
31 P.3d 780 (2001)
CITY OF SEWARD, Appellant,
v.
AFOGNAK LOGGING, a division of Kodiak Lumber, Limited, Appellee.
No. S-9456.
Supreme Court of Alaska.
September 28, 2001.
*781 Richard A. Weinig, Pletcher, Weinig, Fisher & Dennis, Anchorage, for Appellant.
Wevley William Shea, Anchorage, for Appellee.
Before FABE, Chief Justice, MATTHEWS, EASTAUGH, BRYNER, and CARPENETI, Justices.

OPINION
BRYNER, Justice.

I. INTRODUCTION

During a heavy rainfall, the City of Seward asked local contractor Afognak Logging to dispatch two bulldozers with operators to the Lowell Point bridge to help with flood control efforts. One of the bulldozers bogged down and suffered extensive damage in flood water that covered the highway near the bridge. Afognak sued to recover its damages, claiming that the city negligently failed to warn it that the flood had washed away the roadbed. A jury found the city liable, and the superior court awarded Afognak $89,000 in damages. We affirm, holding that the city owed Afognak an actionable duty of reasonable care, that neither discretionary function immunity nor emergency immunity protected the city, and that substantial evidence supports the damage award.

II. FACTS AND PROCEEDINGS

The Lowell Point bridge stands between a waterfall and the Resurrection Bay about 300 yards southwest of downtown Seward. During periods of heavy rain, water collects behind the bridge and overflows the highway at *782 both ends. Heavy rains were falling in Seward on the morning of September 20, 1995. When Seward's engineering and utilities manager, Dave Calvert, checked the bridge, he found the waterfall spewing rock- and gravel-filled water toward the bridge, like a giant hose. Calvert radioed public works superintendent Floyd Ainsworth to report the condition of the waterfall. As he spoke with Ainsworth, Calvert saw the floodwaters chew away the roadbed south of the bridge, collapsing the highway's pavement. Ainsworth knew that the same kind of damage had occurred during previous floods.
Ainsworth came to the waterfall in response to Calvert's report of the washout and saw that the water collecting behind the bridge was threatening to spill north toward a lift station and south toward a cannery. Ainsworth called Afognak Logging and asked Afognak's manager, Steve Schafer, to dispatch a D-9 bulldozer and an operator to control the flooding. Because the city owned no large bulldozers, it had a standing arrangement for Afognak to provide equipment with operators; that day, the city orally agreed to pay $145 per hour for D-9 bulldozers with operators.
Schafer arrived at Lowell Point with a D-9 bulldozer and spent the morning attempting to clear channels for floodwaters to drain over the roadway at both ends of the bridge. Later that morning, at Ainsworth's request, someone from the city's emergency management office called Afognak for an additional bulldozer and operator. Afognak sent Lyle Johnson with a second D-9 bulldozer. While Johnson was working on the north side of the bridge, Ainsworth asked him to pick up some people stranded on the south side and ferry them across in his bulldozer to the north side. Ainsworth next instructed Johnson to cut a channel allowing flood water to drain across the highway on the south side of the bridge. Ainsworth failed to tell Johnson that the pavement on the south side of the bridge had collapsed earlier in the morning. The bridge and adjoining highway on the south side was covered with murky water and gravel, making the condition of the underlying roadbed impossible to see. After working some time without progress, Johnson bogged down in loose gravel and was forced to abandon his bulldozer. The bulldozer could not be retrieved from the waterfall until five days later. It was extensively damaged. Afognak estimated that the reasonable cost of repairing the bulldozer would be more than $100,000.
Afognak sued the city to recover its damages, alleging breach of contract, bad faith, negligence, fraud, and strict liability. The superior court dismissed all but the negligence claim, allowing that claim to survive because the court found sufficient evidence to support a finding that the city negligently failed to warn Afognak of the washed out pavement south of the Lowell Point bridge. Concerning this theory, the court instructed the jury:
Now, in this case the plaintiff claims that the defendant's negligence caused a loss of plaintiff's bulldozer. For the plaintiff to win on this claim, you must decide that [it] is more likely true than not true (1) that the defendant knew that there existed a hidden, unknown and extrahazardous danger at the location where plaintiff was operating its bulldozer; (2) that the existence of the hidden, unknown and extrahazardous danger could not have been reasonably foreseen by plaintiff; and (3) the defendant's failure to inform plaintiff of the hidden and extrahazardous danger at the location where plaintiff was operating the bulldozer was negligent and was a legal cause of the plaintiff's loss.
The jury found Seward negligent. After a non-jury trial on the issue of damages, the superior court awarded Afognak $89,700 plus prejudgment interest and attorney's fees.
Seward appeals.

III. DISCUSSION

On appeal, the city argues that the superior court should have dismissed Afognak's negligence claim because the city owed no duty to warn Afognak that the pavement had washed away and because two forms of statutory immunity protected the city from liabilitydiscretionary function immunity and emergency immunity. The city also challenges the award of damages and prejudgment interest.


*783 A. Standard of Review

We review the denial of summary judgment de novo, applying our independent judgment.[1] We also review de novo whether the trial court correctly applied legal rules pertaining to damages[2] and prejudgment interest.[3] A trial court's damage determination itself is a factual finding that we review for clear error; an award is clearly erroneous if we are "left with the definite and firm conviction on the entire record that a mistake has been committed."[4]

B. Legal Duty

The city maintains that it was entitled to summary judgment or a directed verdict on negligence because it owed only contractual duties to Afognak. Since Afognak was an independent contractor, the city reasons that it had no legal duty to warn Afognak of hazardous job-site conditions.
The superior court accepted this reasoning to a limited extent. Relying on Restatement of Torts § 413which requires an independent contractor's employer to protect against any "peculiar and unreasonable risk of harm to others" arising from the contractor's work[5]the court concluded that the city only had a duty to warn Afognak of "peculiar" dangers to its property. Based on this conclusion, the court instructed the jury that the city would be liable if it negligently failed to warn Afognak of "extrahazardous" conditions that Afognak could not reasonably have foreseen. Afognak alternatively argues that the city owed a duty of due care to warn against danger under the general test adopted in D.S.W. v. Fairbanks North Star Borough School District.[6] The city disputes the court's reliance on § 413, insisting that Afognak and its bulldozers were not "others" to whom a duty of protection extended under this provision.
Whether the city had a legal duty to inform Afognak that the pavement south of the Lowell Point bridge had previously washed away is a legal question that we review de novo.[7] Although we are inclined to agree with the city's assertion that § 413 would not apply in this factual setting,[8] the point is moot since undisputed record evidence points to the existence of a duty under Afognak's alternative theory that the D.S.W. test applies to this situation.
In D.S.W. we described seven relevant factors that courts consider in determining the existence of an actionable duty in situations not governed by settled law:
The foreseeability of harm to the plaintiff, the degree of certainty that the plaintiff suffered injury, the closeness of the connection between the defendant's conduct and the injury suffered, the moral blame attached to the defendant's conduct, the policy of preventing future harm, the extent of the burden to the defendant and consequences to the community of imposing *784 a duty to exercise care with resulting liability for breach, and the availability, cost and prevalence of insurance for the risk involved.[9]
Applied to the circumstances of the present case, virtually every D.S.W. factor points to the conclusion that the city owed an actionable duty to warn Afognak of foreseeable danger that the city was aware of but that might not have been readily apparent to Afognak.[10]
Accepted rules governing the existence of actionable duties in analogous settings confirm this conclusion. Here, the city acknowledges that it controlled the land surrounding the bridge and was attempting to abate flood conditions there at the time of the damage to Afognak's bulldozer. Moreover, uncontroverted evidence establishes that a city employee, Ainsworth, was at the scene of the flooding and specifically requested Johnson to operate his bulldozer in the area south of the bridge, where Ainsworth knew or should have known that the pavement had been washed away.
We have long recognized that a duty of reasonable care generally arises when a person undertakes an action and that "one who assumes to act, even though gratuitously, may thereby become subject to the duty of acting carefully."[11] We have also long recognized a landowner's duty "to use due care to guard against unreasonable risks created by dangerous conditions."[12] Here, Ainsworth's active presence at the scene of the flooding and the specific action that he undertook by directing Johnson's flood control efforts point to the same conclusion as the D.S.W. factors: the city, as Ainsworth's employer, owed a reasonable duty of care toward Johnson and his bulldozer; and this duty applied to the city even though Johnson, as an "independent contractor," might not have been contractually bound to follow Ainsworth's directions.[13]
We find no merit, then, in the city's claim that it owed Afognak no actionable duty of care. We also find that the superior court adequately instructed the jury on the city's duty to warn Afognak of dangerous conditions, even though the court's instructions were unduly favorable to the city insofar as they required the jury to find that the conditions amounted to an "extrahazardous" danger.[14] In response to the court's instructions, *785 the jury returned a special verdict finding: (1) there was a hidden danger at the location where the city asked Afognak's operator to work; (2) the city knew of the danger; (3) Afognak could not reasonably have foreseen the danger; (4) the city was negligent in failing to inform Afognak of the pavement failure that Calvert had observed; (5) the city's negligence caused the bulldozer to become stuck; and (6) Afognak was not itself negligent.
Our review of the record convinces us that Afognak presented sufficient evidence to support this verdict and that the superior court did not err in denying the city summary judgment or a directed verdict on the ground that it had no duty to warn Afognak of dangerous conditions.

C. Immunity

Alaska Statute 09.65.070 permits damage suits against municipalities but creates limited immunity under certain circumstances. The city claims immunity under two of the statute's provisions.
First, the city contends that it was immune under AS 09.65.070(d)(5)'s emergency provision:
(d) An action for damages may not be brought against a municipality or any of its agents, officers, or employees if the claim
....
(5) is based upon the exercise or performance of a duty or function upon the request of, or by the terms of an agreement or contract with, the state to meet emergency public safety requirements....
It is undisputed that the city hired Afognak to assist it in executing its East Zone Emergency Response Plana plan created by the city and the Kenai Peninsula Borough under the Alaska Disaster Act. The city contends that the state's participation in preparing and finally approving this plan renders the plan "an agreement ... with the state to meet emergency public safety requirements," as contemplated by AS 09.65.070(d)(5). But the city's argument is unpersuasive.
The Alaska Disaster Act holds local governments primarily responsible for responding to local disasters.[15] As the Seward City Ordinances expressly acknowledge, "it is a primary responsibility of all municipalities to plan and prepare for response to potential disasters." The city fulfilled this statutory obligation by entering into its response plan with the Kenai Peninsula Borough. That the state reviewed the city's plan for compliance did not transform it from a statutory duty into "an agreement or contract" to perform the state's duties.[16] We hold, then, that AS 09.65.070(d)(5)'s grant of emergency immunity does not insulate the city from liability for the damage to Afognak's bulldozer.
The city also claims discretionary function immunity under AS 09.65.070(d)(2), which holds municipalities immune from liability "based upon the exercise or performance or the failure to exercise or perform a discretionary function or duty by a municipality or its agents, officers, or employees, whether or not the discretion involved is abused."
This provision does not shield municipalities from liability for the consequences of operational negligence. In applying *786 discretionary function immunity, we have consistently distinguished between planning and operational decisions.[17] Discretionary function immunity precludes liability for harm caused by the type of planning decisions that involve policy formulation.[18] In contrast, operational decisionsthose made while executing or implementing existing policiesare not immune.[19] This dichotomy serves "to immunize policy-level (or `discretionary') decisions about whether to undertake activities," while maintaining liability "for negligently performing particular operations to implement the broad policy decision[s]."[20]
The city contends that the planning/operational dichotomy does not apply to cases involving emergencies; it cites Earth Movers of Fairbanks, Inc. v. State[21] to support this contention. But in Earth Movers the plaintiff claimed that a trooper had negligently misread a regulation authorizing him to take emergency action; in rejecting this claim, we concluded that the trooper had read the regulation correctly.[22] Given this conclusion, we had no occasion to discuss the planning/operational dichotomy.[23]Earth Movers thus fails to support the city's immunity claim.
The city has also attempted to characterize its employees' actions as resource allocation measures, which we have sometimes considered to be protected planning decisions.[24] But the resource allocation decisions that we have deemed immune in prior cases fundamentally differ from the decisions at issue here. In Adams v. City of Tenakee Springs,[25] for example, we applied immunity to a municipality's decisions concerning the size of its fire department. And in Estate of Arrowwood v. State,[26] we excluded on grounds of immunity "evidence relating to the effect of reductions in DOT's budget upon the level of road maintenance in the Palmer Wasilla region."[27] The resource allocation decisions in those cases involved broad policy choices about how to expend limited funding. By contrast, in State v. Abbott,[28] we declined to characterize as immune an engineer's decision to send staff and equipment to maintain a specific stretch of highway; while acknowledging that this decision involved a certain amount of planning and discretion, we held that "it [was] not the kind of broad policy decision at which [discretionary function immunity] is aimed."[29]
Here, the disputed actions were not budgetary allocations. Like the engineer in Abbott, Ainsworth and Calvert were performing operational functions. Moreover, their alleged acts of negligence had nothing to do with the manner in which they allocated the city's emergency response resources: Afognak did not challenge Ainsworth's decision to direct Johnson's efforts toward the south side of the bridge; rather, it simply claimed that Ainsworth or Calvert should have warned Afognak that working there would expose Johnson to a hidden danger.
In sum, we find no merit in the city's immunity claims.


*787 D. Damages

The superior court determined that Afognak was entitled to $89,700 in costs-of-repair damages plus prejudgment interest and attorney's fees. The city argues that the court erred in awarding damages for cost of repair without first determining whether those costs were disproportionate to the loss in market value that Afognak's bulldozer sustained as a result of the accident. The city further argues that the award improperly included costs that Afognak would not actually incur, since it sent the bulldozer to the Seward Skill Center, where it would be repaired free of charge.
In Alaska, the owner of negligently damaged property may ordinarily recover either its lost value or its reasonable cost of repair and residual loss in value, whichever is less.[30] The plaintiff bears the burden of proving damages, but once the existence of damage has been established, the amount of loss need not be proved with mathematical precision.[31]
Here, Afognak's evidence indicated that its damaged bulldozer was a particularly valuable model, that it had been renovated shortly before the accident and was in excellent condition, and that machines of similar quality could not be readily found on the market. Afognak's evidence also indicated that a new D-9 bulldozer costs approximately $500,000 or more and that its damaged D-9 was worth approximately $200,000 before the accident. The superior court accepted Afognak's evidence of the bulldozer's pre-accident value. Although it did not expressly determine the bulldozer's post-accident value, the court specifically pointed to evidence indicating that a "worn-out" D-9 had recently been advertised for $30,000. In short, the trial court made it abundantly clear that, in its view, the accident resulted in a loss of value that vastly exceeded the bulldozer's estimated cost of repair.
The court thus properly turned to reasonable cost of repair as an alternative measure of damages. After rejecting the city's cost estimate as incomplete and Afognak's estimate as including $13,500 in potentially unnecessary repairs, the court fixed the reasonable cost of repair at $89,700. The city complains that this estimate did not accurately reflect what Afognak would actually pay to repair its bulldozer. But the superior court recognized that its award might not correspond precisely with the cash cost to Afognak, since the company had elected to have its D-9 repaired by students and to cannibalize another of its machines for replacement parts. The court nevertheless found its estimate of Afognak's costs to be reasonable. In our view, this finding is not clearly erroneous; for when a court or jury determines cost-of-repair damages, "[i]t is the value, not the cost of repairs that is essential."[32] Here, the value fixed by the court is reasonable in light of the totality of the evidence. Accordingly, we affirm its award of damages.

E. Prejudgment Interest

The superior court awarded prejudgment interest on the full $89,700 damage award. The city cites Sebring v. Colver[33] to argue that it should not be required to pay prejudgment interest on the full amount. In Sebring, we concluded that the superior court erred by awarding prejudgment interest on a damage award compensating a family for the cost of repairs that had not yet been made.[34] But we based our conclusion on evidence showing that, because "the financial impact of the passage of time was thus incorporated into the jury's damage award, any award of *788 prejudgment interest on this amount would... constitute a double recovery."[35] Unlike the evidence in Sebring, the record here fails to establish that the superior court's award of damages "already incorporated" "the financial impact of the passage of time."[36] The city bore the burden of proof on this issue;[37] and absent an affirmative showing of double recovery, we will not reverse an award of prejudgment interest.[38]

IV. CONCLUSION

For the foregoing reasons, we AFFIRM the superior court's judgment.
NOTES
[1]  See Fejes v. Alaska Ins. Co., 984 P.2d 519, 522 (Alaska 1999).
[2]  See Curt's Trucking Co. v. City of Anchorage, 578 P.2d 975, 977 (Alaska 1978).
[3]  See Cole v. Bartels, 4 P.3d 956, 958 (Alaska 2000); Navistar Int'l Transp. Corp. v. Pleasant, 887 P.2d 951, 958 n. 10 (Alaska 1994).
[4]  Curt's Trucking, 578 P.2d at 977 n. 6.
[5]  Restatement (Second) of Torts § 413 (1965) provides:

One who employs an independent contractor to do work which the employer should recognize as likely to create, during its progress, a peculiar unreasonable risk of physical harm to others unless special precautions are taken, is subject to liability for physical harm caused to them by the absence of such precautions if the employer
(a) fails to provide in the contract that the contractor shall take such precautions, or
(b) fails to exercise reasonable care to provide in some other manner for the taking of such precautions.
Cf. Moloso v. State, 644 P.2d 205, 214 (1982) (applying Restatement § 413).
[6]  628 P.2d 554, 555 (Alaska 1981).
[7]  See Guerrero v. Alaska Hous. Fin. Corp., 6 P.3d 250, 254 (Alaska 2000); Estate of Breitenfeld v. Air-Tek, Inc., 755 P.2d 1099, 1102 (Alaska 1988). We determine whether a duty exists before addressing immunity questions. See Guerrero, 6 P.3d at 254.
[8]  Cf. Torres v. Reardon, 3 Cal.App.4th 831, 5 Cal.Rptr.2d 52, 56-57 (1992); Conroy v. Sherwin-Williams Co., 168 Ill.App.3d 333, 119 Ill. Dec. 69, 522 N.E.2d 731, 734-35 (1988).
[9]  D.S.W., 628 P.2d at 555 (quoting Peter W. v. San Francisco Unified Sch. Dist., 60 Cal.App.3d 814, 131 Cal.Rptr. 854, 859-60 (1976)).
[10]  Indeed, to the extent that the D.S.W. factors establish that the city owed a duty of due care to warn Afognak of any hidden but reasonably foreseeable danger, Afognak's alternative theory of duty would indicate that the instructions submitted to the jury were unduly favorable to the city in permitting the jury to hold the city liable only upon a finding that "the defendant knew that there existed a hidden, unknown and extrahazardous danger at the location." (Emphasis added.)
[11]  Moloso, 644 P.2d at 212 (quoting Hammond v. Bechtel, Inc., 606 P.2d 1269, 1277 n. 15 (Alaska 1980)).
[12]  Guerrero, 6 P.3d at 255 (quoting Schumacher v. City & Borough of Yakutat, 946 P.2d 1255, 1258 (Alaska 1997)); see also Webb v. City of Sitka, 561 P.2d 731, 732-33 (Alaska 1977), superseded by statute on other grounds, as stated in University of Alaska v. Shanti, 835 P.2d 1225, 1228 (Alaska 1992) (adopting the unitary test articulated in Smith v. Arbaugh's Restaurant, Inc., 469 F.2d 97, 100 (D.C.Cir.1972), and requiring landowners to act reasonably "in view of all the circumstances, including the likelihood of injury to others, the seriousness of the injury, and the burden on the respective parties of avoiding the risk").
[13]  To the extent that our ruling conflicts with the superior court's finding that the city retained no control over the conditions of Afognak's work, we conclude that the superior court erred as a matter of law. Cf. Moloso, 644 P.2d at 211-12; Hammond, 606 P.2d at 1274; Morris v. City of Soldotna, 553 P.2d 474, 478 (Alaska 1976); Hobbs v. Mobil Oil Corp., 445 P.2d 933, 934 (Alaska 1968).
[14]  See note 10 above. The city also complains that the superior court erred in allowing the jury to determine as a matter of fact whether the condition of the highway amounted to an "extrahazardous danger." The city cites Matomco Oil Co. v. Arctic Mechanical, Inc., 796 P.2d 1336, 1341-42 (Alaska 1990), for the proposition that this issue is a question of law for the court, rather than a question of fact for the jury. But Matomco is inapposite, since we dealt there with the particular meaning of "ultra-hazardous activity" for purposes of imposing strict liability. Id. And in any event, any error in submitting this disputed issue to the jury was harmless in this case since the "extrahazardous danger" requirement was superfluous. As our opinion indicates, the city owed a duty of due care to warn Afognak of unforeseen dangers, not "extrahazardous" dangers. Here, the added requirement of an "extrahazardous" danger inured to the city's benefit.
[15]  AS 26.23.060(b) states:

Each political subdivision is responsible for disaster preparedness and coordination of response
(1) by itself;
(2) in conjunction with other political subdivisions by establishing an interjurisdictional planning and service area under AS 26.23.070; or
(3) in conjunction with the Alaska division of emergency services.
[16]  The legislative history of AS 09.65.070(d)(5) confirms this interpretation, making it clear that the statute was designed to offer immunity only for damages incurred when municipalities acted as Good Samaritans by agreeing to perform state functions in lieu of state personnel during emergencies. See 1977-78 Senate Community and Regional Affairs Committee File, microfiche # 374 (explaining the proposed legislation as protecting local governments acting as Good Samaritans and offering as examples state/local mutual aid agreements for assistance at state airports and situations in which local police respond in the absence of a state trooper).
[17]  See Adams v. City of Tenakee Springs, 963 P.2d 1047, 1050 & n. 3 (Alaska 1998) (citing R.E. v. State, 878 P.2d 1341, 1349 (Alaska 1994)).
[18]  See Adams, 963 P.2d at 1050 (citing State, Dep't of Transp. & Pub. Facilities v. Sanders, 944 P.2d 453, 456 (Alaska 1997)).
[19]  See Adams, 963 P.2d at 1051; cf. Guerrero v. Alaska Hous. Fin. Corp., 6 P.3d 250, 259 (Alaska 2000); Sanders, 944 P.2d at 456.
[20]  Brady v. State, 965 P.2d 1, 16 (Alaska 1998).
[21]  691 P.2d 281 (Alaska 1984).
[22]  See id. at 283.
[23]  Cf. Sanders, 944 P.2d at 459.
[24]  See, e.g., Adams, 963 P.2d at 1051 ("Decisions about how to allocate scarce resources are matters of policy immune from judicial review."); Estate of Arrowwood v. State, 894 P.2d 642, 646 (Alaska 1995) ("It is well established that both legislative appropriations and executive department budget decisions are discretionary functions immune from judicial inquiry.").
[25]  963 P.2d at 1050-51.
[26]  894 P.2d 642.
[27]  Id. at 646.
[28]  498 P.2d 712 (Alaska 1972).
[29]  Id. at 722.
[30]  See Era Helicopters, Inc. v. Digicon Alaska, Inc., 518 P.2d 1057, 1061-62 (Alaska 1974); cf. 1 Dan B. Dobbs, Law of Remedies § 5.13(1), at 836-37 n. 11 (2d ed.1993) (describing a rule of measure of damages as the lesser of diminished value or repair costs as a variant on general rule that the measure of damages for harm to chattel is the sum by which market value has been diminished).
[31]  See Conam Alaska v. Bell Lavalin, Inc., 842 P.2d 148, 154 (Alaska 1992); see also Pugliese v. Perdue, 988 P.2d 577, 580 (Alaska 1999).
[32]  Otness v. United States, 178 F.Supp. 647, 652 (D.Alaska 1959).
[33]  649 P.2d 932 (Alaska 1982).
[34]  See id. at 936.
[35]  Id.
[36]  Id.
[37]  See Cole v. Bartels, 4 P.3d 956, 958 (Alaska 2000); Hancock v. Northcutt, 808 P.2d 251, 261 (Alaska 1991) (reversing the denial of prejudgment interest when defendants failed to prove that the award of such interest would result in a double recovery); State Farm Fire & Cas. Co. v. Nicholson, 777 P.2d 1152, 1158 (Alaska 1989) (permitting prejudgment interest on future damages when there was no risk of double recovery).
[38]  See Cole, 4 P.3d at 958.
