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As long as the city completes risk-profiling and gathers information on "values, perils to be considered and level of excess", its brokers have said an insurer would consider whether it would provide cover.
But council finance, strategy and development committee meeting chairman Cr Syd Brown yesterday said he was not impressed with the offer.
It appeared to involve "pretty strict criteria", he said.
While the council would consider the matter today, Cr Brown said the local authority had to "throw that perception out there we're not going to be screwed".
A report to the committee said the council had already set up its own "strategic risk fund", with an initial sum of $250,000 invested with Dunedin City Treasury Ltd, a figure that would have been similar to an insurance premium it would have paid.
That money was the first step for the council to insure itself for earthquake risk, a decision made as the city deals with the fallout from the Christchurch earthquakes.
Those earthquakes had resulted in a "challenging" insurance market, the report said.
It emerged earlier this year the city's $2.4 billion network of above- and below-ground infrastructure assets had been left without insurance after the earthquakes.
International reinsurers, worried about their own exposure, refused to offer new cover for underground assets, while council staff refused to pay inflated premiums for reduced cover for above-ground assets.
The council is instead considering self-insurance to cover 40% of any repair bill, a requirement for obtaining 60% support from the Government.
The report to the committee, from council financial controller Maree Clarke, said the council's insurance brokers had confirmed one of the council's insurers would "consider offering insurance for infrastructure assets for risks other than earthquake".
"To do so, the insurers require accurate information on what assets are to be considered for insurance coverage, the values, perils to be considered and level of excess.
"Once the risk-profiling has been completed, work can be undertaken to compile the information required by the insurers." The insurers would then consider whether they were able to provide cover, and on what basis.
The report said the council transport operations and water and waste services departments had undertaken comprehensive risk assessments.
An update on the the issue, and further information from work being done, would go before the council during budget meetings in January.
Cr Brown said the council would "wait and see what the quote is" for insurance before it considered its next step.
He did not have access last night to information on the name of the insurer involved.