MEMORANDUM

Seagate Technology, Inc. (“Seagate”) appeals and its insurers, National Union Fire Insurance Company of Pittsburgh, PA (“National”), American International Underwriters Insurance Company (“AIU”), and American International Specialty Lines Company (“AISLIC”), cross appeal the district court’s September 2, 2010 Judgment Pursuant to Federal Rule of Civil Procedure 54(b) and the orders that underlie the judgment. We have jurisdiction pursuant to 28 U.S.C. § 1291 . We reverse the district court’s rulings that AIU owed a duty to defend and that the other insurers’ duty to defend terminated. We affirm all remaining issues appealed.

“We review a grant of summary judgment de novo.” Hudson Ins. Co. v. Colony Ins. Co., 624 F.3d 1264, 1266 (9th Cir.2010). In addition, a district court’s interpretation of state law is reviewed de novo. Trishan Air, Inc. v. Fed. Ins. Co., 635 F.3d 422, 426-27 (9th Cir.2011). “When interpreting state law, federal courts are bound by decisions of the state’s highest court. In the absence of such a decision, a federal court must predict how the highest state court would decide the issue using intermediate appellate court decisions, decisions from other jurisdictions, statutes, treatises, and restatements as guidance.” Id. at 427 (internal quotation marks and citation omitted).

1. “[A] liability insurer owes a broad duty to defend,” which arises under California law when “a suit [ ] potentially seeks damages within the coverage of the policy.” Horace Mann Ins. Co. v. Barbara B., 4 Cal.4th 1076 , 17 Cal.Rptr.2d 210 , 846 P.2d 792, 795 (1998) (citation omitted). In fact, the duty to defend is so broad that it only requires “a bare ‘potential’ or ‘possibility’ of coverage as the trigger of a defense duty.” Montrose Chem. Co. v. Superior Court, 6 Cal.4th 287 , 24 Cal.Rptr.2d 467 , 861 P.2d 1153, 1160 (1993). “The determination whether the insurer owes a duty to defend usually is made in the first instance by comparing the allegations of the complaint with the terms of the policy.” Horace Mann, 17 Cal.Rptr.2d 210 , 846 P.2d at 795 . Any doubt, as to whether a duty to defend is triggered, is resolved in favor of the insured. See id. at 796. Here, the complaint in the underlying action alleges that Seagate falsely claims that its technology is equivalent to Convolve Inc.’s technology. Because the duty to defend is broad and the complaint creates a bare potential of coverage for disparagement, the district court did not err in concluding that the underlying complaint potentially created liability for disparagement thereby giving National and AISLIC a duty to defend Seagate.

2. “[W]e generally will not consider arguments raised for the first time on appeal, although we have discretion to do so.” In re Am. W. Airlines, Inc., 217 F.3d 1161, 1165 (9th Cir.2000). Here, the issue, whether AIU had a duty to defend even though it is an excess (or secondary) insurer, was considered by the district court and not waived by AIU. In the district court, Seagate argued that, even though the primary insurers’ policy limits were not exhausted, AIU still owed a duty to defend. The district court also acknowledged the issue by specifically explaining why AIU had a duty to defend even though (a) it was a secondary insurer; (b) the primary insurers did not defend; and (c) the prayer for relief in the underlying action exceeds the policy limits of both primary insurers.

AIU is an excess insurer. Even if the underlying complaint potentially creates liability for an insurer, an excess or secondary insurer has no duty to defend if the primary insurer’s policy limits have not been exhausted. Cmty. Redevelopment Agency v. Aetna Cas. & Sur. Co., 50 Cal.App.4th 329 , 57 Cal.Rptr.2d 755, 759-60 (Ct.App.1996). This rule holds true even if the potential liability exceeds the policy limits, Diamond Heights Homeowners Ass’n. v. Nat’l Am. Ins. Co., 227 Cal.App.3d 563 , 277 Cal.Rptr. 906, 914 (Ct.App.1991), or the primary insurer refuses to defend, see Ticor Title Ins. Co. v. Employers Ins. of Wausau, 40 Cal.App.4th 1699 , 48 Cal.Rptr.2d 368, 374 (Ct.App.1995). Thus, the district court erred in concluding that AIU owed a duty to defend to Seagate, because it is a secondary insurer and the primary insurers’ (National and AISLIC) policy limits have not been exhausted. Further, even though Sea-gate’s potential liability exceeds the primary insurers’ policy limits and the primary insurers refused to defend, AIU owes no duty to defend. For these reasons, the claims against AIU are dismissed.

3. The duty to defend continues “until [the insurers] can conclusively refute th[e] potential” that liability will arise under the policies. Montrose, 24 Cal.Rptr.2d 467 , 861 P.2d at 1160 . Here, the insurers did not meet their high burden. While this is a close issue, the district court erred in ruling that the duty to defend terminated, because, while Convolve made representations to prevent Seagate’s insurers from intervening in the underlying action, the statements did not conclusively refute the potential for a disparagement claim.

4. An insurer acts in bad faith only when “the reason for withholding” a defense was “unreasonable or without proper cause.” Love v. Fire Ins. Exch., 221 Cal.App.8d 1186, 271 CaL.Rptr. 246, 255 (Ct.App.1990). “The mere denial of benefits, however, does not demonstrate bad faith.” Hanson v. Prudential Ins. Co. of Am., 783 F.2d 762, 766 (9th Cir.1985). Here, although a duty to defend existed (based on the allegations in the complaint), that alone does not make the insurers’ denial of a defense unreasonable. Moreover, the insurers investigated the claims, compared the allegations to the insurance policy, and concluded that there was no potential liability. This conclusion is not unreasonable. The district court accurately described the case as a close case regarding the duty to defend. The district court held that the complaint did not trigger a duty to defend, but later reconsidered and held that the complaint did trigger a duty to defend. The district court thereafter terminated the same duty based on facts alleged to have happened after the complaint was filed. Thus, although the insurers’ denial of a defense was erroneous, the insurers did not withhold a defense unreasonably or without proper cause.

5. Seagate argues that it is entitled to punitive damages; however, because there is no bad faith denial of a defense, an argument for punitive damages does not need to be addressed.

6. “Where there is a duty to defend, there may be a duty to indemnify; but where there is no duty to defend, there cannot be a duty to indemnify.” Certain Underwriters at Lloyd’s of London v. Superior Court, 24 Cal.4th 945 , 103 Cal.Rptr.2d 672 , 16 P.3d 94, 102 (2001). Because we have concluded that the duty to defend did not terminate, there may be a duty to indemnify. Accordingly, the district court properly concluded that the question of indemnity is not ripe for consideration.

7. Prejudgment interest under California Civil Code § 3287 is appropriate when the amount owed is certain or capable of calculation. Invoices allow damages to be capable of being made certain by calculation. See Marine Terminals Corp. v. Paceco, Inc., 145 Cal.App.3d 991 , 193 Cal. Rptr. 687, 690 (Ct.App.1983). Thus, the district court did not err in determining that interest is to be calculated from the invoice dates.

8. Because the complaint tendered by Seagate triggered the duty to defend, the district court did not err in finding AISLIC liable for interest related to the period prior to Seagate’s tender of Convolve’s interrogatory response.

The parties shall bear their own costs.

AFFIRMED in part and REVERSED in part.

This disposition is not appropriate for publication and is not precedent except as provided by 9th Cir. R. 36-3. . Because the parties are familiar with the facts and procedural history, we do not restate them here except as necessary to explain our decision. . Seagate sought additional discovery regarding bad faith in order to identify its insurers’ subjective intent and to prevent summary judgment. However, the district court did not abuse its discretion by denying discovery under Rule 56(f) of the Federal Rules of Civil Procedures. See VISA Intern. Serv. Ass'n v. Bankcard Holders of Am., 784 F.2d 1472 , 1475 (9th Cir.1986). First, the subjective intent of the insurer is irrelevant for determining bad faith. Bosetti v. U.S. Life Ins. Co., 175 Cal.App.4th 1208 , 96 Cal.Rptr.3d 744, 769 (Ct.App.2009). Second, Seagate failed to show how additional discovery would preclude summary judgment. See Qualls v. Blue Cross of Cal, Inc., 22 F.3d 839 , 844 (9th Cir.1994).