Parents believe they are worse off or no better off despite a record $2 billion spend on childcare.

In the first major evaluation of the Morrison government’s overhaul of childcare rebates, just one-third of parents believes they are better off.

Surprisingly, one in three parents earning between $65,000 and $170,000 believes they are worse off, despite the fact the reforms were designed to offer more generous rebates to middle-income earners.

Separately, new government data also reveals some centres in metropolitan Sydney, Melbourne and Canberra are charging fees of up to $200 a day.

Under the changes introduced in July 2018, the government subsidises a proportion of families’ childcare fees based on how much parents earn and how much they work.

According to the Morrison government, a “typical family” is about $1300 a year better off under the arrangements.

However, an initial report prepared by the Australian Institute of Family Studies finds parents sceptical about the benefits.

Goodstart Early Learning Centre’s advocacy manager John Cherry said some may be better off in real terms but that was not their perception.

“Incredibly, only about a third of them thought they were better off,” he said.

“A worryingly large number of low-income families are worse off because of the reforms. It’s the first report of the childcare subsidy evaluation study. So, it’s a massive evaluation they are going to do. This is the first phase.”

Education Minister Dan Tehan said the government was also publishing detailed information on childcare costs by region.

“We want parents to have a clear picture of where they can access quality, affordable childcare in their local area,” he said.

“Because of the Morrison government’s Child Care Subsidy, out-of-pocket childcare costs for families are down by 7.9 per cent,” according to the Australian Bureau of Statistics Consumer Price Index.

“Out-of-pocket expenses for 75 per cent of parents with children in centre-based day care is around $50 for a full day of care. Around 200,000 pay just $2 per hour, or $20 for a full day of care.”

But Labor’s education spokeswoman Tanya Plibersek said childcare fees had gone up 28 per cent since the Coalition government was elected, and families were paying thousands of dollars more for care.

“The government has no plans to bring fees under control,” she said.

“The minister says families should shop around. That shows just how out of touch the Liberals are. Families are struggling to find a childcare place and settle their kids in a centre.”