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The case asks for $220 million from the Government's Christchurch Regeneration Acceleration Fund for the construction of the stadium in Christchurch.
Work on the site could begin as early as mid-next year with it fully operational in 2024.
Mayor Lianne Dalziel thought the arena would be a “game-changer” for the city.
“We are staking the claim as to who we are, we have always been New Zealand’s sporting capital, we have always been that,” she said.
“It is going to be an important sports facility but it is also going to be an amazing cultural facility as well, and we will be attracting events that we simply can’t attract right now."
However, city councillor Yani Johanson, who was the only councillor to vote against the investment case, said he was “deeply concerned” by the proposal.
“The most sensible thing to do to save some money would have been to put it back into Lancaster Park. I estimate it is going to an additional $80 million for this investment case to go into this location.
“In my view we should put the stadium back into Lancaster Park. We could save $80 million and we could have greater certainty around future events," he said.
The case, which cost about $3 million to prepare, states that for the arena to be competitive and attract international and national events, it needs a roof, a minimum seating capacity of 25,000, with potential to add 5000 temporary seats, fixed rectangular turf and high-quality acoustics.
It is projected the arena will cost $472.7 million in total to build.
The city council has put aside $253 million in its 2018-28 Long Term Plan for its contribution to the arena's construction costs.
The net operating costs for the arena are anticipated to be $4.2 million a year.
The city council has currently allocated $4.1 million per annum within the Long Term Plan to cover these costs.
It predicts the arena would bring $396 million into the city over about 30 years.
Before the investment case was finalised by the city council, multiple organisations including the Crusaders voiced their support for the investment case.
ChristchurchNZ chief executive Joanna Norris said the arena is essential for the city's regeneration from the earthquakes.
"We need to work really hard at this time to overturn Christchurch’s structural disadvantage, which occurred as a consequence of the 2010 and 2011 earthquakes," she said.
"Other cities leveraged our weakness when we were on our knees and we need to fight to get back into the game, this is urgent and this is compelling."
Canterbury Employers' Chamber of Commerce chief executive Leeann Watson told city councillors not supporting the investment case for the arena "was not an option."
"Making the commitment today will give both businesses and private investors the confidence to invest in the city," she said.