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The options - together with a possible merger of the garden with the neighbouring Otago Settlers Museum - were raised as councillors continued deliberations on the 2011-12 pre-draft annual plan yesterday.
Councillors were last night due to have the size of the rates increase for the draft plan calculated.
But after debate continued into the night, this was delayed until a meeting next Monday.
A report on the Chinese Garden by council community life general manager Graeme Hall to yesterday's meeting showed revenue from admissions and shop sales at the garden had dropped from $516,717 in the first year of operation, beginning in mid-2008, to just $250,880 in 2009-10.
With operating costs of $956,000, and revenue forecasts for 2011-12 revised down to $380,000 for the year, that meant rates funding of $576,000 was needed to run it in 2011-12, councillors were told.
That was on top of $1 million the council had already contributed towards the $14 million cost of developing the garden, as well as the cost of council land to house the garden, councillors were told.
Operating costs - including a staff of two and regular maintenance and repairs - were largely fixed, but work was under way to develop revenue streams including cruise-ship tourists, garden manager Margo Winchester told the meeting.
She was also working to develop "synergies" with other tourist attractions in the city, but was facing stiff competition in trying to crack the cruise-ship market.
However, Cr Lee Vandervis argued the garden's potential appeared to have been "massively oversold", and the council needed to cut its losses.
"I believe we need to look very, very carefully at stanching the bleeding of this particular facility."
He questioned where the garden's future lay, given it appeared Dunedin residents were not returning for repeat visits, and hopes of strong interest from Chinese tourists appeared not to have eventuated.
"Are we flogging a dead dragon or not?"
Mr Hall said he did not believe so, but conceded the aim of reducing the council's share of operating costs by half, to bring it in line with Olveston, was "not yet" possible.
The dire picture prompted Cr Richard Thomson to suggest leasing - but not selling - the garden to a private operator to run, even if the lease did not provide a return to the council.
"[It would] still be half a million dollars less cost to the ratepayers than it currently is," he said.
Mr Hall said that had not been considered but could "certainly be one of the options".
Cr Thomson said the garden should be given another year to try to turn its financial fortunes around, and consideration given to a private operator if it could not.
He also questioned whether even the reduced income expectations of $380,000 for 2011-12 were realistic, given income in the last financial year was just $250,000.
"It's still 50% more than what was achieved last year," he said.
Ms Winchester said better days were expected, with indications the global recession - and its impact on tourists' spending - had reached bottom.
"We are all optimistically thinking that hopefully we have hit the bottom of the recession," she said.
Deputy mayor Chris Staynes also asked for a staff report considering whether the garden could be closed on quiet Mondays and Tuesdays, when cruise ships were not scheduled to visit Dunedin, to reduce operating costs.
That won support from Cr Vandervis, who said the closures should be considered "and perhaps even more beyond that".
Councillors voted to seek a staff report discussing savings that could be achieved by incorporating the garden into the Otago Settlers Museum's operation, and the likely capital costs of doing so.
They also asked for a report on other ways of achieving savings.