WINZ released 9 MB of documents, but the money quote is buried at the back:
The cost of the SNG has been estimated on the basis of supporting 750 single people and 1,250 families at 7 days each at the maximum SNG rate. Once implemented, the SNG will be demand-driven but an estimate of expected cost still needs to be provided as this is a policy change
So, 2,000 grants at $1,000 each. According to the cover letter, the number of grants was estimated from the number of households with "insecure housing" on WINZ's (severely restricted) social housing register (~800 - 950), and the number of households listed in the 2013 census as lacking habitable accommodation (4,200). In other words, they deliberately estimated that only 40% of those eligible would be given a grant - either because they wouldn't apply, or because WINZ would unlawfully refuse it. They also assumed that families would be given such a grant for only 7 days, after which they would miraculously find an affordable home to live in.
The reality, according to MSD's Social Housing Report, is a little different: MSD gave out 11,446 grants totalling $12.6 million to 3,108 individual clients in the March quarter alone. The average grant wasn't just higher - $1,100 instead of $1,000 - but there were significantly more of them. Partly this is because there were more clients, but the biggest factor is that each client received almost a month of support rather than the expected week. And price-gouging by the motels WINZ was hiring didn't exactly help either.
In retrospect, this should have been obvious to WINZ. People don't just find an affordable home in a week, and given that WINZ itself was organising a big chunk of those homes via its social housing programmes, it should have known how long it would take. But like everything from National, the policy seems to have been designed as a PR stunt, so they could claim that something was being done, not as something designed to actually make a difference.
The scary thing is, it could have been worse. WINZ's first budget estimate, in August 2015, was for 750 grants, at $500 each - a mere $375,000. Clearly the organisation responsible for preventing homelessness had no idea of either the scale of the problem, or the cost of fixing it. And there's little evidence that they've learned anything since.