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Cr Vandervis is a Dunedin city councillor and a council appointee on the board of the council-owned museum.
"People have come to realise the state of DCC debt is quite a bit more serious than previously thought," he said at yesterday's board meeting.
He asked if there was "any way we can offer some sort of savings in stage four".
Work is continuing on the $35 million redevelopment project's third stage, which focuses on redeveloping the museum's original brick Burnside building.
Council officials said tender documents had already been sent out for the fourth and final stage, which aims to provide a modern northern entrance and to attract visitors from the highly popular Dunedin Railway Station nearby.
In a later interview, Cr Vandervis said the projected $8.6 million cost of stage four was "$8.6 million of money we don't have".
As a "builder's son" he was sceptical so much money was needed.
He also challenged the aesthetics of the proposed new entry, which he termed "a great triangular wedge of glass".
Its large size and appearance would detract from the museum's existing "lovely old heritage buildings".
Asked if the entry would attract railway visitors, he said: "You don't have to spend $8.6 million to put a sign in." Tenders for stage four close later this month and November 1 is the scheduled start date.
Council community life general manager Graeme Hall was hopeful the market was "going to be competitive" over the tenders.
At the meeting, Mr Hall acknowledged the council's fiscal concerns and said potential cost savings had to be identified in all its projects, including stage four of the Settlers Museum project.
Museum board chairwoman Dr Dot Page defended the appearance of the proposed final-stage building work and said it had also been carefully costed, and the overall project remained on budget.
Stage four included other important functional spaces and involved much more than just an attractive entry.
There would also be significant administrative and commercial areas, including a museum shop and cafe, which would help generate income for the museum, Dr Page said in an interview.
In discussing the board's latest annual financial report (until June 30 this year), another board member, Richard Thomson, asked about a favourable variance of $240,000, arising from unbudgeted interest earnings on Government grant funds held for the redevelopment.
He asked if it was appropriate that this extra income be offset against further city council funding earmarked for the redevelopment.
Such extra interest income had already been factored into redevelopment fundraising efforts, Mr Hall replied.
Mr Hall is to bring a financial report to the next board meeting, clarifying the role of the interest income in the project's overall funding.