This appeal concerns the propriety of a multimillion dollar default judgment entered against defendants-appellants Inver-siones Errazuriz Limitada, Supermercados Unimarc S.A., Pesquera Nacional S.A., Unimarc Abastecimientos S.A., Cidef S.A., Salmones Unimarc S.A., Industria Fores-tal Nacional S.A., Forestal Regional S.A., Cidef Argentina S.A., Corporación de In-versiones y Desarrollo Financiero Cidef S.A., and Socieded Contractual Minera Compañía de Salitre y Yodo Primera Re-gión (collectively “defendants”). In April 2001, plaintiff-appellee State Street Bank and Trust Company (“State Street Bank” or “the bank”) initiated a legal action to recover more than $100 million to which the bank was entitled pursuant to two credit agreements executed in 1994 and 1996 (individually and respectively the “1994 Credit Agreement” and the “1996 Credit Agreement” and collectively the “Credit Agreements”). When the defendants failed to respond to the complaint, the United States District Court for the Southern District of New York, Carter, J., on the application of State Street Bank, entered a default judgment of approximately $136 million.1 Thereafter, the defendants brought two motions to vacate the default judgment pursuant to various provisions of Rule 60(b) of the Federal Rules of Civil Procedure. The district court denied those motions and the defendants appealed.
Defendants contend that the district court improperly denied their efforts to secure relief from the default judgment. Defendants claim that the defenses and counterclaims they asserted justified the vacatur of the default judgment and that State Street Bank would not be prejudiced if that judgment were vacated. They also contend that State Street Bank perpetrated a fraud that merited vacatur. For the reasons that follow, we conclude that the district court properly denied their Rule 60(b) motions and affirm the court’s decisions.
BACKGROUND
The roots of the appeal before us can be traced to certain transactions that took place in 1994 and 1996. State Street Bank initially agreed to supply defendant Inver-siones Errazuriz Limitida (Inverraz), a Chilean company, with $50 million in accordance with the terms of the 1994 Credit Agreement. Subsequently, Inverraz borrowed an additional $65 million from State Street Bank pursuant to the 1996 Credit Agreement.
State Street Bank entered into these financing arrangements on the express condition that certain operating affiliates of Inverraz would guarantee the loans. As such, various Inverraz subsidiaries signed guaranty agreements in 1994 and 1996 (individually and respectively the “1994 Guaranty Agreement” and the “1996 Guaranty Agreement” and collectively the “Guaranty *164Agreements”), making each of them liable for a share of the sums borrowed by In-verraz and for certain penalties if their parent company defaulted on the loans.2
According to the Credit Agreements, the sums borrowed by Inverraz were to be repaid, by and large, through several semiannual installments. Both Credit Agreements expressly provided that the failure to make timely payments would constitute an “Event of Default.” If an Event of Default occurred, State Street Bank could accelerate Inverraz’s debt such that all of the interest and principal outstanding with respect to the loan defaulted on, together with a defined “Make Whole Amount,” would become immediately due and payable. Under the provisions of the Guaranty Agreements, each- guarantor agreed to pay for a specified share of this accelerated debt.
In 1999 and 2000, Inverraz failed to make the semiannual installment payments required by the Credit Agreements. In response, State Street Bank accelerated Inverraz’s debt and demanded repayment of all the sums then due. Nevertheless, neither Inverraz nor any guarantor repaid any portion of Inverraz’s outstanding debt.
In April 2001, State Street Bank filed this legal action against the defendants in an effort to recover the sums to which it was entitled pursuant to the Credit Agreements and the Guaranty Agreements, as well as to secure a declaration that the defendants could not sell certain assets without the bank’s prior consent.3 The defendants did not immediately answer State Street Bank’s complaint. Rather, in June 2001 the district court endorsed a stipulation in which the defendants acknowledged personal jurisdiction as well as service of process and State Street Bank agreed to extend the defendants’ time to respond to the complaint. Notwithstanding this extension of time, the defendants failed to file an answer in the months that followed.
State Street Bank eventually moved for the entry of a default judgment and the district court granted the bank’s motion. With respect to the 1994 Credit Agreement, the court issued a default judgment that held defendants Inverraz, Supermer-cados Unimarc S.A., Pesquera Nacional S.A., Unimarc Abastecimientos S.A., Cidef S.A., Salmones Unimarc S.A., Industria *165Forestal Nacional S.A., Forestal Regional S.A., and Corporación de Inversiones y Desarrollo Financiero Cidef S.A. jointly and severally liable for $57,283,874.86 as well as for prejudgment interest from November 1, 2001, at the rate of $20,011.63 per day. As to the sums owed under the 1996 Credit Agreement, the court held defendants Inverraz, Supermercados Uni-marc S.A., Pesquera Nacional S.A., Uni-marc Abastecimientos S.A., Cidef S.A., Salmones Unimarc S.A., Cidef Argentina S.A., Corporación de Inversiones y Desar-rollo Financiero Cidef S.A., and Sociedad Contractual Minera Compañia de Salitre y Yodo Primera Región jointly and severally liable for $79,180,000.12 as well as for prejudgment interest from November 1, 2001, at the rate of $21,599.47 per day. In addition, the court prohibited the defendants from selling or transferring the assets of Compañía de Salitre y Yodo de Chile S.A. without State Street Bank’s pri- or consent.
Thereafter, the defendants moved the district court to vacate the default judgment pursuant to various provisions of Rule 60(b) of the Federal Rules of Civil Procedure. They argued that the default in question had not been willful and that State Street Bank would not be prejudiced if the default judgment was vacated. They also advanced a host of defenses and counterclaims that allegedly justified the vaca-tur of the default judgment.
In February 2002, the district court held that two of those defenses and counterclaims were not meritorious. See State Street Bank & Trust Co. v. Inversiones Errazuriz, Limitada, 230 F.Supp.2d 313, 319-24 (S.D.N.Y.2002) (State Street Bank I). However, the court determined that the “factual record regarding [the] defendants’ seven remaining counterclaims [and defenses was] simply too incomplete for the court to conclude one way or the other whether they constitute meritorious defenses.” Id. at 324. As such, the court referred the remaining counterclaims and defenses to a magistrate judge and directed him to issue a report and recommendation, after the defendants had “been given an opportunity to flesh out the factual foundation for each counterclaim [and defense],” with respect to whether they were meritorious. Id. The district court also found that there was not enough information, as of yet, for it to decide whether the default had been willful or whether State Street Bank would suffer prejudice in the event of vacatur. See id. at 318-19, 324. Hence, the court also directed the magistrate judge to issue a report and recommendation evaluating these two issues following further briefing and factual inquiry. See id. at 324.
The magistrate judge responded to the district court’s directives by holding a two day hearing in May 2002 and thereafter issued a report recommending that the district court deny the motion to vacate the default judgment. See Street Bank & Trust Co. v. Inversiones Errazuriz Limitada, 246 F.Supp.2d 231, 263 (S.D.N.Y.2002) (State Street Bank II). Although the magistrate judge found that the defendants’ failure to respond to the complaint had not been willful, he nonetheless determined that their motion should be denied because they had failed to establish any meritorious defense or counterclaim and had failed to demonstrate that State Street Bank would not be prejudiced by the vaca-tur of the default judgment. Id.
Defendants objected to several of the magistrate judge’s determinations. The district court reviewed the issues and agreed with the magistrate judge that the remaining counterclaims and defenses were not meritorious and that the defendants had failed to demonstrate that State Street Bank would not be subjected to *166prejudice if the default judgment were vacated. Accordingly, the court denied the defendants’ motion to vacate the default judgment. See id. at 243. The defendants filed an appeal challenging that decision.
Following the denial of their initial motion to vacate the default judgment and before we had an opportunity to consider their appeal therefrom, the defendants brought a second motion pursuant to various provisions of Rule 60(b). They did so in an effort to seek relief from both the district court’s earlier decision in State Street Bank II as well as the underlying default judgment. Their Second Rule 60(b) motion was predicated, for the most part, on a letter that the defendants discovered in their own files after the court denied their previous motion in State Street Bank II. Defendants argued that the information set forth in the letter established a meritorious defense and that the default judgment therefore should be vacated. They also contended that State Street Bank as well as its counsel withheld and concealed the letter from them, thereby both defrauding them and perpetrating a “fraud on the court” that justified relief pursuant to Rule 60(b) and Rule 60(b)(3). Finally, in addition to their reliance on the letter, the defendants asserted that the default judgment was void and relief therefrom should be granted pursuant to Rule 60(b)(4). The district court denied the defendants’ second Rule 60(b) motion in its entirety. See State Street Bank & Trust Co. v. Inversiones Errazuriz, Limitada, 2003 WL 1907955, at *3 (S.D.N.Y. Apr.18, 2003) (State Street Bank III).
Defendants filed a timely appeal challenging the denial of their second Rule 60(b) motion. We consolidated their second appeal with their earlier appeal from the denial of their first Rule 60(b) motion and we now address the issues raised by these consolidated proceedings.
DISCUSSION
Defendants contend that the district court erroneously denied both of their Rule 60(b) motions. We review the denial of each of those motions seriatim.
I. Defendants’ First Motion to Vacate the Default Judgment
In the proceedings below, the defendants advanced a host of defenses and counterclaims in support of their initial motion to vacate the default judgment pursuant to several provisions of Rule 60(b). On appeal, they focus on only two counterclaims and one defense and argue that the district court erroneously concluded that they were not meritorious. The defendants also contend that the district court erred in determining that they had failed to establish that State Street Bank would not be prejudiced by the vacatur of the default judgment.
Rule 60(b)(1) provides, in pertinent part, that a court may relieve a party from a final judgment for “mistake, inadvertence, surprise, or excusable neglect.”4 Fed.R.Civ.P. 60(b)(1). A motion to vacate a default judgment brought pursuant to this provision “is addressed to the sound discretion of the district court and we will not reverse the denial of such a motion except for abuse of discretion.” S.E.C. v. McNulty, 137 F.3d 732, 738 (2d Cir.1998) (citations omitted).
When a district court decides a motion to vacate a default judgment pursuant to the provisions of Rule 60(b), the court’s determination must be guided by three principal factors: “(1) whether the default *167was willful, (2) whether the defendant demonstrates the existence of a meritorious defense, and (3) whether, and to what extent, vacating the default will cause the nondefaulting party prejudice.” Id.; see also American Alliance Ins. Co. v. Eagle Ins. Co., 92 F.3d 57, 59 (2d Cir.1996). In the appeal at bar, only the second and third factors are implicated because State Street Bank has not challenged the magistrate judge’s and the district court’s conclusions regarding the absence of a willful default.
A. Meritorious Defenses and Counterclaims
“In order to make a sufficient showing of a meritorious defense in connection with a motion to vacate a default judgment, the defendant need not establish his defense conclusively, but he must present evidence of facts that, if proven at trial, would constitute a complete defense.” McNulty, 137 F.3d at 740 (citation and internal quotation marks omitted); see also American Alliance Ins. Co., 92 F.3d at 61 (“A defense is meritorious if it is good at law so as to give the factfinder some determination to make.”) (citation and internal quotation marks omitted).
When the defendants moved to vacate the default judgment, they tried to establish a meritorious defense by articulating, among other things, an array of counterclaims. To date, we have never addressed whether a counterclaim, rather than a response to the substance of a complaint, may constitute a meritorious defense. In the instant appeal, State Street Bank contends that at least one of the counterclaims at issue is unrelated to the substance of the bank’s action and should therefore be disqualified from consideration as a meritorious defense. We need not decide that issue here because, even if we were to assume that the counterclaims preserved in these consolidated appeals could be considered as meritorious defenses, they are without merit.
1. The Meritorious Defense Standard
The defendants argue that the district court applied an erroneous standard when the court evaluated whether their defense and counterclaims were meritorious.
When the district court set out to appraise whether the defense and counterclaims at issue in this appeal were meritorious, the court did so under an unusual formulation of the governing standard. The court held that “[w]hen, as here, defendants have been given the opportunity to show that a viable defense exists” through the presentation of evidentiary proof in support of their contentions, “they are required to provide some credible indication that if the default judgment is vacated, defendants will be able at trial to establish with finality a meritorious defense which has a reasonable chance of carrying the day.” State Street Bank II, 246 F.Supp.2d at 242.
The district court’s statements appear to suggest that the defendants needed to present sufficient evidence to establish that they had a “reasonable chance of carrying the day.” Id. Such a test would contravene well settled principles that govern what constitutes a meritorious defense. Whether a defense is meritorious “is measured not by whether there is a likelihood that it will carry the day, but whether the evidence submitted, if proven at trial, would constitute a complete defense.” Enron Oil Corp. v. Diakuhara, 10 F.3d 90, 98 (2d Cir.1993). This standard applies regardless of whether there has been an evidentiary hearing or an opportunity for discovery. Judging the merit of a defense for the purposes of a motion to vacate a default judgment pursuant to a more rigorous standard would be *168inappropriate. Default judgments “are generally disfavored and are reserved for rare occasions.” Id. at 96. As such, the criteria for vacating a default judgment pursuant to Rule 60, including the meritorious defense factor, “should be construed generously.” Id.
Even if we were to assume that the district court set forth an incorrect principle of law in the abstract, the court ultimately found that the defendants had failed “to establish even the rudimentary elements of a meritorious defense.” State Street Bank II, 246 F.Supp.2d at 242. In other words, the court determined that the defense and the counterclaims in question were wholly without merit. See, e.g., id. at 243 (“[The] defendants have failed to present proof even minimally sufficient to show the existence of a meritorious defense.”). Given that determination, the district court could not have found that the defense and counterclaims satisfied the proper meritorious defense standard. Indeed, after independently reviewing the record, we agree, for reasons that will become apparent in the discussion that follows, that the defendants failed to establish a meritorious defense and we may affirm the district court’s denial of their initial Rule 60(b) motion on that ground. Cf. Boy Scouts of America v. Wyman, 335 F.3d 80, 90 (2d Cir.2003) (“[W]e may affirm the judgment of the district court on any ground appearing in the record.”).
2. Implied Covenant of Good Faith and Fair Dealing
Defendants contend that they put forth a meritorious defense when they asserted a counterclaim against State Street Bank for the breach of an implied covenant of good faith and fair dealing. We disagree.
The facts and allegations pertaining to this counterclaim are relatively straightforward. When Inverraz defaulted on the loans by failing to make the necessary semiannual installment payments required by the Credit Agreements, State Street Bank accelerated Inverraz’s debt. Thereafter, Inverraz sought to sell its assets in a purported effort to repay at least a portion of the accelerated debt. As part of this effort, Inverraz entered into negotiations in 2001 with Sociedad Química y Minera de Chile (SQM), another Chilean company, regarding the sale of the nitrate and iodine assets of Inverraz’s subsidiary, Compañía de Salitre y Yodo Primera Región S.A. (Cosayach).
Despite these negotiations, Inverraz did not have an unrestricted right to sell assets. Rather, Inverraz’s ability to do so was qualified by certain provisions in the Credit Agreements. Each of these agreements included negative covenants that provided, among many other limitations, that neither Inverraz nor its “Restricted Subsidiaries” could sell, transfer, or otherwise dispose of any assets where, inter alia, Inverraz had defaulted on the loans enumerated in the agreements. The Credit Agreements defined the term “Restricted Subsidiary” to include “each of the Guarantors” as well as any other entity in certain countries such as Chile of which Inverraz directly or indirectly through other Restricted Subsidiaries owned more than 75% or more of the voting stock or held a 75% financial interest.
Because Inverraz defaulted on the loans, these negative covenants limited the company’s rights, as well as the rights of its Restricted Subsidiaries, to sell assets. Indeed, all the parties agree that the defendants could not have sold the aforementioned nitrate and iodine assets to SQM in 2001 unless State Street Bank first con*169sented to such a sale.5
After extensive negotiations, SQM apparently agreed in principle to purchase the nitrate and iodine assets for approximately $140 million if State Street Bank consented to the sale. This agreement led to a further series of negotiations between the defendants and State Street Bank as the former tried to secure the bank’s consent to the sale. According to the defendants, State Street Bank refused to consent to the sale of the assets unless the defendants (a) paid the bank $87 million from the proceeds of the sale, and (b) agreed to provide the bank with new collateral and new economic benefits to which the bank would not already have been entitled under the Credit Agreements. On October 5, 2001, SQM notified Inverraz that it would not proceed with the purchase of the assets. The defendants maintain that State Street Bank’s refusal to consent to the sale absent its stated conditions led SQM to back away from the transaction.
Defendants contend that the conditions State Street Bank placed on its consent to the sale of the assets to SQM — namely, that the defendants first needed to provide the bank with new collateral and new economic benefits to which the bank was not entitled under the Credit Agreements— were unreasonable. They take the position that, under the law, State Street Bank could only withhold its consent to the sale on reasonable and rational grounds. Because they believe that State Street Bank unreasonably and arbitrarily refused to consent to the sale, they argue that the bank breached a covenant of good faith and fair dealing implied in the Credit Agreements and that this breach constitutes a valid counterclaim for the purposes of their Rule 60(b) motion. However, despite the defendants’ protests to the contrary, New York law does not support their counterclaim.6
“Under New York law, a covenant of good faith and fair dealing is implied in all contracts.” 1-10 Industry Associates, LLC v. Trim Corp. of America, 747 N.Y.S.2d 29, 31, 297 A.D.2d 630, 631 (2d Dep’t 2002). “This covenant embraces a pledge that neither party shall do anything which will have the effect of destroying or injuring the right of the other party to receive the fruits of the contract.” 511 West 232nd Owners Corp. v. Jennifer Realty Co., 98 N.Y.2d 144, 153, 746 N.Y.S.2d 131, 135, 773 N.E.2d 496, 500 (2002) (citations and internal quotation marks omitted). “Where the contract contemplates the exercise of discretion, this pledge includes a promise not to act arbitrarily or irrationally in exercising that discretion.” Dalton v. Educational Testing Service, 87 N.Y.2d 384, 389, 639 N.Y.S.2d 977, 979, 663 N.E.2d 289, 291 (1995) (citation omitted).
*170Nevertheless, the duties imposed by an implied covenant of good faith and fair dealing are “not without limits, and no obligation can be implied that would be inconsistent with other terms of the contractual relationship.” Id., 87 N.Y.2d at 389, 639 N.Y.S.2d at 979-80, 663 N.E.2d at 291-92 (citation and quotations marks omitted). Where a contract allows a bank to withhold consent for particular conduct and sets no express restrictions on the bank’s right to do so, the bank is not prohibited from unreasonably or arbitrarily withholding such consent. See Bonady Apartments v. Columbia Banking Fed. Sav. & Loan Ass’n, 465 N.Y.S.2d 150, 154, 119 Misc.2d 923, 927-28 (N.Y.Sup.Ct.1983), aff'd as modified in non-relevant part, 472 N.Y.S.2d 221, 99 A.D.2d 645 (4th Dep’t 1984); see also Teachers Ins. & Annuity Ass’n of America v. Wometco Enterprises, 833 F.Supp. 344, 349 (S.D.N.Y.1993) (“[I]n the absence of explicit contractual language stating that a party may not unreasonably withhold consent, parties may withhold consent for any reason or no reason, and ... no implied obligation to act in good faith exists to limit that choice.”). Cf. Dress Shirt Sales v. Hotel Martinique Assoc., 12 N.Y.2d 339, 342, 239 N.Y.S.2d 660, 662, 190 N.E.2d 10, 11 (1963) (“[U]nless [a] lease provides that [a] lessor’s consent shall not be unreasonably withheld,” a provision in that lease prohibiting subleasing absent the lessor’s consent “permits the lessor to refuse [consent] arbitrarily for any reason or no reason.”); cf. also Caridi v. Markey, 539 N.Y.S.2d 404, 405, 148 A.D.2d 653, 654 (2nd Dep’t 1989) (same).
Here, the Credit Agreements provided that neither Inverraz nor its Restricted Subsidiaries could sell their assets if In-verraz had defaulted on the loans. As such, all the parties agree on appeal that the defendants could not have sold Cosay-ach’s assets to SQM without State Street Bank’s consent. There are no express restrictions in the applicable negative covenants that limit State Street Bank’s right to refuse to consent to any such sale in the event of a default. Accordingly, the bank had the right under the Credit Agreements to “withhold consent for any reason or no reason.” Teachers Ins. & Annuity Association of America, 833 F.Supp. at 349; see also Bonady Apartments, 465 N.Y.S.2d at 154, 119 Misc.2d at 927-28.
Moreover, even if an implied covenant of good faith and fair dealing had circumscribed State Street Bank’s right to unreasonably or arbitrarily withhold its consent to the sale of Cosayach’s assets, the bank’s refusal to consent to such a sale was neither unreasonable nor arbitrary. The bank’s decision to condition its consent to such a sale on the receipt of additional collateral and economic benefits to which the bank was not entitled under the Credit Agreements was made for a legitimate business purpose. Although State Street Bank might have received $87 million from the proceeds of such a sale, those proceeds fell far short of satisfying the multi-million dollar sum of Inverraz’s outstanding accelerated debt. Furthermore, as an unsecured creditor, State Street Bank faced significant uncertainty as to whether it could recover the substantial portion of Inverraz’s debt that exceeded the $87 million that might come from the sale of Cosayach’s assets to SQM. Under the circumstances, State Street Bank was justified in seeking to protect itself by conditioning its consent to the sale on the receipt of additional collateral and economic benefits. See Rexnord Holdings v. Bidermann, 21 F.3d 522, 526-27 (2d Cir.1994) (holding that the defendant had no viable counterclaim based on any breach of good faith and fair dealing where the defendant had already defaulted on payments due and the plaintiff had refused to *171extend time to remit payment unless the defendant released the plaintiff from other unrelated obligations); cf. Bonady Apartments, 465 N.Y.S.2d at 154, 119 Misc.2d at 928 (“[a] decision by a [bank] to condition its consent to a transfer [of property on an agreement] to pay a higher rate of interest” than the rate set by the original contract was made for a legitimate business purpose exercised in good faith).
Because State Street Bank did not breach a covenant of good faith and fair dealing under New York law, this counterclaim does not constitute a meritorious defense.
3. Tortious Interference with Business Relations
Defendants contend that they have articulated a meritorious defense by advancing a counterclaim for tortious interference with business relations. This counterclaim is also based on SQM’s decision to break away from its aforementioned negotiations with the defendants regarding the sale of Cosayach’s assets. According to the defendants, SQM refused to proceed with the transaction to purchase these assets for $140 million because State Street Bank failed to consent to the sale. The defendants argue that State Street Bank’s refusal to consent to the sale unless the defendants provided the bank with additional collateral and economic benefits to which the bank would not have been entitled under the Credit Agreements constituted tortious interference with business relations.
To prevail on a claim for “tortious interference with business relations” under New York law, a party “must prove that (1) it had a business relationship with a third party;7 (2) the defendant knew of that relationship and intentionally interfered with it; (3) the defendant acted solely out of malice, or used dishonest, unfair, or improper means; and (4) the defendant’s interference caused injury to the relationship.” Carvel Corp. v. Noonan, 350 F.3d 6, 17 (2d Cir.2003); see also Scutti Enterprises, LLC v. Park Place Entertainment Corp., 322 F.3d 211, 215 (2d Cir.2003). On appeal, the defendants vigorously argue that the district court erred in rejecting their tortious interference counterclaim because State Street Bank purportedly employed wrongful means to interfere with the defendants’ business relationship with SQM. In other words, they focus on whether the third element of their tortious interference counterclaim has been satisfied.
We need not address the merits of this argument because the defendants have failed adequately to challenge the district court’s and the magistrate judge’s determinations pertaining to the fourth element of a tortious interference claim, namely the absence of proximate causation. The defendants cannot prevail on their tortious interference counterclaim unless they “demonstrate both wrongful means and that the wrongful acts were the proximate cause of the rejection of the plaintiffs proposed contractual relations.” Pacheco v. United Medical Assoc., P.C., 759 N.Y.S.2d 556, 559, 305 A.D.2d 711, 712 *172(3d Dep’t 2003) (citation and internal quotation marks omitted; emphasis added).
In the proceedings below, the district court and the magistrate judge determined that the defendants’ tortious interference counterclaim did not constitute a meritorious defense for two reasons: both because State Street Bank refused to consent to the sale on the basis of legitimate motivations and because the bank did not cause the defendants’ negotiations with SQM to fall apart. See State Street Bank II, 246 F.Supp.2d at 240-41, 255. In their initial appellate brief, the defendants failed altogether to address the proximate cause issue. Rather, the defendants focused exclusively on whether State Street Bank interfered with their business relationship with SQM through wrongful means. When State Street Bank subsequently emphasized the absence of proximate causation in its opposition brief, the defendants responded in a cursory fashion by arguing that State Street Bank “erroneously claims a lack of record evidence of ‘proximate cause.’ ” However, the defendants failed to advance any factual support or legal arguments in favor of that proposition.8
When a party fails adequately to present arguments in an appellant’s brief, we consider those arguments abandoned. See Schwapp v. Town of Avon, 118 F.3d 106, 112 (2d Cir.1997) (refusing to consider several claims on appeal where the appellant failed to make any legal or factual arguments in support thereof). Cf. Tolbert v. Queens College, 242 F.3d 58, 75 (2d Cir.2001) (citation and internal quotation marks omitted) (“It is a settled appellate rule that issues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived.”); Fed. R.App. P. 28(a)(9)(A) (“The appellant’s brief must contain ... the argument, which must contain ... [the] appellant’s contentions and the reasons for them, with citations to the authorities and parts of the record on which the appellant relies.”). Because the defendants have failed to advance any factual or legal arguments with respect to the district court’s and magistrate judge’s determinations regarding the absence of proximate causation, we conclude that they have, in effect, abandoned any challenge to those findings. As a consequence, they are unable on appeal to demonstrate that they have satisfied the proximate cause element of a tortious interference with business relations counterclaim and cannot establish a meritorious defense on the basis of such a counterclaim.9
*1734. Failure to Fulfill Condition Precedent
In addition to asserting the foregoing counterclaims, the defendants attempt to articulate a meritorious defense by arguing that State Street Bank failed to satisfy the necessary conditions for the initiation of the instant lawsuit. Their arguments are based on certain provisions in several participation agreements.
When State Street Bank loaned Inver-raz money in 1994 and 1996, the bank entered into separate agreements with various institutions (the “Participation Agreements”), defined in the agreements as “Participants,” pursuant to which the bank sold its interest in the loans to the Participants but retained responsibility for, inter alia, collecting on the loans. These Participation Agreements specifically charged State Street Bank with the duty of demanding that Inverraz and the various guarantors perform their obligations under the Credit Agreements and the Guaranty Agreements. However, the Participation Agreements also provided that State Street Bank would “not exercise any ... rights or powers” that the bank possessed with respect to the loans, absent certain exceptions not relevant here, unless the bank did so “in accordance with the written instruction of the Required Participants.” The Participation Agreements defined “Required Participants” as Participants that owned, in the aggregate, more than 50% of the participation interests in the loans.10
The defendants contend that State Street Bank improperly initiated this lawsuit without complying with the “written instruction” condition because the bank failed to secure the written consent of the “Required Participants” to the commencement of this lawsuit before the bank filed this legal action on April 16, 2001. As such, the defendants argue that State Street Bank lacks standing to pursue this lawsuit on the Participants’ behalf.
When the defendants advanced this argument in the proceedings below in an effort to present a “meritorious defense,” State Street Bank responded by introducing two sets of “Written Direction[s]” during the hearing before the magistrate judge. These directions appear to have been signed by the “Required Participants” 11 and direct State Street Bank “to promptly file and serve” the complaint in the lawsuit at bar. The instructions are dated “April 16, 2001;” in other words, they bear the very date on which State Street Bank commenced this legal action. Nevertheless, the defendants maintain that State Street Bank has failed to comply with the condition precedent enumerated in the Participation Agreements because there is no evidence that the Participants signed the foregoing “Written Direction[s]” before State Street Bank initiated this lawsuit on April 16, 2001.
The magistrate judge relied on these written instructions, among other things, to reject the defendants’ condition prece*174dent defense as a matter of fact. See State Street Bank II, 246 F.Supp.2d at 257. The district court found that this factual determination was correct and adopted the magistrate judge’s findings of fact. See id. at 243.
We review for clear error a district court’s findings of fact with respect to the denial of a Rule 60(b) motion to set aside a default judgment. See Audiovisual Publishers v. Cenco, Inc., 580 F.2d 50, 52 (2d Cir.1978). After examining the record, we conclude that the district court’s and the magistrate judge’s factual determinations regarding the condition precedent defense were not clearly erroneous. Nothing in the record suggests that the Participants failed to sign the written instructions directing State Street Bank to institute this lawsuit before the bank actually initiated the legal action. Accordingly, we agree with the district court and the magistrate judge that the defendants’ argument with respect to State Street Bank’s supposed failure to comply with the condition precedent set out in the Participation Agreements does not constitute a meritorious defense.12
B. Prejudice
Defendants argue that the district court erroneously denied their initial motion to vacate the default judgment both because the court incorrectly determined that they had failed to articulate a meritorious defense and because the court mistakenly found that they had failed to demonstrate that State Street Bank would not be prejudiced if the default judgment were vacated. We need not evaluate whether the vacatur of the default judgment would subject State Street Bank to prejudice because we have concluded that the defendants failed to establish a meritorious defense; the absence of such a defense is sufficient to support the district court’s denial of the defendants’ first Rule 60(b) motion. See Commercial Bank of Kuwait v. Rafidain Bank, 15 F.3d 238, 244 (2d Cir.1994). Cf. Sony Corp. v. Elm State Elec., 800 F.2d 317, 320-21 (2d Cir.1986) (affirming the denial of a motion to reopen a default after determining that the defendants failed to' demonstrate that they possessed a meritorious defense).
II. The Defendants’ Second Rule 60(b) Motion
After the district court denied their initial Rule 60(b) motion to vacate the default judgment, an Inverraz employee found a letter “buried within” his files in December 2002. Once they read this letter, the defendants brought a second motion for relief from the default judgment in February 2003 pursuant to various provisions of Rule 60(b). That new motion also sought to vacate the district court’s previous order denying the defendants’ prior Rule 60(b) motion.
The newly discovered letter had been written by Inverraz’s General Manager in January 1999 and sent to State Street Bank. In this correspondence, the General Manager delineated particular Inverraz subsidiaries which, according to Inverraz, had “become” guarantors or “continue[d] to be” guarantors since the execution of the 1996 Credit Agreement. This copy of the letter appears to have been endorsed by Kelley L. Rumps (Rumps), a former Assistant Vice President at State Street Bank. She countersigned the letter under a heading which read “Received and Agreed By.”
*175Much of the information set out in this copy of the letter had been raised in the instant litigation long before the defendants filed a second Rule 60(b) motion in February 2003. State Street Bank had submitted a copy of the letter when the bank moved the district court to enter a default judgment in October 2001. Furthermore, the defendants submitted the letter as an exhibit when they responded to the bank’s opposition brief to their initial motion to vacate the default judgment. Moreover, they successfully persuaded the magistrate judge to admit a copy of the letter as an exhibit during the hearing in May 2002. The defendants tried to rely on this letter as well as a subsequent yet somewhat similar February 2000 letter to articulate a meritorious defense; they argued that such letters corroborated that several of the defendants were not liable as guarantors under the 1996 Credit Agreement. The magistrate judge rejected this argument in his report and recommendation. See State Street Bank II, 246 F.Supp.2d at 258-61. The district court agreed with the magistrate judge in this respect and adopted his findings of fact and conclusions of law. Id. at 243. On appeal, the defendants have not challenged this aspect of the decision denying their initial Rule 60(b) motion.
The countersignature of a State Street Bank employee, however, sets the copy of the January 1999 letter found in December 2002 apart from the previous copy that had repeatedly been admitted as an exhibit. The previous copy had not been countersigned by anyone from State Street Bank.
The defendants relied on this newly unearthed letter to advance several arguments in their second Rule 60(b) motion. They contended, among other things, that the letter allowed them to establish a meritorious defense and therefore justified the vacatur of the default judgment pursuant to Rule 60(b)(1). The defendants also argued, inter alia, that both the district courts order denying their previous Rule 60(b) motion as well as the underlying default judgment should be vacated pursuant to Rule 60(b)(3) because State Street Bank had concealed this critical letter from them over the course of the litigation and thereby perpetrated a fraud against them. In the same vein, they argued that the concealment of this letter also constituted a fraud on the court and thereby merited the vacatur of both the district court’s prior order denying their earlier motion and the underlying default judgment pursuant to Rule 60(b). Finally, separate and apart from their allegations pertaining to the letter, the defendants argued that the district court should vacate the default judgment as void pursuant to Rule 60(b)(4) for reasons related to the district court’s award of damages. The district court rejected each of these arguments, see State Street Bank III, 2003 WL 1907955, at *1-2, and the defendants now appeal.
A. Fraud
Defendants posit that State Street Bank defrauded them and perpetrated a fraud on the court by purportedly withholding a copy of the January 1999 letter countersigned by Kelly Bumps during the course of this legal action and by allowing the litigation to proceed on the basis of the copy of the letter signed solely by Inver-raz’s General Manager. They argue that this alleged fraud merited the vacatur of the default judgment pursuant to Rule 60(b)(3) and Rule 60(b).
The district court rejected the defendants’ allegations regarding fraud and found, inter alia, that there was no evidence that State Street Bank had ever possessed a version of the letter countersigned by Rumps. State Street Bank III, *1762003 WL 1907955, at *1. Although the defendants argue that this determination was clearly erroneous, albeit without advancing any evidence whatsoever to support that allegation, we need not address that contention. Even if we were to assume that State Street Bank had concealed the countersigned letter, we would nevertheless affirm the district court’s rejection of the defendants’ arguments with respect to fraud.
Under Rule 60(b)(3), a district court may relieve a party from a final judgment for “fraud.” Fed.R.Civ.P. 60(b)(3). In addition, Rule 60(b) allows a ' court to set aside a judgment for fraud on the court. See Campaniello Imports, Ltd. v. Saporiti Italia S.p.A., 117 F.3d 655, 661 (2d Cir.1997). However, although the defendants suggest that State Street Bank committed both a fraud and a fraud on the court, we disagree.
As the district court aptly explained, “[i]t is certainly unique to argue that [a] plaintiff concealed a document from [the] defendants that [the] defendants possessed all along in their own files.” State Street Bank III, 2003 WL 1907955, at *1. To prevail on a Rule 60(b)(3) motion, a movant “must show that the conduct complained of prevented the moving party from fully and fairly presenting his case.” Taylor v. Texgas Corp., 831 F.2d 255, 259 (11th Cir.1987) (citations and internal quotation marks omitted); see also Stridiron v. Stridiron, 698 F.2d 204, 207 (3d Cir.1983) (same); Rozier v. Ford Motor Co., 573 F.2d 1332, 1339 (5th Cir. 1978) (same). These same principles apply when a movant seeks to set aside a judgment on the basis of fraud on the court. See Davenport Recycling Associates v. C.I.R., 220 F.3d 1255, 1262 (11th Cir.2000) (“ ‘Fraud on the court must involve an unconscionable plan or scheme which is designed to improperly influence the court in its decision,’ preventing the opposing party ‘from fully and fairly presenting his case.’ ”) (quoting Abatti v. C.I.R., 859 F.2d 115, 118 (9th Cir.1988)); see also Luttrell v. United States, 644 F.2d 1274, 1276 (9th Cir.1980); Keys v. Dunbar, 405 F.2d 955, 957-58 (9th Cir.1969) (per curiam). '
Where a movant admits that a letter that the other party supposedly concealed was already present in the movant’s files, it “cannot claim that it was prevented from fully presenting its ease.” Progressive Casualty Ins. Co. v. Liberty Mutual Ins. Co., 1996 WL 524339, at *2 (S.D.N.Y. Sept.13, 1996); see also Taylor, 831 F.2d at 259-60 (where the defendant already possessed the information supposedly concealed by the plaintiff, the defendant cannot establish that the plaintiffs failure to reveal that same information prevented it from fully and fairly presenting its case). Here, the defendants concede that they possessed the letter countersigned by Rumps in their own files. As such, they cannot prevail as a matter of law on a Rule 60(b)(3) motion predicated on fraud or a Rule 60(b) motion premised on fraud on the court.
B. Meritorious Defense
On appeal, the defendants contend that the district court should have vacated the default judgment pursuant to Rule 60(b)(1) because their new evidence establishes a meritorious defense. They argue that the copy of the January 1999 letter they found buried in their files, which bore Rumps’ countersignature, constituted a binding agreement between Rumps’ former employer, State Street Bank, and Inverraz and thereby modified the particular guarantors that could be held liable for Inver-raz’s debt under the 1996 Credit Agreement.
The district court refused to vacate the default judgment on the basis of the coun*177tersigned copy of the letter. The court found the newly discovered correspondence to be “immaterial.” State Street Bank III, 2003 WL 1907955, at *2 n. 3. The court arrived at this conclusion after explaining that the “recently unearthed document would have had no bearing whatsoever on the court’s determination to uphold the default judgment.” Id. at *1.
We agree with the district court that the 1999 correspondence signed by Rumps was immaterial. We therefore affirm the court’s refusal to vacate the default judgment on the basis of that letter. We also affirm the district court’s denial of the second Rule 60(b)(1) motion on the additional ground that the defendants failed to defend against the default judgment with sufficient diligence to merit its vacatur.
As we mentioned earlier, Rule 60(b)(1) permits a court to vacate a judgment on the grounds of “excusable neglect.” Fed.R.Civ.P. 60(b)(1). However, where a party fails to act with diligence, he will be unable to demonstrate that his conduct constituted “excusable neglect.” See Martella v. Marine Cooks & Stewards Union, 448 F.2d 729, 730 (9th Cir.1971) (per curiam); see also 11 Charles Alan Wright & Arthur R. Miller, Federal Practice and Procedure § 2858, at 288-89 (2d ed. 1995) (“Insufficient showings for relief [under Rule 60(b)(1) ].... include when the party or attorney did not act diligently”); 12 James Wm. Moore et al., Moore’s Federal Practice § 60.41[1][c][ii], at 60-90 (3d ed. 1997) (“Courts repeatedly deny relief [pursuant to 60(b)(1) ] when they find that the facts and circumstance[s] demonstrate a lack of diligence in pursuing or defending litigation.”). Cf. Ramseur v. Beyer, 921 F.2d 504, 506 (3d Cir.1990) (recognizing that a court must be satisfied that attorneys acted with substantial diligence before finding “excusable neglect”). Hence, when a party demonstrates a lack of diligence in defending a lawsuit, a court need not set aside a default judgment. See Florida Physician’s Ins. Co. v. Ehlers, 8 F.3d 780, 784 (11th Cir.1993) (per curiam).
Here, the defendants asserted from the outset that a number of them were not liable as guarantors under the 1996 Credit Agreement. They pressed this legal argument before the magistrate judge in May 2002 and even sought to introduce the January 1999 letter in support thereof, although their copy of the letter lacked Rumps’ countersignature. When they brought their second Rule 60(b) motion in February 2003 on the basis of the countersigned copy of the letter that they unearthed in their own files, the defendants offered no explanation regarding why they could not, with diligence, have found that same exhibit in their inventory during the course of their earlier efforts to defend against the default judgment through the articulation of meritorious defenses. In essence, although they tied up significant judicial resources by advancing a host of defenses and counterclaims as part of an extensive effort to vacate the default judgment, the defendants subsequently tried to get a second bite at the meritorious defense apple by submitting new evidence they apparently possessed all along during the earlier proceedings when the district court and the magistrate judge were specifically reviewing the legal arguments implicated by the new evidence. Under these circumstances, the defendants failed diligently to defend against the default judgment at the appropriate time on the basis of this evidence and the district court properly denied their second Rule 60(b)(1) motion given the absence of excusable neglect.
If anything, the nature of the arguments raised by the defendants with respect to the newly found letter indicate *178that their second Rule 60(b) motion,' although supposedly predicated in part on Rule 60(b)(1), appears more properly to be governed by Rule 60(b)(2). Where a claim “sounds very much like a claim regarding newly discovered evidence,” the claim is “controlled by 60(b)(2)” and should not be labeled as if brought under a different provision of Rule 60(b). Kalamazoo River Study Group v. Rockwell Int'l Corp., 355 F.3d 574, 588 (6th Cir.2004). Here, the facts explain why the defendants apparently failed to label their second Rule 60(b)(1) motion as one properly brought in accordance with Rule 60(b)(2). Under that provision, the problems associated with the “newly” found letter are patently clear. To prevail on a motion for relief pursuant to Rule 60(b)(2), a movant must demonstrate that he was justifiably ignorant of the newly discovered evidence despite due diligence. See United States v. Int’l Brotherhood of Teamsters, 247 F.3d 370, 392 (2d Cir.2001). As our previous recitation of the facts underscores, the defendants have offered no explanation for why they failed to discover the countersigned letter in their own files before December 2002 and to introduce such evidence at the particular time when the district court and magistrate judge were considering, whether certain defendants were liable under the 1996 Credit Agreement. In short, they have failed to, demonstrate that they were justifiably ignorant of the letter in their files despite due diligence.
C. Rule 60(b)(1) Motion
Defendants argue that the district court erred by refusing to vacate the default judgment as void pursuant to Rule 60(b)(4). According to the defendants, the judgment is void for several reasons. First, the defendants fault the district court for awarding damages for “liquidated amounts” despite the prayer in State Street Bank’s complaint seeking “generalized relief.” In addition, the defendants contend that the judgment is void because the court imposed damages in the default judgment without conducting an inquest to ascertain the proper amount of damages against each defendant. They also raise questions about the validity of the judgment where the court awarded damages against the defendants jointly and severally for the entire accelerated debt due pursuant to the Credit Agreements where the Guaranty Agreements required particular entities to pay for only a specific percentage of that debt.
Under Rule 60(b)(4), a district court .may relieve a party from a final judgment if “the judgment is void.” Fed. R.Civ.P. 60(b)(4). Whereas we generally review motions pursuant to the provisions of Rule 60(b) for abuse of discretion, we review de novo a district court’s denial of a Rule 60(b)(4) motion. Central Vermont Public Service Corp. v. Herbert, 341 F.3d 186, 189 (2d Cir.2003). “Under Rule 60(b)(4) a deferential standard of review is not appropriate because if the underlying judgment is void, it is a per se abuse of discretion for a district court to deny a movant’s motion to vacate the judgment under Rule 60(b)(4).” Id. (citations and internal quotation marks omitted).
A default judgment may be considered void if the judgment has been entered “in a manner inconsistent with due process of law.” Fustok v. ContiCommodity Serv., 873 F.2d 38, 39 (2d Cir.1989) (citations and internal quotation marks omitted). However, we need not decide whether the default judgment is void. Even if we were to assume that the default judgment did violate due process, and was void as a result, we would nonetheless affirm the district court’s denial of the defendants’ Rule 60(b)(4) motion because their motion was untimely.
*179On appeal, the defendants fail to acknowledge that the district court denied their Rule 60(b)(4) motion for two independent reasons. On the one hand, the district court found the defendants’ arguments regarding the validity of the judgment to be “meritless.” State Street Bank III, 2003 WL 1907955, at *2. In this respect, the court explained that it had “not merely awardfed] the damages prayed for by [State Street Bank] without investigation.” Id. Rather, the court held that “its determination of damages [rested] on the affidavit of Fred Epstein, who detailed how damages were calculated in accordance with the [Credit Agreements and Guaranty] [A]greements at issue.” Id. As such, the court found that “no violation [of 60(b)(4) ] occurred here.”13 Id.
The district court also denied the defendants’ Rule 60(b)(4) motion because the defendants failed to raise their voidness argument in their prior Rule 60(b) motion even though they “had ample opportunity to do so.” Id. In the appeal at bar, State Street Bank argues that the district court properly denied the defendants’ Rule 60(b)(4) motion as untimely pursuant to this rationale and we agree.
As we explained several years ago,
a Rule 60(b)(4) motion ■ must be made “within a reasonable time” after entry of the judgment. Courts have been exceedingly lenient in defining the term “reasonable time,” with regard to voidness challenges. In fact, it has been oft-stated that, for all intents and purposes, a motion to vacate a default judgment as void “may be made at any time.”
Beller & Keller v. Tyler, 120 F.3d 21, 24 (2d Cir.1997) (citations omitted). Nevertheless, where a party has previously filed a motion to vacate a default judgment that failed to raise a voidness argument and subsequently advances such an argument in a Rule 60(b)(4) motion more than a year after the entry of the default judgment, the Rule 60(b)(4) motion should be denied as untimely. See id. at 22-24; see also Planet Corp. v. Sullivan, 702 F.2d 123, 125-26 (7th Cir.1983).
Here, the default judgment was entered on the docket on December 4, 2001. Not long thereafter, the defendants brought their first motion to vacate the default judgment. Although they litigated that motion for many months, the defendants failed to argue that the default judgment was void for any reason related to the district court’s award of damages. Instead, the defendants advanced such an argument for the first time in the second Rule 60(b) motion they filed in February 2003. Under these circumstances, we conclude that the district court properly denied their Rule 60(b)(4) motion as untimely.14
D. Sanctions
State Street Bank asks us to sanction the defendants as well as their counsel for *180re-litigating many of the unsuccessful arguments they articulated in their Rule 60(b) motions in the proceedings below. The bank suggests that we should impose sanctions pursuant to either Rule 38 of the Federal Rules of Appellate Procedure, 28 U.S.C. § 1927, or our inherent authority to do so.
We begin by noting that sanctions would not be justified under Rule 38. That provision allows a court of appeals to award “just damages and single or double costs to the appellee” if the court has determined that an appeal is “frivolous.” Fed. R.App. P. 38. However, such sanctions may only be imposed “ ‘after a separately filed motion or notice from the court.’ ” Great American Ins. Co. v. M/V Handy Laker; 348 F.3d 352, 354 (2d Cir. 2003) (per curiam) (quoting Fed. R.App. P. 38). “Since neither of those measures has been taken in this case,” we refuse to award sanctions to State Street Bank pursuant to Rule 38. Id.
We also conclude that sanctions would not be appropriate under 28 U.S.C. § 1927.15 Section 1927 authorizes the imposition of sanctions only “when there is a finding of conduct constituting or akin to bad faith.” Sakon v. Andreo, 119 F.3d 109, 114 (2d Cir.1997). “We have held that an award under [section] 1927 is proper when the attorney’s actions are so completely without merit as to require the conclusion that they must have been undertaken for some improper purpose such as delay.” In re 60 East 80th Street Equities, 218 F.3d 109, 115 (2d Cir.2000) (citations and internal quotation marks omitted). Although certain actions taken by defendants’ counsel approach the borders of this standard, particularly with respect to his arguments on appeal pertaining to fraud and fraud on the court, we are ultimately unpersuaded that he articulated various arguments in these consolidated appellate proceedings in bad faith. Hence, sanctions would not be justified under 28 U.S.C. § 1927. Under these circumstances, we also decline to sanction the defendants or their counsel in accordance with our inherent authority to do so.16 See Sakon, 119 F.3d at 114.
CONCLUSION
For the foregoing reasons, we affirm the district court’s denials of the motions the defendants brought pursuant to the provisions of Rule 60(b). We also deny the defendants’ motion to certify certain issues pertaining to the merits of their tortious interference counterclaim to the New York Court of Appeals.
. This figure does not include the interest payments that also were awarded in the default judgment.
. In this respect, Comercial e Inmobiliaria Unimarc S.A., Pesquera Nacional S.A., Cidef S.A., Salmones Unimarc S.A., and Industria Forestal Nacional S.A. signed a Guaranty Agreement pertaining to the 1994 Credit Agreement; in turn, each of the foregoing entities, as well as Compañia de Salitre y Yodo Primera Región S.A. and Cidef Argentina S.A., also signed a Guaranty Agreement pertaining to the 1996 Credit Agreement. In addition, the 1996 Credit Agreement included provisions that allowed for the possibility that the identity of the guarantors responsible for the 1996 loan could change at specified times if certain financial criteria were met.
. State Street Bank brought this action against Inverraz as well as various defendants that it contends are liable as guarantors under the Guaranty Agreements. Some of the defendants — Pesquera Nacional S.A., Cidef S.A., Salmones Unimarc S.A., Industria Forestal Nacional S.A., and Cidef Argentina S.A.— were explicitly named as guarantors in those Guaranty Agreements. The bank contends that two of the defendants, Supermercados Unimarc S.A. and Sociedad Contractual Min-era Compañia de Salitre y Yodo Primera Re-gión, were formerly known as, respectively, the named guarantors Comercial e Inmobilia-ria Unimarc S.A. and Compañia de Salitre y Yodo Primera Región S.A. In addition, State Street Bank brought this action against defendants Unimarc Abastecimientos S.A., Forestal Regional S.A., and Corporación de Inver-siones y Desarrollo Financiero Cidef S.A.; according lo State Street Bank, these entities allegedly became liable as guarantors for the sums owed to the bank because they were successors-in-interest to certain of the original guarantors.
. Rule 55(c) of the Federal Rules of Civil Procedure expressly allows a court to set aside a default judgment pursuant to Rule 60(b). See Fed.R.Civ.P. 55(c).
. In the proceedings below, the defendants argued that Cosayach was not a Restricted Subsidiary within the meaning of the Credit Agreements. Nonetheless, in their appellate brief, the defendants concede that the asset-sale to SQM could not have gone forward without State Street Bank's prior consent.
. Early in the litigation, the district court rejected the defendants' argument that State Street Bank's lawsuit should be dismissed on the grounds of forum non conveniens. State Street Bank I, 230 F.Supp.2d at 322-23. In so doing, the court determined that State Street Bank’s claims against the defendants were governed by New York law. Id. at 322. Subsequently, both the district court and the magistrate judge similarly analyzed the defendants' counterclaims and defenses in accordance with New York law. See State Street Bank II, 246 F.Supp.2d at 240-43, 254-61. The defendants and State Street Bank have also done the same, both in the proceedings below and on appeal. As such, we will proceed on the assumption that the defendants’ counterclaims as well as their defense are governed by New York law.
. Because we ultimately hold that the defendants’ tortious interference claim fails for other reasons, we express no opinion regarding whether the relationship here — consisting of competitors that engaged in failed negotiations over the sale of assets — may constitute "a continuing business or other customary relationship not amounting to a formal contract” sufficient to prove a claim under New York law for tortious interference with business relations. Scutti Enterprises, LLC v. Park Place Entertainment Corp., 322 F.3d 211, 215 (2d Cir.2003) (citation and internal quotation marks omitted).
. We note that this is not the first occasion on which the defendants have failed to address the issue of proximate cause. When the magistrate judge recommended that the defendants' initial motion to vacate the default judgment should be denied, the defendants submitted objections to the district court. However, although the magistrate judge had determined that the defendants could not prevail on their tortious interference counterclaim because, inter alia, they had failed to establish proximate causation, see State Street Bank II, 246 F.Supp.2d at 255, the defendants failed to offer specific objections to that aspect of his report. Instead, they focused for the most part on the merits of their implied covenant of good faith and fair dealing counterclaim and whether State Street Bank would suffer prejudice in the event of vacatur. In most other respects, they merely objected in a cursory fashion to the remaining portions of the magistrate judge’s report pertaining to meritorious defenses.
. Immediately prior to oral argument, the defendants moved to certify certain issues pertaining to their tortious interference counterclaim to the New York Court of Appeals. Those issues implicate the contours of the third element of their tortious interference counterclaim — namely, when a party's alleged interference has been accomplished through “improper” or "wrongful” means. However, because the defendants have not adequately challenged on appeal the district court’s and magistrate judge’s determinations regarding *173their failure to satisfy the fourth element of their counterclaim (i.e., proximate cause), we need not address whether these issues should be certified to the New York Court of Appeals. We therefore deny the defendants' motion for certification.
. The 1994 and 1996 Participation Agreements differ somewhat in how they define which Participants qualify as "Required Participants.” However, these differences are irrelevant to this appeal.
. These "Written Direction[s]” were introduced before the magistrate judge without objection by the defendants. Moreover, the defendants have never argued, either at the evidentiary hearing, before the district court, or on appeal, that these instructions were not signed by all of the Required Participants.
. Given our conclusion regarding this factual determination, we need not address the defendants' argument that they have standing to pursue this defense as third-party beneficiaries of the Participation Agreements.
. We express no opinion, in light of our conclusion that the defendants' Rule 60(b)(4) motion was untimely, regarding whether a challenge to a district court’s determination of damages in a default judgment is properly brought through the vehicle of a Rule 60(b)(4) motion rather than through a direct appeal.
. We end our discussion of the two Rule 60(b) motions at issue in this appeal by noting that, in the final footnote of their initial appellate brief, the defendants argue that if the default judgment is not vacated on the various specific grounds enumerated in their brief, that judgment should, in the alternative, be vacated pursuant to Rule 60(b)(6) "in the interests of due-process, justice and international comity.” They do not expand on this contention beyond that statement. An argument "is not sufficiently presented for appeal if it is conclusorily asserted only in a footnote.” Tolbert, 242 F.3d at 76. Accordingly, we do not address the defendants’ Rule 60(b)(6) argument on appeal.
. Section 1927 provides:
Any attorney or other person admitted to conduct cases in any court of the United States or any Territory thereof who so multiplies the proceedings in any case unreasonably and vexatiously may be required by the court to satisfy personally the excess costs, expenses, and attorney’s fees reasonably incurred because of such conduct.
28 U.S.C. § 1927.
. Nothing in our holding regarding sanctions should be read to prohibit State Street Bank, as the prevailing party, from seeking costs in accordance with Rule 39 of the Federal Rules of Appellate Procedure. See Fed. R.App. P. 39 (providing that, "if a judgment is affirmed, costs are taxed against the appellant”).