rate of interest to be allowed to the plaintiffs.
*725 Market Value
The judge was acting within reasonable limits when he determined that the market value of Garden Arena stock on July 18, 1973, was $26.50 a share. Each party challenges this determination. The plaintiffs’ contention is that market value should be disregarded because it was not ascertainable due to the limited trading in Garden Arena stock. 6 The defendant argues that the judge was obliged to reconstruct market value based on comparable companies, and, in doing so, should have arrived at a market value of $22 a share.
Market value may be a significant factor, even the dominant factor, in determining the "fair value” of shares of a particular corporation under G. L. c. 156B, § 92. Shares regularly traded on a recognized stock exchange are particularly susceptible to valuation on the basis of their market price, although even in such cases the market value may well not be conclusive. See
Martignette
v.
Sagamore Mfg. Co.,
In this case, Garden Arena stock was traded on the Boston Stock Exchange, but rarely. Approximately ninety per cent of the company’s stock was held by the con *726 trolling interests and not traded. Between January 1, 1968, and December 4, 1972, 16,741 shares were traded. During this period, an annual average of approximately 1.5% of the outstanding stock changed hands. In 1972, 4,372 shares were traded at prices ranging from $20.50 a share to $29 a share. The public announcement of the proposed merger was made on December 7, 1972. The last prior sale of 200 shares on December 4, 1972, was made at $26.50 a share. The judge accepted that sale price as the market price to be used in his determination of value.
The judge concluded that the volume of trading was sufficient to permit a determination of market value and expressed a preference for the actual sale price over any reconstruction of a market value, which he concluded would place "undue reliance on corporations, factors, and circumstances not applicable to Garden Arena stock.” The decision to consider market value and the market value selected were within the judge’s discretion.
Valuation Based on Earnings
The judge determined that the average per share earnings of Garden Arena for the five-fiscal-year period which ended June 30, 1973, was $5.26. To this amount he applied a factor, or multiplier, of 10 to arrive at $52.60 as the per share value based on earnings.
Each party objects to certain aspects of this process. We reject the plaintiffs’ argument that the judge could not properly use any value based on earnings and also reject the parties’ various challenges to the judge’s method of determining value based on earnings.
Delaware case law, which, as we have said, we regard as instructive but not binding, has established a method of computing value based on corporate earnings. The appraiser generally starts by computing the average earnings of the corporation for the past five years. 8 Universal
*727
City Studios, Inc.
v.
Francis I. duPont & Co.,
The judge chose not to place "singular reliance on comparative data preferring to choose a multiplier based on *728 the specific situation and prospects of the Garden Arena.” He weighed the favorable financial prospects of the Bruins: the popularity and success of the team, the relatively low average age of its players, the popularity of Bobby Orr and Phil Esposito, the high attendance record at home games (each home team retained all gate receipts), and the advantageous radio and television contracts. On the other hand, he recognized certain risks, the negative prospects: the existence of the World Hockey Association with its potential, favorable impact on players’ bargaining positions, and legal threats to the players’ reserve clause. He concluded that a multiplier of 10 was appropriate. There was ample evidentiary support for his conclusion. He might have looked to and relied on price-earnings ratios of other corporations, but he was not obliged to.
The judge did not have to consider the dividend record of Garden Arena, as the defendant urges. Dividends tend to reflect the same factors as earnings and, therefore, need not be valued separately., See
Felder
v.
Anderson, Clayton & Co.,
The judge did not abuse his discretion in including expansion income (payments from teams newly admitted to the NHL) received during two of the five recent fiscal years. His conclusion was well within the guidelines of decided cases. See
Gibbons
v.
Schenley Indus., Inc.,
Valuation Based on Net Asset Value
The judge determined total net asset value by first valuing the net assets of Garden Arena apart from the Bruins franchise and the concession operations at Boston Garden. He selected $9,400,000 (the June 30, 1973, book value of Garden Arena) as representing that net asset value. Then, he added his valuations of the Bruins franchise ($9,600,000) and the concession operation ($4,200,-000) to arrive at a total asset value of $23,200,000, or $103.16 a share. 10
The parties raise various objections to these determinations. The defendant argues that the judge included certain items twice in his valuation of the net assets of Garden Arena and that he should have given no separate value to the concession operation. The plaintiff argues that the judge undervalued both the Boston Garden and the value of the Bruins franchise.
The defendant objects to the judge’s refusal to deduct $1,116,000 from the $9,400,000 that represented the net asset value of Garden Arena (exclusive of the net asset value of the Bruins franchise and the concession operation). The defendant’s expert testified that the $9,400,-000 figure included $1,116,000 attributable to the good will of the Bruins, net player investment, and the value *730 of the AHL franchise. The judge recognized that the items included in the $1,116,000 should not be valued twice and seemingly agreed that they would be more appropriately included in the value of the Bruins franchise than in the $9,400,000. He was not plainly wrong, however, in declining to deduct them from the $9,400,000, because, as is fully warranted from the testimony of the defendant’s expert, the judge concluded that the defendant’s expert did not include these items in his determination of the value of the Bruins franchise. 11 The defendant’s expert, whose determination the judge accepted, arrived at his value of the Bruins franchise by adding certain items to the cost of a new NHL franchise, but none of those items included good will, net player investment, or the value of an AHL franchise. Acceptance of the defendant’s argument would have resulted in these items being entirely omitted from the net asset valuation of Garden Arena. 12
The plaintiffs object that the judge did not explicitly determine the value of the Boston Garden and implicitly undervalued it. Garden Arena had purchased the Boston Garden on May 25, 1973, for $4,000,000, and accounted for it on the June 30, 1973, balance sheet as a $4,000,000 asset with a corresponding mortgage liability of $3,437,-065. Prior to the purchase, Garden Arena had held a long-term lease which was unfavorable to the owner of the Boston Garden. 13 The existence of the lease would tend to depress the purchase price.
*731 The judge stated that the $9,400,000 book value "includes a reasonable value for Boston Garden” (emphasis supplied). He did not indicate whether, if he had meant to value the Boston Garden at its purchase price (with an adjustment for the mortgage liabilities), he had considered the effect the lease would have had on that price. While we recognize that the fact-finding role of the judge permits him to reject the opinions of the various experts, 14 we conclude, in the absence of an explanation of his reasons, that it is possible that the judge did not give adequate consideration to the value of the Garden property. The judge should consider this subject further on remand.
A major area of dispute was the value of the Bruins franchise. The judge rejected the value advanced by the plaintiffs’ expert ($18,000,000), stating that "[although the defendant’s figure of [$9,600,000] seems somewhat low in comparison with the cost of expansion team franchises,
the Court is constrained
to accept defendant’s value as it is the more creditable and legally appropriate expert opinion in the record” (emphasis supplied). Although the choice of the word "constrained” may have been inadvertent, it connotes a sense of obligation. As the trier of fact, the judge was not bound to accept the valuation of either one expert or the other. He was entitled to reach his own conclusion as to value.
Loschi
v.
Massachusetts Port Auth.,
*732 Because the judge may have felt bound to accept the value placed on the Bruins franchise by the defendant’s expert, we shall remand this case for him to arrive at his own determination of the value of the Bruins franchise. He would be warranted in arriving at the same valuation as that advanced on behalf of the defendant, but he is not obliged to do so.
The defendant argues that, in arriving at the value of the assets of Garden Arena, the judge improperly placed a separate value on the right to operate concessions at the Boston Garden. We agree with the judge. The fact that earnings from concessions were included in the computation of earnings value, one component in the formula, does not mean that the value of the concessions should have been excluded from the computation of net asset value, another such component.
The value of the concession operation was not reflected in the value of the real estate. Real estate may be valued on the basis of rental income, but it is not valued on the basis of the profitability of business operations within the premises. See
Amory
v.
Commonwealth,
We do conclude, however, that the judge may have felt unnecessarily bound to accept the plaintiffs’ evidence of
*733
the value of the concession operation. He stated that "since the defendant did not submit evidence on this issue, the Court will accept plaintiffs’ expert appraisal of the value of the concession operation.” Although the judge did not express the view that he was "constrained” to accept the plaintiffs’ valuation, as he did concerning the defendant’s valuation of the Bruins franchise, he may have misconstrued his authority on this issue. The judge was not obliged to accept the plaintiffs’ evidence at face value merely because no other evidence was offered. See
Martin
v.
Otis,
On remand, the judge should reconsider his determination of the value of the concession operation and exercise his own judgment concerning the bases for the conclusion arrived at by the plaintiffs’ expert. However, the evidence did warrant the value selected by the judge, and no reduction in that value is required on this record.
Weighting of Valuations
The judge weighted the three valuations as follows:
Market Value — 10%
Earnings Value — 40%
Net Asset Value — 50%
We accept these allocations as reasonable and within the range of the judge’s discretion.
Any determination of the weight to be given the various elements involved in the valuation of a stock must be based on the circumstances.
Heller
v.
Munsingwear, Inc.,
The judge might have reached different conclusions on this record. He was not obliged, however, to reconstruct market value and, as the defendant urges, attribute 50% weight to it. Nor was he obliged, as the plaintiffs argue, to consider only net asset value. See
Martignette
v.
Sagamore Mfg. Co.,
Although we would have found no fault with a determination to give even greater weight to the price per share based on the net asset value of Garden Arena, the judge was acting within an acceptable range of discretion in selecting the weights he gave to the various factors.
Evidentiary Objections
The defendant objects to the introduction and consideration of evidence of events arising after the statutory valuation date. The judge carefully noted his statutory obligation to value the shares "as of the day preceding the date of the vote approving the proposed corporate action” and "exclusive of any element of value arising from the expectation or accomplishment of the proposed corporate action.” G. L. c. 156B, § 92. Much of the evidence to which the defendant objects was presented to the judge by stipulation, but without a concession as to its relevance or materiality. Obviously, the judge properly received the stipulated facts and documents. Some of the challenged evidence was withdrawn; some did not relate to post-July 18, 1973, events; and some was duplicative. Even more significant is the plain fact that there is no showing that the judge relied on any evidence of events occurring after July 18, 1973, or on any expert opinion that was based on any such events.
*735 Interest Allowance
The defendant objects to the judge’s determination to award interest at 8% per annum. It does not object to the judge’s decision to award interest, a matter within his discretion (see G. L. c. 156B, §§ 92 and 95), nor to his decision to compound interest annually. The judge heard evidence specifically directed toward the question of the appropriate rate of interest. The defendant’s own witness testified on cross-examination that a prudent investment in corporate bonds, rated AAA by Moody’s, would have yielded interest in excess of 8% uncompounded. The amount selected fairly compensated the plaintiffs for their inability to use the money during the period in question, a factor which the judge fairly could consider, and the judge reasonably could have concluded that 8% per annum reflected "the rate of interest at which a prudent investor could have invested money.”
Universal City Studios, Inc.
v.
Francis I. duPont & Co.,
Conclusion
We have concluded that the judge’s method of valuing the Garden Arena stock was essentially correct. In this opinion, we have indicated, however, that the case should be remanded to him for clarification and further consideration on the record of three matters: his valuation of the Boston Garden, the Bruins franchise, and the concession operation.
So ordered.
Notes
The plaintiffs took all the necessary, preliminary steps to preserve their rights. Each plaintiff objected in writing to the proposed merger; *722 none of their shares was voted in Favor of the proposed corporate action (see G. L. c. 156B, § 86); each plaintiff seasonably demanded in writing payment from the defendant for the fair value of his stock (see G. L. c. 156B, § 89); and no agreement as to that fair value was reached within thirty days of the demand (see G. L. c. 156B, § 90).
The judge determined the market value, earnings value, and net asset value of the stock and then weighted these values as follows:
This is not a case in which the statute of another jurisdiction was subsequently enacted here. Compare
Rollins Environmental Servs., Inc.
v.
Superior Court,
Under the previously applicable statute, a panel of three appraisers (rather than a judge) valued the stock. See G. L. c. 156, § 46.
This argument also bears on the relative weight to be assigned to market value as against net asset value and earnings value, a subject we shall consider subsequently.
The Delaware cases require the reconstruction of market value only when the actual market value cannot be determined and a hypothetical market value can be reconstructed. Compare
Application of Del. Racing Ass’n,
A 1976 amendment to the Delaware statute requires the court to appraise the stock rather than appoint an appraiser. 60 Del. Laws c. 371, Del. Code tit. 8, § 262(f).
Although Delaware courts have relied on, and continue to rely on, Professor Dewing’s capitalization chart (see 1 A.S. Dewing, The Financial Policy of Corporations 390-391 [5th ed. 1953]), they have recognized that it is somewhat outdated and no longer the "be-all and end-all” on the subject of earnings value. See
Universal City Studios, Inc.
v.
Francis I. duPont & Co., supra
at 219;
Swanton
v.
State Guar. Corp.,
$23,200,000 -f- 224,892 (the number of outstanding shares).
The defendant makes no special argument concerning the judge’s failure to deduct certain relatively minor, intangible assets, including merger costs.
One of the points on which we shall remand this case is the valuation of the Bruins franchise. Since, as discussed below, the judge need not have felt constrained to accept the defendant’s expert’s opinion on this issue, on remand he will be free to determine the value of the franchise based on such evidence as he chooses to accept. Assignment of a different value to the franchise may require an adjustment in the net asset value of Garden Arena if the franchise value determined by the judge includes some or all of the items supposedly included in the $1,116,000.
The lease, which ran until June 1, 1986, contained a fixed max *731 imum rent and an obligation on the lessee to pay only two-thirds of any increase in local real estate taxes. In a period of inflation and rising local real estate taxes, the value of the lease to the lessor was decreasing annually.
The lowest value expressed by any expert for the plaintiffs was $8,250,000 (exclusive of mortgage liabilities), based on depreciated reproduction cost. The defendant offered no testimony concerning the value of the property on July 18, 1973.