With an average of about $7000 spent on each student under fees-free, National MP Simeon Brown said that would amount to about $18m that the Government paid to tertiary providers for students that had later withdrawn.
National MP Nikki Kaye then asked about the students who failed courses paid for by the Crown.
"What are the people of New Zealand paying for? How many students have failed and effectively had their fees paid for by the Crown?"
Commission chief executive Tim Fowler said the average fail-rate was about 12 per cent - or about 5000 of the 41,700 students in fees-free tertiary education.
That would cost about $35m, assuming $7000 per student.
Brown said that would mean the Government had spent about $53m on fees-free courses that students had either withdrawn from or failed to pass.
Nigel Gould, chair of the commission's board, said the Government already subsidised tertiary classes that students failed, but Brown argued that it was an additional cost because it was due to the fees-free policy.
"About $50 million is the ballpark figure," Brown said.
Gould replied: "The calculation is correct but offsetting that is, under the previous year, there would have been an exposure in all probability of not a dissimilar amount for a student loan."
Brown said: "Which the individual would then pay back."
Fowler said he would come back to the committee with more certainty.
"There's a possibility that you're conflating withdrawal and fail rates, which are different things."
After the meeting, a spokesperson for the TEC said that Gould "accepted the maths used" but not the validity of the figures.
"The figures appear to include double counting, and assume that every withdrawal involves a full year of fees (which is not the case)," the spokesperson said.
"Complete figures will be available next year after Tertiary Education Organisations have provided their reporting for 2019."
The spokesperson said that students withdrawing from courses can lead to a full or partial refund if they withdraw within a timeframe set by the tertiary provider.
"If the student was entitled to fees-free, any refund would be offset from TEC's overall payment to their place of study."
Fowler also told the committee that less than 20 people faced the possibility of prosecution for deliberately trying to rort the system.
People wanting access to fees-free courses have to sign a statutory declaration, and Fowler said that 246 declarations had been declined or overturned - 0.000018 per cent of all those who applied.
Less than 20 of those people appeared to have tried to cheat the system, and the TEC was discussing those cases with the Crown solicitor.
"It's an extremely small number, but that's not going to preclude us from prosecuting [where appropriate]," Fowler said.
Every declaration was assessed and later matched against data, and Fowler said more false applications could come to light because applications could have passed the assessment and may still fail the data-matching.
Under questioning from NZ First MP Mark Patterson, Fowler said enrolments in agricultural courses were the lowest in the last decade.
"It's definitely a branding and image issue. It's just not well liked.
"The long-run solution is careers' advice and the information, quite apart from the fact that the agricultural sector has to step up, frankly, and get involved in supporting training."
