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This week, the council released figures showing a revised estimate provided to it by Opus International Consultants in 2009 came to $48 million with adjustments made by the council for costs and revenue bringing it to $53 million - much higher than the consultants' 2004 estimate of $21.4 million.
Mr Woodhead said the council had asked for a revised scheme estimate in 2008 and received it after several delays in late 2009.
"It came as a huge shock to council."
After absorbing the information, the council decided it was "not at all" confident in the figures provided, he said.
"Obviously, it meant we were not in a position to take it to the community."
The council then embarked on a "value engineering exercise" internally.
That work had taken quite some time and it was presented to council this week.
Part of that work covered the implications of the University of Otago's master plan, as it included proposals that would affect the council's plans for flood protection works within the campus.
Mr Woodhead said he rejected any suggestion the master plan added to the cost or delays of the project.
In a coincidence, the master plan was being developed at the same time the council was doing its value engineering work, providing an opportunity to work with the university to deliver a better outcome, he said.
"We are looking forward to working with the university."
It was hoped to integrate the plan with the Leith Lindsay scheme implementation, he said.