Australia Post will face a one-month investigation examining the organisation’s gift and expense culture after watches worth almost $20,000 were handed to senior executives.

The federal government on Monday released the terms of reference for the communications department inquiry which will be assisted by a private law firm.

Australia Post chief executive Christine Holgate and former chair John Stanhope’s involvement in four Cartier watches being gifted to senior staff will be scrutinised.

The management culture at the government-owned enterprise, in relation to gifts, rewards and expenses, will form part of the investigation.

That will include personal expenses of executives.

Luxury watches with a combined price tag of $19,950 were dished out to four senior executives for helping clinch a deal to facilitate banking in post offices.

Bonus payments worth more than $97 million were made, with the majority going to staff in senior roles.

Labor used Question Time to quiz Communications Minister Paul Fletcher about how many of Australia Post’s eight non-executive board members were linked to the Liberal Party.

“A hint, the number’s four,” opposition frontbencher Tony Burke told parliament after Mr Fletcher dodged the question.

The minister retorted by listing a number of Australia Post board appointments with Labor ties made under previous governments.

The probe will check if Australia Post meets public expectations around leadership and governance, while also looking at how it spends taxpayers’ money.