CUDAHY, Circuit Judge.

The parking lot is as old as the automobile. But, while driving a car seems simple and routine, running a parking facility remains a challenge, at least at O'Hare International Airport. The City of Chicago (the City), which runs O'Hare Airport, "operates parking services [at O'Hare] by means of a highly complex computerized parking system manufactured by Electron, Inc., a California-based company that ceased doing business in 1987." Durasys, Inc. v. Leyba, No. 90 C 5115, slip op. at 1, 1992 WL 3703 (N.D.Ill. Jan. 3, 1992) (hereinafter Mem.Op. Ord.). While still in business, Electron provided the City with a number of on-site technicians, including the appellees Jeffrey Leyba and Lawrence Walker, to operate and maintain the parking system at O'Hare.

Following Electron's demise, the city made several attempts to keep the system operating. Each proved less than satisfactory. Then, in spring 1988, three former Electron employees, Christopher Raymer, Dan Parks and William O'Brien, formed Durasys, Inc. for the primary purpose of maintaining and operating parking systems manufactured by Electron. On May 16, 1988, the City and Durasys entered into an Emergency Maintenance Services Agreement, and on July 29, 1988, the same parties executed a Maintenance Services Agreement, a one-year, fixed-price contract, under which Durasys agreed to operate and maintain the O'Hare parking facilities. Durasys hired Leyba and Walker as on-site technicians, and parking operations at O'Hare generally improved.

Notwithstanding the improved performance, relations between the City and Durasys were strained. The City was apparently concerned about its continuing dependency on a sole operator for the O'Hare facilities. Mem.Op. Ord. at 2-3. The City was, therefore, interested in having Durasys train city employees to operate the parking system; but the apparent inability to achieve this goal — possibly but not certainly the fault of Durasys — created some tension between the City and Durasys. Mem.Op. Ord. at 3. As a result, when the Maintenance Services Agreement expired in June 1989, the two parties were unable to reach agreement on another one-year contract. They instead entered into a series of short-term contract extensions, the last of which was scheduled to expire on February 28, 1990.

On January 20, 1990, however, the City terminated Durasys and replaced it with Digitron, Inc., a new corporation formed by Leyba and Walker. The loss of the O'Hare contract by Durasys was, at least in part, a product of its own devising — the result of a bargaining strategy that backfired. As the Maintenance Service Agreement's expiration date neared, the City became increasingly dissatisfied with Durasys's performance. As part of its negotiating strategy, Durasys sent termination notices to Leyba, Walker and other on-site employees. Durasys instructed Leyba to make sure that Norman Whitenhill, the City's Director of Parking, saw the termination notices. Durasys apparently believed that this ploy would drive home the message that it would pull out of the O'Hare site if agreement were not reached soon. Durasys believed that this strategy would illustrate the City's dependency and thereby strengthen Durasys's negotiating position. Mem.Op. Ord. at 4-5.

The City did not react quite as Durasys may have hoped. With Durasys posturing to pull out of O'Hare, the City began searching in earnest for an alternate vendor. In the fall of 1989, the City issued a request for bids to operate the O'Hare parking system. Digitron submitted a bid, competing with Durasys. In January 1990, after being told that Digitron had bid the job, Durasys's vice-president Dan Parks visited the O'Hare site and fired Leyba. Walker quit the same day. Two days later, Digitron was awarded the contract.

Durasys filed suit in the district court in August 1990 seeking monetary and injunctive relief. Durasys alleged that Leyba and Walker had breached their fiduciary duties and that they and Digitron had interfered with Durasys's prospective advantage and had induced the City to breach its contract with Durasys. The parties agreed that the case be assigned to a magistrate judge with direct appeal to this court. The matter was tried to the court without a jury in May 1991 and Magistrate Judge Gottschall issued her decision in January 1992. She ruled that Leyba and Walker had breached their fiduciary duties to Durasys, a decision from which Leyba and Walker have not appealed. The district court set damages against Leyba in the amount of $19,825 and against Walker in the sum of $17,870.46 as a disgorgement of the salaries they earned from Durasys during the period that they were in breach of their fiduciary duties. Leyba and Walker have likewise not challenged this portion of the magistrate judge's decision. The district court also found all appellees jointly and severally liable for lost profits in the amount of $12,419 with an additional sum of $10,000 for unrecovered fixed expenses. Finally, the district court denied Durasys's request for punitive damages and injunctive relief.

Durasys filed timely motions for a new trial or, in the alternative, to alter or amend the judgment. The court denied these motions, except to the extent that it amended its judgment to find all appellees also liable for interference with Durasys's prospective advantage. Durasys appeals and we affirm.

The district court concluded that Durasys was entitled to lost profits it would have earned during the time remaining in the contract extension then in effect (from January 13 though February 28, 1990) as well as in any additional extensions which Durasys was reasonably likely to have received. Mem.Op. Ord. at 13. The magistrate judge then determined that, under the circumstances, Durasys would have continued to service the O'Hare parking facilities for only six months beyond the date on which Durasys had been terminated. Id. The parties agree that the district court adopted a proper framework in calculating damages. Durasys, however, argues that the conclusion that it would have been awarded the parking contract at O'Hare for only an additional six months is without any support in the record. We review this factual determination for clear error. Fed.R.Civ.P. 52(a).

Durasys points out that the City was between a rock and a hard place in the management of the parking system at O'Hare. The City was plainly dissatisfied with Durasys's performance and disturbed at its continuing dependence on a sole vendor. But as unsatisfactory as the City may have perceived Durasys to be, since Electron went out of business the O'Hare parking system functioned best under Durasys. Durasys also notes that, when the City put the O'Hare parking contract out for bids, only Durasys and Digitron responded. Durasys thus contends that, absent the appellees' breach of their fiduciary duties, the City would have had no choice but to continue its relationship with Durasys. But the district court rejected Durasys's claim of indispensability in the following passage:

Durasys maintains that the City would never have found an adequate alternative and eventually would have been forced to give Durasys a contract. This was not adequately proven, and is difficult to believe. Even, however, if Durasys is correct that it alone has the competence to manage the City's current Electron equipment, the City could, if it chose, change the equipment.

Mem.Op. Ord. at 11. We do not believe that this conclusion is clearly erroneous.

Durasys quite understandably ignores the City's complaints about its performance or ascribes them to various misunderstandings or misperceptions. The City's perceptions, however, are key to deciding how long Durasys would have retained the O'Hare contract absent the appellees' breach. In selecting Digitron over Durasys, the City characterized Durasys's performance as "inept," "unprofessional" and "abysmal." Defendants' Exh. 6. The testimony of several City employees also confirmed the City's dissatisfaction with Durasys. See, e.g., tr. at 329, 336, 342, 345, 357 419. Considered in its entirety, therefore, the record evidence supports the district court's conclusion that Durasys could reasonably have expected to keep the O'Hare contract for no more than six months past the date when it was terminated. The City's extreme dissatisfaction with Durasys suggests that it would have taken some steps to replace Durasys even if Digitron had not appeared on the scene. The City could have rehired one of the other companies, such as Standard Parking or Anchor Parking, that had previously managed the O'Hare facility following Electron's demise. Or, faced with the prospect of perpetual dependence on Durasys, the City could have taken the admittedly drastic step of replacing the Electron equipment. It is entirely possible that the City would have cut off its nose to spite its face. In any event, it is reasonable to conclude that Durasys was on its way out. The district court thus properly limited damages to the six month period following Durasys's termination.

Durasys next argues that the district court improperly calculated the lost profits to which it was entitled. Under Illinois law, lost profits are calculated by subtracting from revenue lost as a result of a breach those costs avoided as a result of the same breach. See, e.g., Central Info. Fin. Servs., Ltd. v. First Nat'l Bank of Decatur, 128 Ill.App.3d 1052, 84 Ill.Dec. 226, 232, 471 N.E.2d 992, 998 (4th Dist. 1984). This calculation, however, is complicated in a case, such as this, involving a cost-plus contract. With a cost-plus contract, the costs of performance are, almost by definition, equal to the revenue lost as a result of the breach. Therefore, in applying the usual "net profit" formula, we may be simply adding and subtracting the same amounts. As a result, the "net profit" calculation must be modified to accommodate the circumstances of a cost-plus contract.

The net profit rule is, of course, based on the notion that a party harmed by another's breach of contract is entitled to collect the net revenue that would have helped defray inescapable costs and, beyond that, contributed to profit. Under a cost-plus contract, profit is not simply the surplus after payment of expenses, but is specified in the contract as a percentage of certain incurred costs. Consequently, profit is guaranteed. As long as the party performs according to the terms of the contract, it will be reimbursed for its expenses and will also receive an agreed-upon profit.

This leaves the central question of what is a party to a cost-plus contract, such as Durasys, entitled to collect in the event of the other party's breach? The aggrieved party, of course, is entitled to be put in the position it would have been in had the breach not occurred. Variable costs, i.e., those costs that vary with output, are not recoverable since they are, in the event of a breach, not incurred. Fixed costs, however, are recoverable because even though the breach excuses the non-breaching party's performance under the contract, these costs cannot be avoided. Finally, the non-breaching party may recover the profit specified in the cost-plus contract since, had the contract been completely performed, that party would have received this specified amount.

What Durasys is theoretically entitled to recover is obviously a somewhat different question than what it may recover given the record before us. The district court employed the proper analysis in assessing damages, concluding that Durasys was entitled to profit, as that term is understood in the context of a cost-plus contract, as well as to its fixed costs allocable to the O'Hare contract. Durasys complains though that the district court used the wrong multiplier in calculating profit and ignored evidence showing that its fixed costs were much higher than those awarded.

The party seeking to recover damages bears the burden of proving them to a reasonable certainty. See, e.g., Hentze v. Unverfehrt, 237 Ill.App.3d 606, 178 Ill.Dec. 280, 284, 604 N.E.2d 536, 540 (5th Dist. 1992); F.E. Holmes Son Constr. Co. v. Gualdoni Elec. Serv., Inc., 105 Ill.App.3d 1135, 61 Ill. Dec. 883, 886, 435 N.E.2d 724, 727 (5th Dist. 1982). We review the district court's findings regarding the sufficiency of proof of damages for clear error. Lincoln Nat'l Life Ins. Co. v. NCR Corp., 772 F.2d 315, 320 (7th Cir. 1985). In determining the profit component of the damage award, the district court used the multiplier specified in the contract between the City and Digitron. Durasys objects, arguing that because its bargaining position was so much stronger than Digitron's the district court should have used a larger multiplier. The court rejected Durasys's position, stating that "[t]here was not a shred of evidence [in the record] respecting Durasys' actual profit experience or projected actual profit." Durasys, Inc. v. Leyba, No. 90 C 5115, slip op. at 4 (N.D.Ill. April 17, 1992) (ruling on plaintiff's motion to alter or amend judgment). Durasys was certainly confident in its dealings with the City and expected to negotiate a large profit in connection with any contract. But whether Durasys would ultimately have been successful in achieving this objective is pure speculation. Hence, it was not error for the district court, in determining damages, to use the multiplier to which the City actually agreed with another party.

Durasys also asserts that the district court impermissibly ignored certain evidence in awarding the "concededly arbitrary figure of $10,000 for associated fixed expenses. . . ." Mem.Op. Ord. at 14. Although at first blush the district court's characterization of its award of expenses as "arbitrary" is troubling, we conclude, after considering the court's opinion in its entirety, that its decision was not erroneous. The district court admitted difficulty in calculating damages. But this trouble arose because Durasys failed to establish a record from which recoverable fixed expenses could be readily calculated. Mem.Op Ord. at 14 ("The court will allow some recovery [for fixed expenses] . . . even though in the court's judgment the evidence concerning overhead was not adequate to permit its quantification."). Certainly there was evidence in the record supporting Durasys's position that its fixed expenses were considerably greater than $10,000. There was also testimony, however, supporting the conclusion that any estimate of Durasys's fixed expenses was merely a guess and that the district court was generous in awarding Durasys any damages in this regard. E.g., tr. at 134 ("Q. Do you know the dollar amount of overhead that Durasys incurred for the O'Hare work during 1989? A. No, I don't know that. . . .") (cross-examination of Durasys's financial officer William O'Brien). Considering the record in its entirety, and bearing in mind that Durasys was obligated to prove damages to a reasonable certainty, we conclude that the district court was justified in finding that the evidence "did not permit it to make a well-founded estimate of overhead and administrative losses chargeable to the loss of the O'Hare contract." Mem.Op. Ord. at 14 n. 5. Accordingly, the district court's award of damages may be approved.

Finally, Durasys contends that the district court erred in denying its motion for a permanent injunction. Durasys sought to enjoin Digitron from bidding on and performing parking maintenance services at O'Hare. The parties' discussion regarding the proper standard of review of the permanent injunction question has been particularly unenlightening. Durasys has confronted the issue, but the cases it cites all involve preliminary injunctions. Digitron points out this flaw in Durasys's argument, but offers no suggestions of its own. In any event, it seems clear that our review of this matter should observe customary norms: we will review for clear error the district court's findings of facts, and will review de novo the district court's conclusions of law.

We agree with Durasys that under Illinois law an injunction may issue to prevent disloyal employees from arrogating their former employer's customers and with them a so-called "incumbent's advantage" with respect to these patrons' future business. Cross Wood Prods., Inc. v. Suter, 97 Ill.App.3d 282, 52 Ill.Dec. 744, 747, 422 N.E.2d 953, 956 (1st Dist. 1981); ABC Trans Nat'l Transp., Inc. v. Aeronautics Forwarders, Inc., 62 Ill. App.3d 671, 20 Ill.Dec. 160, 169, 379 N.E.2d 1228, 1237 (1st Dist. 1978). But an injunction to protect this interest necessarily works a restraint of trade and thus implicates a variety of other issues. Included among these are the potential public harm from the reduced competition accomplished by the injunction and the concomitant requirement that the restraint imposed by the injunction be no broader than necessary to protect the injured party. Agrimerica, Inc. v. Mathes, 199 Ill.App.3d 435, 145 Ill.Dec. 587, 598, 557 N.E.2d 357, 368 (1st Dist.), appeal denied, 135 Ill.2d 553, 151 Ill.Dec. 379, 564 N.E.2d 834 (1990). The district court seems to have been keenly aware of these concerns when, in denying Durasys's request for a permanent injunction, it stated:

If Durasys is, as it contends, indispensable, it should be able to compete for the City's business in the future. The court is also reluctant to force the City to deal with a supplier it apparently does not wish to deal with, a likely result of an injunction.

Mem.Op. Ord. at 13. We are not inclined to disturb this decision.

If Digitron were enjoined from performing the O'Hare contract, the City would likely be forced to deal with Durasys or another unsatisfactory vendor. It does not seem prudent to give Durasys this sort of extraordinary market advantage, particularly when the public purse must make good the price. Moreover, it does not appear to be necessary to give Durasys such a benefit in order to protect its interests. Durasys has repeatedly maintained that it is uniquely qualified to service the O'Hare parking facilities and that the City would ultimately have no choice but to select Durasys for the O'Hare job. If this is indeed the case, Durasys would suffer little in being denied the "incumbent's advantage" when the parking contract is again let for bids. According to Durasys, its return to O'Hare is inevitable. On the other hand, the City's extreme dissatisfaction with Durasys, whether justified or not, makes it unlikely that Durasys would ever again receive the parking contract at O'Hare under any circumstances. See discussion supra at 1468-69. In any event, Durasys may have lost little as a result of the defendants' breach. Durasys will either regain the O'Hare contract because it is the far superior vendor, or the City will simply never do business with Durasys again. The "incumbent's advantage" is of minimal value under either scenario. Taking into account, therefore, the significant public harm that a permanent injunction might inflict in this case, as well as the marginal benefit it might confer upon the aggrieved party, we conclude that Durasys's request for a permanent injunction was properly denied.

For the foregoing reasons, the judgment of the district court is AFFIRMED.