On this appeal from a judgment in amount of $164,431.40 entered January 8, 1975, after a three day bench trial in the Southern District of New York, Charles L. *422Brieant, Jr., District Judge, 387 F.Supp. 1310 (S.D.N.Y. 1974), in a prívate damage action for alleged violations of Sections 10(b) and 14(a) of the Securities Exchange Act of 1934, 15 U.S.C. §§ 78j(b) and 78n(a) (1970), and Rules 10b — 5 and 14a — 9 promulgated thereunder, 17 C.F.R. §§ 240.10b-5 and 240.14a-9 (1975), in connection with a corporate merger, the question which we find to be dispositive is whether the district court erred in awarding damages to plaintiffs upon an estoppel theory, there being no proof of actual damages. For the reasons below, we hold that the district court did err. Accordingly, while we affirm the district court’s dismissal of two claims, we reverse and remand with directions to dismiss the remaining action.

I.

We shall summarize those facts which we believe necessary to an understanding of our ruling on the dispositive question before us. We assume familiarity with the more detailed statement of facts by the district court. 387 F.Supp. 1313-28.

The six named plaintiffs were stockholders of Atron Corporation (Atron). On April 30, 1971, Atron was merged into defendant MDS-Atron, Inc. (MDS), which was a subsidiary of defendant Mohawk Data Sciences Corporation (Mohawk).1 Pursuant to the merger Atron’s former stockholders received one share of Mohawk common stock for every four shares of Atron. Five of the six plaintiffs were among the overwhelming majority of Atron stockholders who voted in favor of the merger. The vote of plaintiff Intercontinental Technology & Natural Resources, S.A. (ITNR) was not cast for or against the merger.2

Plaintiffs acquired their restricted Atron stock directly from Atron in private placements during 1968 and 1969. Atron stock was traded in a thin over-the-counter market. Atron was a small, young company. It was engaged in the manufacture and sale of peripheral computer equipment to computer manufacturers such as Mohawk. Ninety per cent of Atron’s sales were to Mohawk at the time of the merger.

Prior to the instant merger, Atron had taken some preliminary steps with an eye to some form of merger. Nothing had come of these efforts. In January 1971, however, Atron was informed by Mohawk that the latter intended to exercise its contractual right to terminate its agreement with Atron and to begin producing itself the component which had been Atron’s most important product. Two days following Atron’s annual meeting of shareholders which had been attended by Mohawk, Mohawk proposed a merger which was agreed to upon the first and only discussion by Atron.

The January 29 merger agreement, announced the day it was proposed, provided for an exchange of stock at the 4:1 ratio stated above. This reflected the prevailing market price of the stock of the two companies.

The merger agreement was disclosed immediately to the public in a press release. The agreement was approved by Mohawk’s Board of Directors on March 2. It was dated as of March 12. A proxy statement was mailed on April 16 to the Atron stockholders.

Focusing on the Atron stockholders, since their approval is all that we are concerned with here, each of the six named plaintiffs received and read the proxy statement. Five of the six plaintiffs voted in favor of the merger. The merger was approved by the Atron stockholders on April 30 by a 99.7 per cent majority: 924,756 in favor, 3,600 against.

*423Under the law of Minnesota where Atron was incorporated an affirmative vote of two-thirds of Atron’s stockholders was necessary for approval of the merger. More than the statutory majority approved. Also under Minnesota law, as explained in the proxy statement, any dissenting stockholder who voted against the merger and followed the prescribed procedure was entitled to an appraisal of the “fair cash value” of his Atron stock and then was entitled to receive cash in that amount instead of Mohawk stock in exchange for his Atron stock.3 No Atron stockholder sought to exercise his appraisal rights.

The instant action was commenced on May 25, 1972, more than a year after the merger. The theory of the complaint essentially was twofold.

First, under plaintiffs’ “free stock deception” claim, they alleged that they were induced to vote in favor of the merger by a promise that they would receive unrestricted Mohawk stock in exchange for their restricted Atron stock. The district court found against plaintiffs on this claim for lack of proof, including determinations of credibility adverse to plaintiffs. 387 F.Supp. at 1318-24. We affirm the dismissal of this claim as not clearly erroneous.

Second, plaintiffs claimed that material information was omitted from the proxy statement. This claim was based chiefly on allegations that Mohawk had decided, but had not disclosed prior to the Atron stockholders meeting on April 30,1971, to change its fiscal year from one ending July 31 to one ending April 30, to change the system of financing a small portion of its equipment, and to change from the financing method to the operating method of account-

ing for sales of leased equipment to unaffiliated third parties.

It was upon the second theory — alleged omission of material information from the proxy statement — that the district court awarded damages in favor of the five plaintiffs and against the two corporate defendants. It dismissed plaintiff ITNR’s claim against the corporate defendants and the claims of all plaintiffs against the two individual defendants. 387 F.Supp. at 1331-32. See notes 1 and 2 supra.

Defendants Mohawk and MDS appeal from the judgment in amount of $164,-431.40, plus interest at 6% from April 30, 1971, entered against them jointly and severally on January 8, 1975. Plaintiff ITNR cross-appeals from that part of the judgment which dismissed the complaint as to it. We affirm on ITNR’s cross-appeal; but on the appeals of Mohawk and MDS we reverse and remand with directions to dismiss the remaining action.

II.

We turn directly to the issue which we find to be dispositive of this appeal — the estoppel theory which neither side urged upon the district court but upon which the court based its award of damages in the absence of proof of actual damages.

The crux of the court’s decision in this respect is that plaintiffs gave up appraisal rights to the fair cash value of their Atron stock worth $8.60 per share and received in exchange Mohawk stock worth $5.38, thus damaging plaintiffs in amount of $3.22 per Atron share. The manner in which the court arrived at these figures is set forth in the margin.4

Although we would go a long way to prevent escape from liability for the is*424suance of a materially misleading proxy statement, see Mills v. Electric Auto-Lite Co., 396 U.S. 375 (1970);5 J. I. Case Co. v. Borak, 377 U.S. 426 (1964); Gerstle v. Gamble-Skogmo, Inc., 478 F.2d 1281 (2 Cir. 1973), there are limits and plaintiffs have outrun them here. Even if the proxy statement here involved was materially misleading — an issue which we do not reach — we find no basis whatever for the court’s creation sua sponte of an “equitable estoppel” of defendants from asserting that Atron stock did not have a value of $8.60, i. e., one-quarter of the market value of a Mohawk share, on March 12 when the merger agreement was signed. Plaintiffs urge that the court’s remedy was “rescissional in nature”. On the contrary, it strikes us as an attempt to hold defendants not only to a promise they made but to one they did not make, namely, to pay cash in amount of $8.60 per Atron share.

Under elemental principles of equity, “a representation of fact made by a party who relies thereon with the right to so rely may not be denied by the party making the representation if such denial would result in injury or damage to the relying party.” 1 Williston, Contracts § 139, at 601-02 (3d ed. 1954); see Restatement (Second) of Contracts § 90 (Tent.Draft No. 2, 1965). That is the doctrine of equitable estoppel.

In the instant case, at no time did Mohawk represent to the Atron stockholders that their shares had a fair cash value of $8.60 per share. And yet that is the value the district court held that Mohawk is es-topped from denying. The merger was a stock-for-stock exchange, not a stock-for-cash one. Whatever might be said regarding an estoppel approach if the merger had been a stock-for-cash one, we are not called upon to decide that issue. The stock-for-stock exchange here, as defendants point out, was based on the fact of commercial life that paper flows more freely than money. Furthermore, it is not uncommon for a company proposing a merger to offer a price including a premium which reflects a special value of the target company to the company proposing merger or is regarded as a necessary inducement to the voting shareholders of the target company to accept the proposal. We hold that the district court’s award of damages based on a theory of equitable estoppel ignored the facts and is untenable as a matter of law.

This would not end the matter if plaintiff had presented any other competent proof of value. But the district court found that neither side presented persuasive evidence of the true value of Atron common stock as of April 30,1971, contrasted with the market value. 387 F.Supp. at 1329. Rather than rely on that finding, we have made an independent search of the record ourselves to see if there is any proof of actual damages, whether adduced by plaintiffs or by anyone else. We have found none.

Absent the estoppel theory which we reject, our careful examination of the record discloses that plaintiffs failed to prove the value of what they gave up when they voted for, rather than against, the merger. In terms of Minnesota law, note 3 supra, they failed to prove the “fair cash value”, i. e., the appraisal value, of their holdings of Atron stock as of the date the merger was authorized. Loss of the value of their ap*425praisal rights is the underpinning of their claim of damages. In short, they failed to prove what actual damages, if any, they sustained as a result of the exchange. Note 5 supra.

If such appraisal rights had any value, we have no doubt that such value could have been proven in accordance with well recognized corporate appraisal methods. There is no dearth of corporate valuation experts. They testify every day in various contexts, as indicated by many recent decisions of our Court.6

Since plaintiffs had ample opportunity, but simply declined, to adduce proof of what actual damages, if any, they sustained as a result of the exchange, we direct the district court to dismiss the action.

In view of our holding on the dispositive issue of damages, we do not reach any of the other claims of error raised by defendants or the cross-appeal of plaintiff ITNR from the dismissal of its complaint.

We affirm the district court’s dismissal of plaintiffs’ “free stock deception” claim for failure of proof and its dismissal of the complaint as to plaintiff ITNR; but we reverse and remand with directions to dismiss the remaining action against defendants Mohawk and MDS for failure to prove actual damages.

Affirmed in part; reversed in part and remanded with directions.