ORDER GRANTING IN PART AND DENYING IN PART PLAINTIFF’S MOTION FOR PARTIAL JUDGMENT ON THE PLEADINGS

Between September 2012 and January *873 2013, four women 1 filed suit in California state court alleging that as students in the 1990s, they were sexually abused by Mora-ga School District (“the District”) teachers. Each of the women claimed that her emotional injuries were in part caused by a 2012 investigative report that revealed that school administrators received ample notice of the abuse but never reported it and actually conspired to hide it. Westport Insurance Corporation (“Westport”), the District’s insurer in the 1990s and Plaintiff here, paid for the defense of all three suits and the settlement of two. 2 Westport then filed the instant action against. Northern California Relief (“NCR”), the District’s insurer in 2012, demanding that NCR pay its share of the litigation and settlement expenses. After this Court denied NCR’s motion to dismiss in June 2014, Westport brought this motion for partial judgment on the pleadings, in which it seeks a determination that: (1) NCR owes a duty to pay some portion of the defense costs and settlement payments incurred in the underlying lawsuits (Counts I, V, VI, and X); and (2) NCR owes one hundred percent of the defense costs and settlement payment incurred in one of the lawsuits, brought by Kristin Cunnane (Counts II, III, and IV). Because there is no question of fact as to whether the three underlying lawsuits allege injury that occurred at least partly in 2012, the Court GRANTS Westport’s motion as to Counts I, V, VI, and X. This is so despite the affirmative defenses NCR pleaded in its answer. But because the underlying complaints also allege injury that occurred in the 1990s and early 2000s, the Court cannot determine as 'a matter of law that NCR owes Westport one hundred percent of the costs incurred in the Cun-nane suit. Therefore, Westport’s motion is DENIED as to Counts II, III, and IV.

I. BACKGROUND

In March 2012, a local newspaper published an investigation into allegations that the District had covered up child sexual abuse that occurred in the 1990s. Compl., Ex. A ¶ 14, Ex. D ¶ 65. The newspaper’s investigation unearthed letters and internal memoranda from 1994 to 1996 that showed the District knew about the abuse, did nothing to stop it, and then concealed its inaction. Id. In the months following the newspaper investigation, four former students filed three complaints against the District. 3 Id. at Ex. A (Cunnane Compl. of September 25, 2012); Ex. D (Does # 1 and #2 Compl. of January 29, 2013); Ex. G (Doe # 3 Compl. of January 17, 2013). All three complaints alleged that Dan Witters, a teacher employed by the District from 1989 through November 1996, had sexually molested the young women on various occasions between 1990 and 1996. Id. at Ex. A ¶¶ 1, 3; Ex. D ¶¶ 14-17, 23-24, 35-36, 40-41; Ex. G ¶ ll. 4 Based on information *874 that was revealed to them through the 2012 newspaper investigation, the women further alleged that the District ignored numerous written and verbal warnings of Witters’ conduct, thereby creating an environment in which sexual predators could thrive. Id. at Ex.'A ¶¶ 15-24, 47-56; Ex. D ¶¶ 18-22, 25-34, 43-46; Ex. G ¶¶ 13, 18-39.

Westport and NCR insured the District at different time periods. Westport covered the District from October 1, 1991 to October 1, 1999. Compl. 11 35-36. NCR bégan insuring the District in 2002, but this litigation involves only NCR’s annual policy effective from July 1, 2011 to July 1, 2012. Id. ¶ 39. NCR’s Memorandum of Coverage (“MOC”) states that it “is the intent of [NCR] to provide the broadest form of Coverage to each Covered Party to avoid coverage disputes.” Id. ¶40 (citing Ex. K at 6). The District and its administrators are “Covered Parties” as defined by the MOC. Id. (citing Ex. K at 23).

The parties contest two important issues. First is whether the Cunnane and Doe complaints triggered NCR’s duty to cover legál expenses. Westport argues that mere allegations of injury are enough to trigger NCR’s duties under the MOC. Mot. (dkt. 45) at 9-10. NCR argues that coverage is only triggered when damages are proven, not merely alleged. Opp’n to Mot. (dkt. 53) at 11.

Second, the insurance companies disagree as to when the alleged injuries-occurred. Westport claims the injuries occurred at least in part in 2012, pointing to language in all three complaints that alleges new emotional injuries in 2012 upon the women’s discovery of the District’s coverup. Mot. at 11-12. Westport further maintains that Cunnane’s injuries occurred exclusively in 2012 because at a demurrer hearing in state court, her attorney denied any damages claim on account of 1990s abuse, which Westport alleges makes NCR wholly liable for the District’s legal expenses as to her complaint. Id. at 13-14. NCR argues that any emotional injuries the women claim to have suffered in 2012 were caused by continuing or permanent psychological harm that was inflicted in the 1990s. Opp’n to Mot. at 13-14. Regarding the Cunnane complaint, NCR maintains that arguments by counsel cannot be regarded as evidence that Cunnane disavowed any injury in the 1990s. Id. at 1516. According to NCR, the 2012 investigative report was not a new and separate injury, but merely an “accrual anchor” that allowed the complaints to proceed around the statute of limitations. Id. at 15-17. NCR argues that in any event, its answer raises material issues of fact as to whether Westport waived its right to seek indemnity by covering the legal expenses. Id. at 5-19,

Because the parties’ first dispute centers around the interpretation of terms contained in NCR’s MOC, key sections of the contract are reproduced below. The MOC provides as follows:

Compl. ¶ 41 (citing Ex. K at 7).

The MOC defines the relevant highlighted terms in section A. as follows:

Id. (citing Ex. K at 24-27, 32).

The parties’ second dispute revolves around whether the women alleged injuries that occurred within NCR’s coverage period. Regarding the Cunnane complaint, Westport points to four paragraphs to support its contention that she alleged new injuries in 2012:

Compl., Ex. A ¶¶ 57, 94-96.

Westport also relies on statements that Cunnane’s counsel filed in opposition to a demurrer:

Compl., Ex. B at 10 (emphasis added).

Regarding the Does #1 and #2 complaint, Westport points to two paragraphs in support of its position that the women alleged new injuries in 2012:

Compl., Ex. D ¶¶ 67, 82. Westport also points to statements that Does # 1 and # 2 filed in opposition to a demurrer. 5 Compl. ¶ 28.

Finally, ■ regarding the Doe # 3 complaint, Westport points to two paragraphs in support of its contention that she alleged injuries in 2012:

Compl., Ex. G ¶¶ 71-72. Westport also points to the statements made in Doe # 3’s opposition to demurrer. Id. ¶ 34; see supra note 5.

NCR admitted that it received notice of the injury underlying all three lawsuits. Compl. ¶¶ 42, 44, 46; Answ. (dkt. 39) ¶¶ 42, 44, 46. But only Westport defended the District and its administrators. Compl. ¶ 48; Answ. ¶ 48. In May 2013, Westport funded a $2.85 million settlement in the Cunnane lawsuit under a reservation of rights, which allowed it to recoup the amount from the District and/or NCR. Compl. ¶ 51. In September 2013, West-port also funded a settlement in the Doe # 3 lawsuit for an undisclosed amount under a resérvation of. rights. Id. ¶ 54. Westport continues to defend the District and its administrators in the pending Does # 1 and # 2 lawsuit. Id. ¶ 48; Answ. ¶ 48. NCR denied responsibility for these claims and refused to issue coverage. Compl. ¶47; Answ. ¶47; see generally Ex. T.

This Court denied NCR’s motion to dismiss on June 6, 2014 in an order issued from the bench. Transcript of Proceedings (dkt. -40) at 16. NCR then answered Westport’s complaint. Westport filed the instant motion for partial judgment on the pleadings on August 26, 2014. Mot. at 15. Westport seeks declaratory relief establishing that NCR owes at least some portion of the defense and settlement costs to Westport (Counts I, V, VI, and X) and an order that NCR reimburse Westport for one hundred percent of the defense and settlement costs in the Cunnane suit, the specific amount of those costs to be determined in further proceedings (Counts II, III, and IV). Id. at 2.

II. LEGAL STANDARD

Federal Rule of Civil Procedure 12(c) provides that after the pleadings are closed, but early enough hot to delay trial, a party may move for 'judgment on the pleadings. Fed. R. Civ. P. 12(c). The standard for judgment on the pleadings is virtually identical to that for a 12(b)(6) motion to dismiss. Wood v. County of Alameda, 875 F.Supp. 659, 661 (N.D.Cal.1995); see also Harris v. County of Orange, 682 F.3d 1126, 1131 (9th Cir.2012). That is, the moving party must clearly establish on the face of the pleadings that there is no material issue of fact and that the moving party is entitled to judgment as a matter of law. Hal Roach Studios, Inc. v. Richard Feiner and Co., 896 F.2d 1542, 1550 (9th Cir.1990). A court must construe the pleadings in the light most favorable to the nonmoving party. Doyle v. Raley’s, Inc., 158 F.3d 1012, 1014 (9th Cir.1998). A court may not look beyond the pleadings to resolve an issue; such a proceeding is instead properly treated as a motion for summary judgment. See Hal Roach, 896 F.2d at 1550 ; cf. Bonilla v. Oakland Scavenger Co., 697 F.2d 1297, 1301 (9th Cir.1982) (discussing Fed. R. Civ. P. 12(b)(6)). A court may, however, properly consider exhibits to the pleadings as part of the pleadings themselves. See Fed. R. Civ. P. 10(c): Samiere v. San Francisco Unified School Dist., No. C-07-1217-PJH, 2007 WL 2214039 , at *1 (N.D.Cal. July 31, 2007).

III. DISCUSSION

Contrary to NCR’s assertions, the Court may determine as a matter of law. whether the underlying complaints triggered NCR’s coverage duties. NCR admits that the MOC and the women’s underlying complaints attached to Westport’s complaint are true and.correct copies. See Mot. at 1. Notwithstanding its admission, NCR asserts that its answer established factual issues as to the meaning of MOC terms and as to the truthfulness of the allegations in the underlying complaints. *878 ,Opp’n to Mot. at 6-10. NCR’s position essentially is that although it admitted the existence of the MOC and the underlying complaints, its disagreement with West-port as to the meaning of those documents establishes a material issue of fact. Id. at 7,12-14.

The Court disagrees. The MOC is a contract, and under California law, the interpretation of a contract, including the resolution of any ambiguity, is a question of law for the court. See Sprinkles v. Associated Indem. Corp., 188 Cal.App.4th 69, 76 , 114 Cal.Rptr.3d 887 (2010). Looking to the plain language of the MOC and the underlying complaints, the Court concludes that there is no material issue of fact as to .whether allegations of injury triggered NCR’s coverage duties or as to whether the women alleged injury occurring at least partly in 2012. For that reason, the Court GRANTS Westport’s motion as to Counts I, V, VI, and X. This is true despite-NCR’s affirmative defenses, which fail to raise material factual disputes. There remains an issue of fact, however, as to whether Cunnane alleged injury in the 1990s as well as in 2012. For that reason, the Court cannot determine as a matter of law that NCR owes Westport one hundred percent of the costs in the Cunnane matter and so Westport’s motion is DENIED as to Counts II, III, and IV.

A. The Meaning of the Relevant Terms in NCR’s MOC Is Capable of Interpretation as a Matter of Law.

The insurance policy at issue here is a contract that can be interpreted as a matter of law. See, e.g., Reynolds v. Allstate Ins. Co., 855 F.Supp.2d 989, 996 (N.D.Cal.2012); Pavlina v. Safeco Ins. Co. of America, No. 12-cv-534-LHK, 2012 WL 5412796 , at *2 (N.D.Cal. Nov. 6, 2012); Loughney v. Allstate Ins. Co., 465 F.Supp.2d 1039, 1041 (S.D.Cal.2006). NCR argues that Keshish v. Allstate Ins. Co., 959 F.Supp.2d 1226, 1233-34 (C.D.Cal.2013), is contrary authority, but that ease related to whether an insurance company acted in bad faith in denying coverage (because an insurer acts in bad faith only where there is no genuine dispute over coverage), not whether there was a dispute of fact for purposes of summary adjudication. And NCR’s status as a Joint Powers Authority is irrelevant to the interpretation of the MOC, which is simply a contract subject to California law. Under California law, contract interpretation is a legal question for the court. Legendary Investors Group No. 1, .LLC v. Niemann, 224 Cal.App.4th 1407, 1413 , 169 Cal.Rptr.3d 787 (2014). 6 Specifically, courts in California are “guided by the principle that interpretation of an insurance policy is a question of law.” Hartford Cas. Ins. Co. v. Swift Distribution, Inc., 59 Cal.4th 277, 288 , 172 Cal.Rptr.3d 653 , 326 P.3d 253 (2014) (quoting Waller v. Truck Ins. Exchange, Inc., 11 Cal.4th 1, 18 , 44 Cal.Rptr.2d 370 , 900 P.2d 619 (1995)). As such, the MOC can be interpreted under the rules of contract law regardless of whether NCR is a traditional insurance company or whether the MOC is an insur- *879 anee policy. 7

NCR admitted in its answer that Exhibit K (NCR’s MOC for the period from July 1, 2011 to July 1, 2012) to Westport’s complaint was a true and correct copy of the MOC. Compl. ¶ 39; Answ. ¶ 39. Thus, the Court need look no further than the MOC itself to determine the essential question of whether the MOC provided coverage for allegations of injury or only for proven injuries.

B. The Clear and Explicit Language of the MOC Provides that Allegations of Injury Are Sufficient to Trigger NCR’s Duties.

Both the plain language of the MOC and California law establish that NCR’s coverage duties were triggered by the women’s allegations of injury during NCR’s coverage period. California law establishes that the mutual intent of the ■parties at the time a contract is formed governs interpretation. Hartford, 59 Cal.4th at 288 , 172 Cal.Rptr.3d 653 , 326 P.3d 253 (quoting Cal. Civ. Code ¶ 1636). That intent is to be inferred, if possible, solely from the written provisions of the contract. Waller, 11 Cal.4th at 18 , 44 Cal.Rptr.2d 370 , 900 P.2d 619 (emphasis added). The “clear and explicit” meaning of contract terms, interpreted in their “ordinary and popular sense,” governs judicial interpretation. Id. (citations omitted). A contract term will be considered ambiguous when it is capable of two or more constructions, both of which are reasonable. Id. (citation omitted). But “courts will not strain to create an ambiguity where none exists.” Id. (citations omitted).

The unambiguous language of the MOC provides that NCR will pay “Ultimate Net Loss” for each “Loss Occurrence” for which the District becomes obligated to pay for “Damages.” Compl., Ex. K at 7. Significantly, the MOC defines “Ultimate Net Loss” to mean “all sums actually paid or payable ... in the settlement ... of losses ... for which [the District] is liable either by adjudication or compromise ... and includes attorney’s fees.... ” Id. at 32 (emphasis added). Thus, NCR agreed to cover the District for settlement payments as well as sums the District was ordered to pay by a court. Further, the definition of “Loss Occurrence” includes allegations of wrongful acts. A “Loss Occurrence” can be, among other things, “an Error or Omission ... which results in Damages ... which were not expected nor intended by [the District].” Id. at 27 . An “Error or Omission” is further defined to include “an actual or alleged misstatement, misleading statement, act, [or] omission by [the District].” Id. at 25 (emphasis added). Thus, replacing the term “Loss Occurrence” with its contractual definition, the MOC provides that NCR will pay “Ultimate Net Loss” for each “alleged misstatement, misleading statement, act, or omission” for which the District becomes obligated to pay for “Damages.” This unambiguous language requires that the Court conclude that NCR agreed to cover the District for costs that the District incurred as a result of settling claims for alleged misconduct.

*880 NCR next challenges whether “Damages” occurred during the coverage period. Opp’n to Mot. at 10. Specifically, NCR argues that “because the underlying lawsuits were settled by Westport prior to extensive discovery being done, it was never conclusively established whether damages existed, what those damages were, and when those damages occurred.” Id. at 10-11 . NCR points out that “[t]he policy states ‘damages,’ not ‘alleged damages.’ ” Id. at 11 . But neither does the MOC specify that damages be “actual” or “proven.” To the contrary, the MOC defines “Damages” as “the sums owed to an entitled Claimant as compensation for a covered Loss Occurrence.” Compl., Ex. K at 24.

The Court holds that under this unambiguous language, the money paid to the four women as compensation for a “Loss Occurrence,” i.e., an “alleged misstatement, misleading statement, act, or omission,” constitutes “Damages” within the meaning of the MOC, thereby triggering NCR’s coverage duties. NCR’s position that “damages in fact during the coverage period must be shown and proved, not merely alleged,” Opp’n to Mot. at 11, is contrary to the MOC’s clear and explicit language. The money the District paid to settle the Cunnane and Doe # 3 lawsuits is plainly “sums owed to an entitled Claimant as compensation, for a covered Loss Occurrence.” And the money the District paid to litigate each of the lawsuits falls under the umbrella of “Ultimate Net Loss.” Thus, if the women indeed alleged injury in 2012, the MOC required NCR to contribute a share of the defense costs and settlement payments for injuries that were alleged during its coverage period in 2012. Westport need not prove that the District was liable for misleading statements or omissions; the settlement of those allegations was sufficient to trigger NCR’s coverage duties under the contract. This only corroborates the parties’ express intent in the MOC, in which NCR stated that “it is the intent of [NCR] to provide the broadest form of Coverages to each Covered Party to avoid coverage disputes.” Compl., Ex. K at 6.

This conclusion also comports with California law. Normally, an insurer’s duty to indemnify runs only to claims that are “actually covered,” and will “arise only after liability is established.” Safeco Ins. Co. of America v. Superior Court, 140 Cal.App.4th 874, 880 , 44 Cal.Rptr.3d 841 (2006). NCR invokes this premise to argue that it has no duty to indemnify for the settlement costs because the District’s liability was never established. But NCR ignores the fact that, where settlement is involved, “parties forego their right to have liability ‘established’ by a trier of fact, and the settlement becomes ‘presumptive evidence of the [insured’s] liability and the amount thereof....” Id. (citations omitted). The presumption can be overcome by a showing from the nonparticipating insurer that there was no coverage. Id. But the presumption is necessary in order to preserve the utility of the right to settle. See id. (“A contrary rule would make the right to settle meaningless ....”) (citation omitted). Thus, although no trier of fact determined the District’s liability and the amount of damages, the settlements in the Cunnane and Doe # 3 cases are presumptive evidence of the District’s liability, which triggered NCR’s duty to indemnify. As discussed above, given the explicit language of the MOC, NCR cannot make the showing of “no coverage” necessary to overcome the presumption.

Therefore, the Court determines that there is no material issue of fact as to whether allegations of injury were sufficient to trigger NCR’s coverage duties under the MOC.

*881 C. The Underlying Complaints Allege Injury That Occurred in 2012.

NCR admitted that Westport’s complaint accurately reproduced the allegations in the Cunnane, Does # 1 and # 2, and Doe # 3 complaints, each of which alleged injury in 2012. See Compl. ¶¶ 18-19, 26, 32; Answ. ¶¶ 18-19, 26, 32. Notwithstanding this admission, NCR argues that it disagrees with Westport’s characterization of the injuries as occurring partly in 2012. Opp’n to Mot. at 15. As with its argument regarding the meaning of MOC terms, NCR’s distinction is meaningless. Because NCR has admitted that the underlying complaints are true and accurate copies, the Court need look no further than the complaints themselves to determine when the women alleged that their injuries occurred.

Cunnane specifically alleged that “[the District’s] concealment” of the abuse caused her emotional harm, and that she only discovered this concealment when the newspaper published its 2012 investigation. Compl., Ex. A ¶¶ 57, 94-96. Even if Cun-nane also alleged injury for the underlying abuse (which Westport claims she did not), it is clear from those sections of her complaint that the District’s concealment-and her discovery of the concealment-caused at least part of her alleged injuries. The District’s concealment of the abuse occurred from the time the District first learned of the abuse in the mid-1990s until the time the cover-up was revealed in 2012. Therefore, at least some portion of Cunnane’s injuries occurred in 2012.

The two Doe complaints also explicitly alleged injury occurring in 2012. Paragraph eighty-two of the Doe # 1 and Doe # 2 complaint states that “[Does # 1 and #2] subsequently suffered extreme and severe emotional distress in 2012 when they learned that all of the sexual abuse they endured could have been prevented....” Compl., Ex. D ¶82. And the Doe # 3 complaint highlights that Doe # 3 suffered from the “additional and different harm arising from the recent discovery that [the District] ... [was] aware of multiple allegations of illegal conduct ... chose not to report the abuse ... and actively concealed their prior knowledge of [Witters’] behavior.” Compl., Ex. G ¶¶ 71-72. It does not matter whether any of these 2012 allegations were serious enough to result in compensable injury. What matters is that those injuries were alleged, and that the District had to defend against the allegations. As shown above, the MOC established that allegations of injury were sufficient to trigger NCR’s duties. Because the three complaints all alleged injury that occurred at least in part in 2012, the Court finds as a matter of law that NCR must pay some portion of the defense and settlement costs.

This holding is consistent with this Court’s earlier determination that the women alleged new injuries in 2012. NCR made the same argument on its motion to dismiss as it makes here: that it is not liable to Westport because the women did not allege injuries occurring during NCR’s coverage period. See generally Mot. to Dismiss (dkt. 20). But in June 2014, the Court rejected NCR’s argument, stating that “it’s one thing to have one’s trust violated by the acts of molestation, but it’s a whole separate situation [to discover that the District was] engaging in a coverup. That a — quite a different injury.” Transcript of Proceedings at 3-4. The Court sees no reason to depart from its earlier conclusion on this motion. Therefore, the allegations in the women’s complaints triggered NCR’s duties.

NCR maintains that even if the women alleged injuries in 2012, the Cunnane and Doe # 3 allegations of fraud are not covered because fraud is an intentional tort, *882 and the MOC explicitly denies coverage for damages that result from intentional injury. Opp’n to Mot. at 11; see also Compl., Ex. K at 27 (“Loss Occurrence means ... an Error or Omission ... which results in Damages ... during the coverage period ... which were not expected nor intended by the Covered Party.”). But even assuming that the fraud counts in the Cunnane and Doe #3 complaints were not covered, those complaints also alleged causes of action that resulted from unintentional injury in 2012. Both complaints allege negligence in addition to intentional conduct. See, e.g., Compl., Ex. A ¶¶ 59-87. It would be for a further proceeding to determine which allegations were unintentional and covered and which ones were intentional and not covered. But the fact that there may be some uncovered claims does not mean that NCR is absolved of all responsibility. The complaints still alleged injury that partially fell within NCR’s coverage period.

In sum, because NCR has admitted that the MOC and the underlying complaints attached to Westport’s complaint are true and correct copies, the Court may examine those documents to determine the parties’ responsibilities as a matter of law. The Court finds that the clear language of the MOC renders allegations of injury sufficient to trigger NCR’s duties. And the underlying complaints show that all four women alleged injury occurring, at least in part, in 2012. For those reasons, the Court concludes that there is no question of fact as to whether NCR owes some portion of the defense and settlement costs in all three lawsuits (Counts I,'V, VI, and X). This ruling is consistent with the Court’s earlier reasoning on the motion to dismiss.

Factual issues remain, however, as to the precise amount of NCR’s obligation in each of the underlying matters. Because the complaints alleged a cover-up that effectively lasted from the late 1990s until 2012, it is unclear from the pleadings exactly which portion of the defense and

settlement costs should be apportioned to NCR in any of the underlying matters. For that reason, the Court concludes that questions of fact remain as to Counts II, III, and IV and that the case should proceed as to those claims.

D. The Affirmative Defenses Raised by NCR’s Answer Are Insufficient to Prevent Judgment on the Pleadings.

NCR’s last and perhaps most tenable argument is that its answer raised affirmative defenses — specifically, lack of notice, waiver, and estoppel — that establish material questions of fact. Opp’n to Mot. at 5, 17-19. But these affirmative defenses do not compel a different holding here. NCR is correct that affirmative defenses usually preclude judgment on the pleadings. See General Conference Corp. of Seventh-Day Adventists v. Seventh-Day Adventist Congregational Church, 887 F.2d 228, 230 (9th Cir.1989). But to withstand the motion, those affirmative defenses must be adequately pleaded-that is, they must contain sufficient factual matter to state a defense that is “plausible on its face”. Ramirez v. Ghilotti Bros. Inc., 941 F.Supp.2d 1197, 1204 (N.D.Cal.2013) (citing Ashcroft v. Iqbal, 556 U.S. 662, 678 , 129 S.Ct. 1937 , 173 L.Ed.2d 868 (2009)). All of NCR’s affirmative defenses are inadequate under the Twombly and Iqbal pleading standard. See id. at 1210. And even if the affirmative defenses were adequately pleaded, they still fail to create a material issue of fact for the reasons outlined below.

1. Lack of Notice Defense

NCR’s fifteenth affirmative defense states: “[a]ny alleged right to contri *883 bution, subrogation, or similar relief is barred in whole or in part because the policyholder failed in accordance with the terms of defendant’s alleged policies to give timely and proper notice of the injury or damage.” Answ. ¶ 155. NCR’s answer did not cite to any provision of the MOC in order to make this affirmative defense “plausible on its face.”

During oral argument on October 17, 2014, NCR attempted to provide the necessary factual support. NCR pointed to a section of the MOC that provides: “[n]o Ultimate Net Loss ... shall be incurred on behalf of [NCR] without its pri- or consent due to any Loss Occurrence that appears likely to exceed the Member Retained Limit.” Compl., Ex. K at 35. NCR argued that this provision prevented any recovery by Westport on the Cunnane matter because although the District notified NCR of Cunnane’s claim, no one notified NCR that the claim had ripened into a lawsuit. According to NCR, Westport and the District settled the Cunnane suit without NCR’s consent and the quoted provision NCR bars any recovery by Westport. As NCR did not reference this provision in its answer or Opposition, the Court ordered supplemental briefing to clarify the issue.

In its supplemental letter, NCR pointed to an entirely different provision of the MOC and brought up the new argument— directly contradictory to its admissions— that Westport never provided NCR notice of the lawsuit or subsequent demurrer hearings in each of the underlying lawsuits. Letter from NCR (dkt. 60) at 1-2. The MOC provision NCR discussed in its supplemental letter states:

The following provisions are conditions precedent to coverage under this Memorandum of Coverage ...

Id. (citing Compl., Ex. K at 37-38). ' According to NCR’s letter, this provision bars judgment for Westport because neither Westport nor the District gave NCR notice of the lawsuits or the subsequent state court hearings.

Notwithstanding these eleventh-hour defenses, NCR’s argument fails for two reasons. First, the notice defense is inadequate as a matter of pleading. For the Court to agree with NCR would require it to consider two new defenses — one raised in oral argument and the other raised in the supplemental letter — that fall outside the pleadings. Such an action would contravene the legal standard for Rule 12(c). See Hal Roach, 896 F.2d at 1550 . The Court is not obligated to — and indeed should not — look beyond the pleadings to an argument raised for the first time in supplemental briefing. See id.

Second, NCR’s notice defense fails as a matter of law. The text of NCR’s affirmative defense alleges only that the District failed to provide notice of the injury or damage. Answ. ¶ 155 (emphasis added). The notice provision to which NCR cites on pages 37 and 38 of the MOC, however, requires notice not of injury or damage, but of “demand ... summons or other process.” Compl., Ex. K at 37-38.

The pleadings show that NCR received notice of the injury or damage in each of the three underlying lawsuits. NCR admitted that the District notified NCR twice about Cunnane’s claims shortly after she filed them. Compl. ¶¶ 42, 44; Answ. ¶¶ 42, 44. The pleadings do not establish whether the District or Westport notified NCR of the subsequent lawsuits or demurrer hearing in the Cunnane matter. But *884 as discussed above’, NCR cannot prevail on this ground because it did not raise this issue in its answer or opposition. Therefore, the pleadings on their face establish that NCR had notice of the “injury or damage” — the only ground on which NCR did argue in its pleadings that it is not liable.

NCR also admitted that the Does lawsuits were tendered to it, thereby constituting notice of “injury or damage” as to those complainants. Compl. ¶ 46; Answ. ¶ 46. NCR later attempted to argue in its letter that Westport tendered only the claims in the Does matters, NCR’s Letter at 3, but the complaint unequivocally used the word “lawsuit.” Compl. ¶46. NCR cannot now contend that it is absolved of liability because Westport did not forward to it each and every subsequent document in the matters when NCR did not mention that defense in its answer.

NCR’s argument, moreover, appears to confuse the terms of its own MOC. The purported notice provision to which NCR referred in oral argument, the one on page 35 of the MOC, is not in fact a notice provision, but a “consent to settle” provision. The surrounding text of the portion NCR cited establishes that NCR has the right (but not the duty) to participate in the defense of claims or suits against the District. Compl., Ex. K at 34. If NCR chooses to exercise its right to participate, then that provision establishes that the District cannot settle without NCR’s consent. See id. at 35. But where, as here, NCR does not exercise that right, the consent to settle provision is not triggered at all. The actual notice provision in the MOC, which is on pages 37 and 38 (and was only brought up by NCR in its supplemental letter), does not prevent judgment for Westport for the reasons stated above: NCR did not raise this defense in its pleadings, and NCR admitted to receiving notice of the “injury or damage.” Accordingly, the Court finds that NCR’s notice defense is insufficient to prevent partial judgment on the pleadings.

2. Waiver Defense

NCR’s eighth affirmative defense states: “[b]y its conduct, plaintiff has waived any right to recover any relief under its complaint or any purported cause of action alleged therein.” Answ. ¶ 148. This affirmative defense is insufficient to prevent partial judgment on the pleadings.

First, the defense is inadequately pleaded. NCR does not identify which “conduct” on the part of Westport resulted in waiver. As such, the defense does not contain sufficient factual matter to state a defense that is “plausible on its face.” Ramirez, 941 F.Supp.2d at 1204 .

Second, the defense fails as.a matter of law. California courts will find waiver where a party intentionally relinquishes a right, or when that party’s acts are so inconsistent with an intent to enforce the right as to induce a reasonable belief that such right has been relinquished. Intel Corp. v. Hartford Acc. & Indem. Co., 952 F.2d 1551, 1559 (9th Cir.1991) (discussing and citing California cases). In the insurance context, the party seeking to assert waiver generally must show misconduct by the insurer or detrimental reliance by the insured. See id. The gravamen of NCR’s waiver argument — as styled in its briefs, as none is .specified in its answer — is that Westport failed to timely and accurately inform NCR of the lawsuits, and that by funding the defense and settlement on its own, Westport waived its right to seek contribution or indemnity. Opp’n to Mot. at 17. NCR’s central premise is flawed for the reasons stated above: NCR admitted that it had notice of the suits. Thus, there was no misconduct on Westport’s part or detrimental reliance on NCR’s part that would *885 lead to waiver because NCR knew about the claims all along.

Moreover, Westport’s actions do not suggest that it intended to relinquish its right to seek indemnity from NCR. West-port funded the defense and settlement costs under a reservation of rights, which allowed it to later seek contribution from the District and/or NCR. Compl. ¶¶ 48, 51, 54: Answ. ¶¶ 48, 51, 54. Westport alleged, and NCR admitted, that within a few weeks of funding these legal expenses, Westport wrote to NCR requesting contribution. Compl. ¶¶ 52, 55; Answ. ¶¶ 52, 55. Waiver always rests upon intent. DRG/Beverly Hills, Ltd. v. Chopstix Dim Sum Café & Takeout III, Ltd., 30 Cal.App.4th 54, 60 , 35 Cal.Rptr.2d 515 (1994). The facts contained within the pleadings defeat the facial plausibility of a defense that alleges Westport intended to fund the legal expenses entirely on its own.

3. Estoppel Defense

NCR’s seventh affirmative defenses states: “Plaintiff is estopped by its conduct from recovering any relief on its complaint, or any purported cause of action therein.” Answ. ¶ 147. This affirmative defense is also insufficient to prevent judgment on the pleadings. As with the notice and waiver defenses, the estoppel defense is inadequately pleaded. By arguing only that Westport’s “conduct” creates estop-pel, without alleging specific actions, NCR fails to state a defense that is “plausible on its face.” See Ramirez, 941 F.Supp.2d at 1204 .

Substantively, estoppel is slightly different than waiver. While waiver looks to the act of one side only, estop-pel looks to the parties’ actions in relation to each other and “is applicable where the conduct of one side has induced the other to take such a position that it would be injured if the first should be permitted to repudiate its acts.” Intel Corp., 952 F.2d at 1559 . Estoppel requires the party seeking to assert the defense to show that: (1) the party to be estopped knew the facts; (2) the other party was ignorant of the true facts; (3) the party intended his or her conduct to be acted upon, or acted in a manner that the party asserting estop-pel had a right to believe it so intended; and (4) the other party relied on the conduct to his injury. Dollinger DeAnza Associates v. Chicago Title Ins. Co., 199 Cal.App.4th 1132, 1155 , 131 Cal.Rptr.3d 596 (2011).

NCR’s estoppel argument fails for much the same reasons as its waiver argument. NCR has not pleaded that it was ignorant of the facts — in fact, its answer admits that it was aware of all the lawsuits and . failed to involve itself. NCR’s bare allegation of estoppel also does not show how it has been injured by Westport’s funding of the defense.

Because each of NCR’s affirmative defenses are defective as a matter of pleading and as a matter of law, they do not establish the factual dispute necessary to prevent judgment on the pleadings. Therefore, the Court does not consider the affirmative defenses a bar to granting the motion as to Counts I, V, VI, and X.

IV. CONCLUSION

For the aforementioned reasons, the Court concludes that there is no material issue of fact as to whether NCR owes Westport some portion of the defense and settlement costs. The motion is therefore GRANTED as to Counts I, V, VI, and X. But because questions of fact remain as to whether Cunnane alleged injury occurring both in the 1990s and in 2012, the Court determines that material questions of fact remain as to whether NCR owes Westport one hundred percent of those costs. *886 Therefore, the motion is DENIED as to Counts II, III, and IV.

IT IS SO ORDERED.

. Two of the women, Doe # 1, and 'Doe # 2, sued jointly. Compl. (dkt. 1), Ex. D.

. The Does # 1 and # 2 suit is still pending. Compl. ¶ 48.

. The Cunnane and Doe #3 complaints alleged the same eight causes of action: (1) negligence; (2) negligence per se; (3) negligence per se in violation of California Penal Code Section 11166 (requiring reporting of child abuse); (4) negligent supervision and retention; (5) negligent infliction of emotional distress; (6) fraudulent concealment; (7) conspiracy to commit fraud; and (8) intentional infliction of emotional distress. See generally Compl., Ex A, Ex. G. Does # 1 and # 2 allege five overlapping, but different causes of action: (1) child sexual abuse; (2) intentional infliction of emotional distress; (3) negligent hiring, supervision, and retention; (4) breach of ^ mandat01y duty t0 report suspected child aW; and (5) negligence. See general ly CompLj Ex. D Does # i and #2 do not allege causes of action for fraudulent concealment or conspiracy to commit fraud. Id.

. Cunnane further alleged that she was abused by Julie Correa, a physical education teacher employed by the District. Compl., *874 Ex. A ¶¶ 27-43. Cunnane alleged that Correa abused her from 1993 to 2000. Id. After a police investigation and a twenty-three count indictment in 2011, Correa pled no contest to three felony counts of lewd and lascivious acts with a child and one felony count of sexual penetration against a victim's will by means of force, fear, duress, or menace. Id. ¶ 44.

. In Does #1, #2, and # 3, the superior court ruled for plaintiffs on the demurrers. Compl., Ex. F at 2, 4. The court estopped the District from asserting that the actions were time-barred. Id. It found that plaintiffs had reasonably relied on the .District's alleged misrepresentations and deceptions in deciding not to investigate further at the time of the incidents in the 1990s. Id.

. An exception, not relevant here, applies if the contract interpretation depends upon the credibility of extrinsic evidence. Badie v. Bank of Am., 67 Cal.App.4th 779, 799 , 79 Cal.Rptr.2d 273 (1998). Extrinsic evidence is usually admitted to resolve ambiguities in a contract. See, e.g. Wolf v. Superior Court, 114 Cal.App.4th 1343, 1350 , 8 Cal.Rptr.3d 649 (2004). Additionally, whether the terms of a contract are ambiguous is a question of law. Christensen v. Smith, 171 Cal.App.4th 931, 937 , 90 Cal.Rptr.3d 57 (2009). Therefore where, as here, a court concludes that no ambiguity exists, the court need not consider extrinsic evidence or its credibility.

. NCR relies on Orion Tire Corp. v. Goodyear Tire & Rubber Co., 268 F.3d 1133, 1138 (9th Cir.2001), for the idea that the interpretation of contract terms is typically a question of fact for the jury. But Orion Tire Corp. and the few cases that follow it are factually distinct from the present case, as most involve interpretation as to the scope of assignment, and appear to be contrary to the great weight of California cases holding that contract interpretation is a legal question for the court. See, e.g., Jade Fashion & Co., Inc. v. Harkham Industries, Inc., 229 Cal.App.4th 635 , 177 Cal.Rptr.3d 184, 199 (2014).