UNITED STATES COURT OF APPEALS FOR THE SEVENTH CIRCUIT 
768 F.2d 942; 1985 U.S. App. LEXIS 20986

 The Mid-City National Bank of Chicago was merged into Mid-City Bank, N.A., which immediately became a subsidiary of Mid-Citco, a newly formed bank holding company. All three entities are under common ownership, the purpose of the chain of transactions being simply to enable Mid-City National Bank to operate in the bank holding company form. However, the first step -- the merger of Mid-City National Bank into Mid-City Bank, N.A., a so-called "interim bank," see 12 C.F.R. § 5.21(a) -- required the Comptroller's approval under 12 U.S.C. § 215a. Beerly, trustee of 2,061 shares, dissented from the merger. When the party-designated appraisers were unable to agree on a neutral appraiser, Beerly, pursuant to 12 U.S.C. § 215a(d), requested the Comptroller to do the appraising, who after considering written submissions from the parties fixed a value of $282.39 per share for Beerly's stock. Beerly thought the appraisal too low, sued the Comptroller under 28 U.S.C. § 1331, lost in the district court, and appeals to us. The record is silent on the current price of Mid-City's stock.

 Even though section 215a(d) states that the Comptroller's appraisal is "final and binding" on all parties, and no procedure for judicial review of an appraisal is specified, it has not been suggested that Congress wanted to insulate the Comptroller's appraisal from judicial review. We cannot rest on the parties' concession of subject-matter jurisdiction, but our independent analysis leads us to the same conclusion. The presumption that final administrative action substantially affecting personal and property rights is judicially reviewable is a powerful one, see, e.g., Abbott Laboratories v. Gardner, 387 U.S. 136, 140-41, 18 L. Ed. 2d 681, 87 S. Ct. 1507 (1967), and we can find nothing in the history or setting of the appraisal provisions to overcome it. The valuation of dissenters' shares is a traditional judicial function, see Simonds v. Guaranty Bank & Trust Co., supra, 492 F. Supp. at 1081-82, and, when performed by an administrative agency rather than a court, invites judicial review. It is not a managerial or political judgment, the kind of judgment that a court cannot usefully review because it lacks the proper analytic tools. The statutory words "final and binding" have no necessary reference to judicial review; they may just mean that the Comptroller's appraisal is the last appraisal.

 When no statute prescribes the procedure for judicial review of a particular administrative action, review is in the district court under 28 U.S.C. § 1331, the general federal-question jurisdictional statute, see Administrative Procedure Act, § 10(b), 5 U.S.C. § 703; General Finance Corp. v. FTC, 700 F.2d 366, 371 (7th Cir. 1983), with a right of appeal to the court of appeals. That was the route followed here.

 Our review of the district court's decision is plenary, Stop H-3 Ass'n v. Dole, 740 F.2d 1442, 1450 (9th Cir. 1984), since that court and this court have the identical information on which to base review of the challenged administrative action, namely the written record compiled in the administrative proceedings. So it is as if we were reviewing the Comptroller directly; and the parties agree as they must that the scope of judicial review of the Comptroller's decision is for the usual reasons narrow, deferential. See E.I. DuPont de Nemours & Co. v. Collins, 432 U.S. 46, 56-57, 53 L. Ed. 2d 100, 97 S. Ct. 2229 (1977); City Federal Savings & Loan Ass'n v. Federal Home Loan Bank Bd., 600 F.2d 681, 688 (7th Cir. 1979). Thus the issue for us is not whether the Comptroller's decision was correct but whether it was reasonable -- not "arbitrary, capricious, [or] an abuse of discretion," 5 U.S.C. § 706(2) (A); cf. Camp v. Pitts, 411 U.S. 138, 141-42, 36 L. Ed. 2d 106, 93 S. Ct. 1241 (1973).

 There are many ways to value a share of stock. The Comptroller considered four: book value, adjusted book value, market value, and investment value.

The methodology of appraisal used by the Comptroller resembles that used in appraising dissenting shareholders' rights under state corporation laws. See, e.g., Fischel, The Appraisal Remedy in Corporate Law, 1983 Am.Bar Foundation Research J. 875, 889-96; Note, The Valuation of a Close Corporation Glimpses of Objectivity in an Inflationary Period, 13 Loyola U. L.J. 107, 114-25 (1981); Note, Valuation of Dissenters' Stock Under Appraisal Statutes, 79 Harv. L. Rev. 1453, 1456-71 (1966). Although this methodology has frequently been criticized (as in the articles just cited), the fact that the Comptroller was following a conventional approach goes far to shield his results from judicial invalidation. It is not for a reviewing court to tell an administrative agencyto defy the conventional wisdom, to innovate, to be daring. And one of the principal criticisms of the conventional methodology of appraisal -- that market value is a better index of value than any valuation formula -- is, as we shall see, inapplicable to this case. The criticisms of the Comptroller's appraisal that Judge Keeton made in the Simonds case, supra, 492 F. Supp. at 1084, are also inapplicable.

 The purpose of an appraisal is to give the owner of the property being appraised the cash equivalent of what he has given up by relinquishing his ownership. In the case of stock what he gives up is the opportunity to sell the stock or to keep it and obtain an income from it. Ordinarily the best estimate of what an opportunity to sell is worth is found in recent sales of the same thing, which would mean, recent sales of stock in Mid-City National Bank. See, e.g., Metlyn Realty Corp. v. Esmark, Inc., 763 F.2d 826, 835-36 (7th Cir. 1985). If the Comptroller had used this method of estimation, it would have turned out very badly for Beerly, because the market value of the stock in the relevant period was only about $160 a share.

It is true that when stock is traded infrequently, past sales may not be a reliable guide to current value, because they impound valuations by only a few buyers and sellers, and because circumstances may have changed since those sales took place. (The other side of the coin is that if a stock has a "thick" market, not only is market value the only rational measure of value, but appraisal rights are unnecessary since the dissenting shareholder can fully protect his interests by selling his shares. On this ground, Delaware does not recognize appraisal rights in such settings. See Del. Gen. Corp. Law § 262(b)(1) (1984). ) But the fact remains that if Beerly had wanted to cash in his stock he would have had to take his chances in a market in which the demand was weak. Indeed, since he owned 4 percent of the stock of the company -- 16 times as much stock as had been sold in any recent year -- he might not have been able to unload all of his stock at $160 a share.

 And it is necessary to distinguish between a "squeeze-out" and a change merely in the form of the shareholder's rights. When a stock is thinly traded, so that its market value is not a reliable index of its true value, controlling shareholders may be tempted at a time when the market valuation is unreasonably low to force minority shareholders to give up their shares in exchange for the market value of the shares, which by hypothesis is less than their true value. But Beerly was not squeezed out; he was offered what appears to have been equivalent shares in the reorganized firm; he left voluntarily. The Comptroller was generous in giving no weight at all to the (low) market value of Beerly's stock.

Book value is a virtually meaningless index of what a share of stock is worth to the shareholder, and the Comptroller properly disregarded it.   The main component of book value is the original cost of the firm's assets, as depreciated. Wholly apart from the well-known vagaries of depreciation, if a firm's assets are specialized to the firm's business they may have very little sale value. Their only value may be to generate the firm's earnings. But then it is clear that the value of the firm is some multiple of its earnings, and not some function of the original cost of its assets. Evidently the book value of middle-sized Chicago banks in the relevant period was greater than their market value, for the stock of Mid-City's "peer group" was trading in the market at an average of only 46 percent of book value per share. Such discounts are common, as any owner of railroad stock knows.

 It is true that Beerly presented evidence that some middle-sized Chicago banks had been bought for more than their book value. But there is a big difference between the value of a minority shareholder's interest and the value of a controlling interest, which is what is at stake when the whole firm is acquired and not just some shares of its stock. Someone who thinks he can run a firm better than its present owners -- that is, thinks he can get more value out of the firm's assets than they can -- naturally will be willing to pay more (if he must!) for a controlling interest than the current market value of the firm's stock; that stock is worth more to him. But the qualification is vital; the stock is worth more to him only if he has control of the firm, so that he can run it; and for control he needs more than 4 percent. Of course the analysis would be more complicated if a buyer were not allowed to pay a premium for a controlling block of stock -- if he had to pay all shareholders the same price for their shares. But federal law contains no such requirement, which would make transfers of corporate control more costly and therefore reduce the effectiveness of the market for corporate control in disciplining managers and in moving corporate resources into the hands of those who can get the most value out of them. See Easterbrook & Fischel, Corporate Control Transactions, 91 Yale L.J. 698 (1982). All shareholders may be better off, ex ante, with a rule that facilitates takeovers, even though, ex post, some may get lower prices for their shares if a takeover occurs.

The two measures of value that  the Comptroller used are more consonant with economic reality than book value is and more favorable to Beerly than market value. The Comptroller's "adjusted book value" was essentially a measure of the market value of a portfolio of comparable banks, and thus corrected for the thinness of the market in Mid-City's own stock. The Comptroller's "investment value" assumed quite sensibly that the value of bank stock is as an income-producing asset and is therefore a function of the bank's income. The precise form of that function depends on investors' estimates of the riskiness of the bank's stock and the prospects for the bank's future earnings; and while it is possible that Mid-City is less risky than its peers or has brighter prospects, the Comptroller was entitled to assume, in the absence of more direct evidence of Mid-City's prospects, that investors were unlikely to consider it a more valuable asset, per dollar of earnings, than a portfolio of stocks of similar banks.

 The two measures the Comptroller used are closely related. In effect he made two adjustments to the average market value of the stock of the peer firms to derive the market value of Beerly's shares in Mid-City: He multiplied it first by the ratio of Mid-City's book value to the peer group's average book value and then by the ratio of Mid-City's earnings, and then he took the average of these two products. He assumed, in other words, that Mid-City's stock would be worth more, relative to the market value of comparable banks' stock, the more its book value exceeded the average book value of the comparable banks and the more its earnings exceeded their earnings. This is a defensible procedure (ratios of book values may be a little more meaningful than absolute book values), and on the whole one generous to Beerly.

The Comptroller gave no weight to the appraisal made by Beerly's own appraiser, in the aborted private appraisal that preceded the Comptroller's intervention: $743.77. But, contrary to Beerly's suggestion, the Comptroller was not required to average that appraisal with his own in coming up with a valuation for Beerly's shares. If the parties had agreed on a neutral appraiser, he would not have averaged his own estimate with those of the party-designated appraisers. People estimate value differently, and there is no difficulty in finding an expert from the upper tail of the distribution.  Metlyn Realty Corp. v. Esmark, Inc., supra, 763 F.2d at 836. The search for extremes in valuation should not be encouraged by requiring that the highest appraisal be averaged in with the others.

 The most questionable feature of the Comptroller's valuation (apart from his giving no weight to the bank's market value -- an omission that favored Beerly, however) was the refusal to count any part of the bank's reserve for bad loans as an asset, rather than a liability. The reserve, $2 million, had remained unchanged for many years during which the bank wrote off an average of only $10,000 a year in bad loans. The recent and well-publicized difficulties of large Chicago banks, together with the uncertainties that have been created by the deregulation (though as yet partial) of banking, seem to confirm the prudence of the Comptroller's conservative approach to bank reserves -- and in any event we can think of few areas less suitable for judicial second-guessing than the Comptroller's determination of how large a reserve is suitable for a bank of Mid-City's size and condition. But the point is not whether the Comptroller acted reasonably in requiring a large reserve for bad loans; it is whether investors would have considered the reserve excessive, for if so they would have treated the excess as an asset rather than a liability in valuing the firm. However, an adjustment to take account of this possibility would not have altered the appraisal significantly. The reserve was equal to only 7 percent of the bank's book value. Suppose it was twice as large as investors would have thought proper. The effect on adjusted book value (equal to 46 percent of book value) would be to increase that value by only 1.6 percent (46 percent of 3.5 percent is 1.6 percent); and since adjusted book value was given a weight of one-half in valuing Beerly's stock, the result would be a less than 1 percent (0.8 percent, to be precise) increase in the value of his stock. If there was an error in the treatment of the reserve for bad loans -- and that is uncertain -- it was trifling.

 We do not understand Beerly's complaint that the bank paid lower dividends than comparable banks. That would just go to increase the bank's capital, and hence book value, and hence the valuation of Beerly's shares.

 Beerly argues that the statutory procedure for appraisal by the Comptroller violates the Fifth Amendment's due process clause because it does not provide for an evidentiary hearing. Although the due process clause comes into play only when there is a deprivation of life, liberty, or property, there was a deprivation of property here. Granted, the merger itself did not deprive Beerly of his stock. He was not squeezed out; he opted out; he could have exchanged his stock for shares in the interim bank. But the new shares would not have been the exact equivalent of the old; at common law he could have vetoed the transaction, Chicago Corp. v. Munds, 20 Del. Ch. 142, 149, 172 A. 452, 455 (1934); a forced exchange is still a deprivation. A less metaphysical point is that once Beerly chose appraisal, as the statute entitled him to do, he was stuck with the result of that appraisal; and if the Comptroller violated due process of law in conducting the appraisal, and as a consequence valued Beerly's stock at less than the minimum reasonable estimate of its true value, the Comptroller could be said to have deprived him of property without due process of law. It is true that we have found the valuation reasonable, but this conclusion is based on the record compiled by the Comptroller; if that record is tainted by his failure to accord Beerly a hearing, our conclusion is undermined. So we must determine whether the procedure denied Beerly due process.

The process that is due depends on the nature of the inquiry. Since time out of mind, appraisal by informal procedures not involving oral hearings has been used to value property, including property as valuable as Beerly thought his stock was. Generally, appraisers are not arbitrators; they do not weigh in a trial setting conflicting opinions of value that have been subjected to cross-examination; they make their own evaluation. See Hayes v. Allstate Ins. Co., 722 F.2d 1332, 1340 (7th Cir. 1983) (dissenting opinion) (citing cases). The procedure for valuing dissenting shareholders' rights under state law is various. See 12B Fletcher Cyclopedia of the Law of Private Corporations § 5906.8 (Van Swearingen rev. ed. 1984). In some states the court does the appraising; in others appraisers are appointed and use their own judgment in valuing the shares; in still others the appraisers take evidence before making their valuation. In none so far as we know is an oral evidentiary hearing with cross-examination either required or customary. The procedure used by the Comptroller in this case was as formal as any used in cases of this general nature and more formal than many.

 Thus if the appraisers designated by the parties had been able to agree on a neutral appraiser, and the committee of appraisers had then set about to appraise Beerly's stock, in all likelihood it would not have done so with an oral hearing or any of the other traditional accouterments of formal procedure. We need not decide, however, whether the Comptroller could, consistently with due process, have proceeded as informally as private appraisers. He weighed the written submissions by Beerly and the bank and having done so made his appraisal in a reasoned opinion that considered all of Beerly's evidence and argument. The only thing missing was oral testimony and the opportunity for cross-examination. Beerly has not shown how the use of these expensive and time-consuming procedures would have reduced an otherwise high probability of a serious error in the appraisal. The procedure was therefore constitutionally adequate. See, e.g., Mathews v. Eldridge, 424 U.S. 319, 335, 47 L. Ed. 2d 18, 96 S. Ct. 893 (1976); cf. Richardson v. Perales, 402 U.S. 389, 402, 28 L. Ed. 2d 842, 91 S. Ct. 1420 (1971); Chicago & North Western Transport Co. v. United States, 678 F.2d 665, 671 (7th Cir. 1982).

 Beerly's final complaint is that the statute makes no provision for the payment of interest. The merger took place in February 1982, and that fixed the date for valuing Beerly's shares. The Comptroller made his valuation in June 1983, about 15 months later. Assuming purely for illustrative purposes that the market rate of interest on such an investment was 9 percent, Beerly lost $65,000 as a result of the delay between the merger and the valuation. The delay was not unreasonable, but the consequences for Beerly's wealth position were significant and, he argues, unreasonably deprived him of property. But we shall not consider the merits of the argument. It appeared for the first time in Beerly's reply brief. That was too late. Christmas v. Sanders, 759 F.2d 1284, 1291-92 (7th Cir. 1985).

 AFFIRMED.