Plaintiff Catholic Healthcare West (“CHW”), a non-profit Catholic hospital system, was the surviving entity after a merger between Marian Medical Center and the hospitals previously constituting CHW. Its claim here relates to depreciation taken by Marian in the years before the merger. CHW argues that the merger transaction revealed the inadequacy of that depreciation and that, under the statute and regulations applicable to the merger, the deficiency was subject to re-coupment as part of Medicare providers’ general entitlement to compensation for the “reasonable cost” of services rendered, 42 U.S.C. § 1395f(b)(l). The defendant Secretary of Health and Human Services rejected the claim, reasoning that the implicit selling price (namely, the value of CHW’s assumption of Marian’s liabilities) showed a transfer for much less than Marian’s true worth, so that the merger did not represent a “bona fide sale” between “unrelated parties,” a prerequisite for use of the transaction as evidence that the prior depreciation had been inadequate, 42 C.F.R. § 413.134. In reaching this conclusion the Secretary estimated Marian’s true worth on a basis of “cost” — meaning roughly, in this context, replacement cost as of the time of the merger, adjusted for depreciation. CHW objects, arguing that the choice of “cost” over other valuation approaches was arbitrary and was based on a guidance document that the Secretary had adopted without notice and comment rulemaking, namely, Clarification of the Application of the Regulations at 42 C.F.R. 413.134(i) to Mergers and Consolidations Involving Non-profit Providers, Program Memorandum A-00-76 (Oct. 19, 2000) (“PM”).
In the end we find it unnecessary to evaluate the PM’s effectiveness. Even under the valuation methods permitted prior to the PM and in fact championed by CHW here and in the administrative proceedings, there was a gross disparity between Marian’s value and the implicit price paid. We therefore affirm the district court’s judgment affirming the Secretary.
The Secretary’s regulations governing a Medicare provider’s reasonable costs have long provided for an “appropriate allowance” for depreciation in assets used for Medicare services. 42 C.F.R. § 413.134(a). The annual allowance is calculated by dividing the cost of acquiring the asset by the asset’s years of estimated useful life, § 413.134(a), and then multiplying by the fraction of the asset applied to Medicare services.
The regulations also provide that for assets disposed of before December 1, 1997 — the CHW-Marian merger occurred in August 1997 — the Secretary will recognize gains or losses on the sale of an asset (defined in a way that includes this merger), calculated as the difference between the consideration received for the asset and its “net book value” (i.e., the cost of acquisition less previous depreciation payments, § 413.134(b)(9)). (The Balanced Budget Act of 1997, Pub.L. No. 105-33, § 4404, 111 Stat. 251, 400 (1997), amended 42 U.S.C. § 1395x(v)(l)(0) so as to eliminate the statutory basis for such adjustments for assets sold after December 1, 1997. But the recoupment scheme continues for prior transactions such as the Marian-CHW merger.) So, subject to some conditions discussed below, if an asset is sold for less than its net book value, the Secretary makes an additional payment to the provider, reflecting an understanding that the previous depreciation payments *353fell short of reflecting true cost. Conversely, of course, the provider pays the government if the asset is sold at above book value.
The regulatory conditions are aimed at ensuring that the consideration exchanged for a depreciable asset constitutes a meaningful indication of the asset’s market value, and hence a sound basis to assess whether a depreciation recoupment to (or from) the provider is in order. In particular, the Secretary makes such adjustments only for depreciation discrepancies evidenced by “bona fide sales” of depreciable assets, § 413.134(f)(2); the adjustments and the “bona fides” requirement are extended to transfers in a “statutory merger,” as here, by § 413.134(k)(2)1 and its incorporation of § 413.134(f)’s requirements. The regulations further specify that a triggering merger must not be between “related” parties, § 413.134(k)(2)(i)-(ii), as defined in § 413.17.
After the merger here, CHW filed a claim for a loss of roughly $8.1 million on the disposal of depreciable assets. In pursuit of that claim it then suffered a string of adjudicatory defeats — before a Medicare contractor, the Provider Reimbursement Review Board (“PRRB”), and ultimately the Administrator of the Centers for Medicare and Medicaid Services (“CMS”), whose decision was the Secretary’s final action. CMS found a large disparity between the consideration received and Marian’s “fair market value,” calculated, as we noted, on the basis of replacement cost adjusted for depreciation, and thus found no bona fide sale. It also decided that CHW and Marian were related parties for the purposes of the regulations, an aspect of the decision we needn’t address. CHW appealed to the district court, which dismissed the case on a motion for summary judgment. Catholic Healthcare West v. Sebelius, 919 F.Supp.2d 34 (D.D.C.2013).
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Our review is de novo, as though on direct appeal from the agency, Tenet HealthSystems HealthCorp. v. Thompson, 254 F.3d 238, 244 (D.C.Cir.2001), and under the Administrative Procedure Act we set aside an agency action if it is “arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law,” 5 U.S.C. § 706(2)(A); Pharm. Research & Mfrs. of Am. v. Thompson, 362 F.3d 817, 821 (D.C.Cir.2004).
Under the Secretary’s interpretation of the regulations, “reasonable consideration” must be exchanged in a merger to support a finding of a bona fide sale. We have previously upheld this interpretation, St. Luke’s Hosp. v. Sebelius, 611 F.3d 900, 905-06 (D.C.Cir.2010), which CHW doesn’t contest. Recoupment may be disallowed under the regulations either on the ground that no bona fide sale occurred, § 413.134(f), or that the transaction was between related parties, § 413.134(k)(2).
CHW commissioned an appraisal of Marian, which included a calculation of its value under three methods — market value, income, and the Secretary’s “cost” approach. CMS used the latter, arriving at a figure of approximately $51.1 million. That estimate excludes working capital, such as cash and cash equivalents. So CMS then added $15.9 million in cash and cash equivalents transferred from Marian to CHW, arriving at a total of about $67 million. By comparison, the total consideration received by Marian was $32.7 mil*354lion in the form of assumed liabilities, implying a disparity of over $34 million.
CHW argues that the Secretary erred in disregarding the two rival methods of valu-' ation used in the appraiser’s report (the income and market approaches). The Secretary did so on the basis of the PM’s interpretation of the regulations. We have affirmed the Secretary’s invocation of the PM in two prior cases, Forsyth Mem’l Hosp., Inc. v. Sebelius, 639 F.3d 534, 536-37 (D.C.Cir.2011), and St. Luke’s Hosp., 611 F.3d at 905-07, but in both cases only for the anodyne view that the regulations require a “reasonable consideration.” Neither involved flat-out preclusion of either the market value or the income method. Indeed, the PM itself, while precluding both those methods for non-profits, offers an explanation only as to the income approach. See PM at 3-4.
We can resolve the case, however, without considering whether the PM (or the regulations themselves) provided an adequate basis for excluding the market and income approaches. E.g., Molycorp, Inc. v. EPA 197 F.3d 543, 546 (D.C.Cir.1999) (an agency may not amend a rule “under the guise of reinterpreting it”). Even though those approaches yield lower figures than does the “cost” approach, they indicate a value high enough to sustain the Secretary’s finding -of a gross disparity between value and the implicit price paid by CHW.
The appraiser’s report indicates that the market and income approaches produce value estimates of $37 million, and $28.5 million, respectively, excluding working capital. The appraiser’s report characterizes these estimates as “mutually supportive;” and concludes that the market value of the hospital is $30 million, “including working capital.” It appears inescapable that the word “including” is a typo, as it is inconsistent with every other page in the document, see, e.g., Appraiser’s Report 84, 92 (recording income and market-based estimates of $37 and $28.5 million, respectively, excluding working capital; corresponding estimates of $47 and $38.5 million including working capital), inconsistencies CHW acknowledged at oral argument, Oral Arg. Tr. 5-6.
The Administrator’s decision was based on the large disparity between Marian’s value and the consideration received. It is true that the Administrator discusses only the cost approach, not the income or market approaches, and that we do not affirm agency decisions on a legal analysis other than that expressed by the agency. SEC v. Chenery Corp., 318 U.S. 80, 95, 63 S.Ct. 454, 87 L.Ed. 626 (1943). But here, even if CHW’s proposed appraisal method were used, the record shows a large disparity between the fair market value of Marian and the consideration received. In view of the conclusion the Administrator drew from valuation under the cost approach, it would be futile to remand for reassessment of whether a bona fide sale occurred under the income or market approach.
Consider the income approach, the one most favorable to CHW, yielding the most conservative appraised value for Marian. It produces an estimate of $28.5 million, excluding working capital. To this we then add the appraised value of Marian’s “other assets,” not reflected in the $28.5 million figure, including vacant sites and construction in progress, a total of roughly $5.3 million, as' well as the $15.9 million in cash and cash equivalent assets. Grade-level arithmetic reveals that, after adding these three figures, the full market-based estimate of Marian’s value would be $49.7 million. The disparity between this figure and the consideration received by Marian is $17 million. Thus, even by the most conservative estimate of Marian’s value, CHW paid only about 66 cents on the *355dollar in this transaction ($82.7 million exchanged for $49.7 million).
Though the parties cite no sharp rule on the size of the disparity between value and consideration relevant to determining whether a bona fide sale has occurred, CHW bears the burden to prove a bona fide sale, Forsyth Mem’l Hosp., Inc., 639 F.3d at 539, and nothing in the briefing or administrative record suggests that a bona fide sale could be found in the face of such a discrepancy. Cf. Via Christi Reg’l Med. Ctr., Inc. v. Leavitt, 509 F.3d 1259, 1277 (10th Cir.2007) (suggesting that the reasonable consideration requirement would not be satisfied if $32.7 million in assets are exchanged for $26.1 million in consideration).
During oral argument, CHW advanced a new argument that the $15.9 million in cash and cash equivalents consisted primarily of accounts receivable, and that CHW is unlikely to “collect dollar for dollar,” Oral Arg. Tr. 11, suggesting a closer alignment between the paid consideration and Marian’s true value. But we do not normally consider arguments first sprung at oral argument. Roth v. Dept. of Justice, 642 F.3d 1161, 1181 (D.C.Cir.2011). Under these circumstances, we cannot say that the Secretary failed to consider relevant factors or committed a clear error in judgment when she determined that a bona fide sale had not occurred. See also 5 U.S.C. § 706 (“due account shall be taken of the rule of prejudicial error”); City of Portland, Or. v. EPA, 507 F.Sd 706, 711 (D.C.Cir.2007); PDK Labs. Inc. v. DEA 362 F.3d 786, 799 (D.C.Cir.2004).
The judgment of the district court is
Affirmed.