Increasing family tax benefits for families with children under one would cost the government $1.4bn over the next decade, figures released by the Parliamentary Budget Office have revealed.

The costings found that boosting family tax benefit part B by $1,000 for single-income families with infants earning less than $100,000 would have an impact on the budget bottom line.

The changes to the tax were part of a deal struck between Malcolm Turnbull and the Nationals shortly after Turnbull took the prime ministership in September.

Labor said the payment amounted to a “baby bonus bribe”. “The new baby bonus was nothing more than a bribe by Malcolm Turnbull to buy off the Nationals so he could get the top job,” said Labor’s families spokeswoman, Jenny Macklin.

“Mr Turnbull is cutting family payments which will see Australian families as much as $5,000 a year worse off, yet at the same time he’s bringing back a $1.4bn baby bonus that is unnecessary and unaffordable.”

In December the government enacted changes to family payments so parents would no longer receive assistance once their child turned 13. Grandparent carers and single parents under the age of 60 would still be eligible for payments until their child turns 18.

Legislation to scrap the end-of-year supplement in exchange for a $10-a-week increase in the base rate of the assistance measure are yet to be introduced in the Senate, after Labor, the Greens and some on the crossbench expressed concern.

In answers to questions on notice, the Department of Social Services released figures that show the extent of the cuts to families’ budgets.

Couples with young children who have a combined annual income of about $80,000 fare the best but are still out of pocket to the tune of about $281 a year.

Couples earning $80,000 with two teenagers would fare the worst, losing about $4,117 a year, after losing family tax benefit part B when their children turn 13.

All family types that were modelled, including single parents, would lose out under the proposed changes, which the government said is needed to fund extra money going into childcare.

“It is not looking good,” the Greens senator Rachel Siewert said. “Every cohort we asked about would lose out financially from the family tax benefit cuts.”

Siewert said the families who would lose the most from the family assistance payments were the least likely to need childcare.

“A coupled family with two children aged 14 and 16 earning $80,000 would lose over $4,000,” she said. “This is just one example of a family that would be hit by these cuts. With kids at that age I am sure they will not be making use of the childcare package.

The Department of Social Services figures show that lower-income families are most likely to lose out under the changes, which are designed to give tax relief to those earning less than a certain amount. About 1.3 million families will have family tax benefit part B phased out, nearly half of them – 620,000 – earning $40,000 or less.

A spokesman for the social services minister, Christian Porter, said the government would press on with the changes but would not give a timeline for when the legislation would be introduced into the Senate.