Appeal from an order of the Supreme Court (Devine, J.), entered October 10, 2012 in Albany County, which granted defendant’s motion to dismiss the complaint.
Plaintiff Kevin McKenna, a sergeant with the City of Albany Police Department, allegedly pointed a loaded firearm at a coworker, Shirley Morton. Based on that incident, McKenna was charged criminally. He retained plaintiff Paul DerOhannesian II to represent him. Pursuant to the collective bargaining agreement (hereinafter CBA) between his union and defendant, McKenna sought reimbursement of his defense costs from defendant. Defendant denied the request on the basis that Mc-Kenna’s conduct was outside the scope of his employment, an exclusion under the CBA. McKenna was ultimately acquitted of the criminal charge. Morton then commenced a federal civil action and, later, a state action against, among others, McKenna and defendant. DerOhannesian represented McKenna in both civil actions. McKenna also requested reimbursement of his defense costs in the civil actions, which defendant denied, prompting McKenna to file a grievance.
In January 2009, while the grievance was pending, John Reilly, defendant’s corporation counsel, sent a letter to DerOhannesian noting that the CBA required defendant to pay defense costs while the grievance was pending and requesting a cost estimate for his services. DerOhannesian responded by sending Reilly a proposal for his firm’s hourly rates, including $225 for partners and lesser amounts for other staff. Reilly sent a letter rejecting those rates and offering to pay a rate of $150 per hour. DerOhannesian apparently did not respond to that letter. In October 2009, DerOhannesian sent defendant a letter and invoice for his representation of McKenna in the federal ac*1289tion, charging various rates for different staff members, including $350 per hour for his time. Defendant did not respond to this invoice.
The federal action was dismissed. The state action was dismissed as against defendant, but Morton obtained a verdict against McKenna for approximately $23,000. After the civil actions concluded, the arbitrator denied McKenna’s grievance, finding that the CBA did not require defendant to reimburse McKenna for any of his defense costs.1 Plaintiffs commenced this action alleging six causes of action to obtain payment for McKenna’s defense costs. Supreme Court granted defendant’s motion to dismiss the complaint. Plaintiffs appeal.
Initially, we reject defendant’s contention that this action is barred by collateral estoppel. Although collateral estoppel is applicable to determinations rendered in arbitration proceedings (see Matter of American Ins. Co. [Messinger — Aetna Cas. & Sur. Co.], 43 NY2d 184, 189-190 [1977]; Matter of Kibler v New York State Dept. of Correctional Servs., 91 AD3d 1218, 1220 [2012], lv denied 19 NY3d 803 [2012]), that doctrine does not bar the present action based on the arbitration determination here. There is no identity of issues, as the issue in the grievance arbitration proceeding was the right to reimbursement pursuant to the CBA, whereas the issue in this action is the right to reimbursement based on an alleged contract or agreement separate from the CBA (see Matter of Howard v Stature Elec., Inc., 20 NY3d 522, 525-526 [2013]; Alaimo v McGeorge, 69 AD3d 1032, 1034 [2010]; see also Kaufman v Eli Lilly & Co., 65 NY2d 449, 456-457 [1985]). Additionally, DerOhannesian did not have a full and fair opportunity to litigate any issues as he was not a party to that arbitration proceeding nor in privity to a party (see Matter of Juan C. v Cortines, 89 NY2d 659, 667-668 [1997]). Thus, collateral estoppel does not apply here.
Nevertheless, Supreme Court did not err in dismissing the breach of contract cause of action. When considering whether to dismiss a complaint pursuant to CPLR 3211 (a) (7), “the pleading is to be given a liberal construction, the allegations contained within it are assumed to be true and the plaintiff[s] [are] to be afforded every favorable inference” (Simkin v Blank, 19 NY3d 46, 52 [2012]). This liberal standard, however, will not save allegations that consist of bare legal conclusions or factual claims that are flatly contradicted by documentary evidence or are inherently incredible (see Tenney v Hodgson Russ, LLP, 97 AD3d 1089, 1090 [2012]; Mesiti v Mongiello, 84 AD3d 1547, *12901549 [2011]). “For a contract to be created, regardless of whether it is bilateral or unilateral, ‘there must be a manifestation of mutual assent sufficiently definite to assure that the parties are truly in agreement with respect to all material terms’ ” (Thome v Alexander & Louisa Calder Found., 70 AD3d 88, 103-104 [2009], lv denied 15 NY3d 703 [2010], quoting Matter of Express Indus. & Term. Corp. v New York State Dept. of Transp., 93 NY2d 584, 589 [1999]; see Wilson v R. Patrick Ledger, 97 AD3d 1028, 1029 [2012]). Price is a material term of a contract (see Tufano v Morris, 286 AD2d 531, 534 [2001]; Village of Lansing v Triphammer Dev. Co., 193 AD2d 919, 920 [1993]).
The complaint here alleges that Reilly’s January 2009 letters constituted a unilateral contract whereby defendant agreed to pay DerOhannesian at the rate of $150 per hour, and that the contract became binding when DerOhannesian performed under the contract by representing McKenna. Plaintiffs cannot prevail because their allegations are flatly contradicted by documentary evidence. DerOhannesian’s October 2009 invoice billed defendant at the rate of $350 per hour for his time and at other rates— all higher than listed in his January 2009 estimate — for his staff. This invoice contradicts plaintiffs’ assertion that the parties had agreed on all material terms of a contract, namely a price of $150 per hour (see John Anthony Rubino & Co., CPA, P.C. v Swartz, 84 AD3d 599, 599 [2011]).2 As documentary evidence refutes the allegations and establishes that no valid contract had been formed, Supreme Court properly dismissed the cause of action for breach of contract (see Tenney v Hodgson Russ, LLP, 97 AD3d at 1090).
Plaintiffs’ promissory estoppel cause of action must be dismissed for the same reason. While the complaint facially makes out a cause of action by alleging a clear promise, reasonable and foreseeable reliance by DerOhannesian and an injury based on reliance on the promise (see Clifford R. Gray, Inc. v LeChase Constr. Servs., LLC, 31 AD3d 983, 986-987 [2006]; Fleet Bank v Pine Knoll Corp., 290 AD2d 792, 797 [2002]), the documentary evidence contradicts these allegations. In the October 2009 cover letter sent with his invoice, DerOhannesian stated that, while defendant had declined McKenna’s request for indemnification of his legal fees, it was plaintiffs’ “under*1291standing” that defendant was required to pay for McKenna’s legal services while the grievance was pending. The letter never referred to Reilly’s January 2009 letter or any agreement for defendant to pay him $150 per hour. DerOhannesian stated in his cover letter that he continued his representation based on plaintiffs’ “understanding.” Significantly, DerOhannesian made such statement with the knowledge that defendant had repeatedly rejected the requests for defense costs and did not refer to defendant’s alleged promise. This letter, along with the invoice in which DerOhannesian billed defendant at $350 per hour, establish that he did not rely on defendant’s alleged promise to pay him, let alone to pay him at the rate of $150 per hour. Similarly, the cause of action for account stated is deficient because the invoice was based on a compensation rate that had not been agreed upon by the parties, and that invoice “cannot be made the instrument to create liability when none exists” (Gurney, Becker & Bourne v Benderson Dev. Co., 47 NY2d 995, 996 [1979]; see M. Paladino, Inc. v Lucchese & Son Contr. Corp., 247 AD2d 515, 516 [1998]).
The unjust enrichment cause of action also fails. An unjust enrichment cause of action requires that defendant be enriched, at DerOhannesian’s expense, and that equity and good conscience do not permit defendant to retain what plaintiffs seek to recover (see Georgia Malone & Co., Inc. v Rieder, 19 NY3d 511, 516 [2012]; Mandarin Trading Ltd. v Wildenstein, 16 NY3d 173, 182 [2011]). In the complaint, plaintiffs alleged that defendant was unjustly enriched at DerOhanessian’s expense and that it is against equity and good conscience to permit defendant to retain the fair and reasonable value of the legal services he “performed under the contract to and in reliance on the promise of [defendant].” Although these factual allegations facially state a cause of action for unjust enrichment (see id.), the documentary evidence — particularly DerOhannesian’s October 2009 cover letter — shows that DerOhannesian was aware that defendant rejected McKenna’s request for defense costs several times and DerOhannesian did not represent him or continue his representation based on any promise by defendant. As DerOhannesian acknowledged that defendant had repeatedly rejected the requests to pay for McKenna’s defense costs, but DerOhannesian nonetheless continued to represent McKenna and accrue associated legal fees, it is not against equity or good conscience to permit defendant to retain the amount of such legal fees. Thus, defendant was not unjustly enriched when it refused to pay McKenna’s legal costs (see Baron v Pfizer, Inc., 42 AD3d 627, 629-630 [2007]; Clifford R. Gray, Inc. v LeChase Constr. Servs., LLC, 31 AD3d at 988).
*1292For the same reasons, the quantum meruit cause of action must fail. That cause of action requires a plaintiffs performance of services in good faith, acceptance of those services by a defendant, an expectation of compensation and proof of the reasonable value of the services provided (see Precision Founds. v Ives, 4 AD3d 589, 591 [2004]). We need not address the confusing question of whether defendant accepted DerOhannesian’s services, because plaintiffs’ allegations on two other elements are contradicted by documentary proof. DerOhannesian’s cover letter, acknowledging that defendant had declined McKenna’s request to pay for his legal fees, constituted documentary evidence refuting the allegations that DerOhannesian performed his services in good faith and with a legitimate expectation of compensation from defendant (cf. Estate of Goth v Tremble, 59 AD3d 839, 841-842 [2009]; Rowley, Forrest, O’Donnell & Beaumont, P.C. v Beechnut Nutrition Corp., 55 AD3d 982, 983-984 [2008]). Thus, DerOhannesian cannot collect from defendant under a theory of quantum meruit.
Supreme Court also properly dismissed the fraud cause of action. The elements of fraud include a misrepresentation that is false and that the defendant knows is false, made to induce the other party to rely on it, justifiable reliance on the misrepresentation by the other party, and injury (see Mandarin Trading Ltd. v Wildenstein, 16 NY3d 173, 178 [2011]). Plaintiffs alleged that defendant falsely represented that defendant was required to pay McKenna’s legal expenses until an arbitrator ruled on his grievance. This was not a false statement, as defendant had such an obligation under the CBA. While defendant may not have intended to pay for the legal services, allegations of an intention not to perform an obligation are insufficient to allege fraud (see Yenrab, Inc. v 794 Linden Realty, LLC, 68 AD3d 755, 757-758 [2009]; WIT Holding Corp. v Klein, 282 AD2d 527, 528 [2001]).3 Accordingly, the court properly dismissed the complaint.
Peters, P.J., Stein and Spain, JJ., concur. Ordered that the order is affirmed, without costs.
. Supreme Court confirmed the arbitrator’s determination. That decision is apparently being appealed.
. We are unpersuaded by plaintiffs’ belated and unsupported attempt, raised for the first time at oral argument, to challenge the validity of a document created by DerOhannesian’s own office by alleging that the hourly rates enumerated in his October 2009 invoice may have constituted billing errors, or may have been an attempt to renegotiate the contractual price.
. Indeed, defendant did not pay the legal fees while the grievance was pending. Defendant might have been required to do so under the CBA, but the arbitrator eventually ruled that, if defendant had paid any legal fees, Mc-Kenna was required to refund them to defendant. While this may raise a question as to whether defendant failed to comply with the CBA by paying DerOhannesian, then later seeking to recoup its payments from McKenna, that is a question under the CBA. This action was not brought based on the CBA, but on the basis of an alleged separate contract or agreement. Thus, this question, while possibly intriguing, is not before us.