A statement from Customs said most of the cost was aircraft fuel.
"As part of its border protection work Customs will occasionally undertake aerial patrols to identify vessels of interest within New Zealand's economic zone. An allocation for this type of surveillance is budgeted for on an annual basis.''
The Nilaya was last sighted by officials in late January, when the plane circled the vessel and made numerous attempts to hail it.
There was no response, and there were no further sightings.
At the time of the sighting the Nilaya was in international waters.
A decision on whether Andhoey would be prosecuted or costs sought could not be made until he returned to New Zealand and officials had spoken with him, a Customs spokeswoman said.
That outcome seems unlikely, with Norwegian media last month reporting Andhoey had abandoned his polar trip and was heading for South America.
Andhoey and his crew believed they would face prosecution if they returned to New Zealand for sailing into Antarctic waters without the proper authorisation.
It was not known whether a New Zealander on board the Nilaya, Busby Noble, would travel to South America or try to return to New Zealand.