PETROBRAS used to impress the oil world with its expertise at tapping the black stuff thousands of metres beneath the ocean floor. Now Brazil’s oil behemoth is better known for plumbing a different kind of depth. It is mired in a multi-billion-dollar bribery scandal, indebted to the hilt and worth a third of the 405 billion reais ($250 billion) it was valued at shortly after its initial public offering in 2010. On February 4th its beleaguered boss, Maria das Graças Foster, succumbed to pressure and resigned, along with five senior executives.

Investors rejoiced: Petrobras’s shares, which had sunk by 17% the previous week, rebounded. Yet most of its woes are not Ms Foster’s fault. The government, which has a controlling stake, makes most of the big decisions. These have included making Petrobras hire and buy parts from inefficient local firms; telling it to build refineries in unappealing places, in the name of regional development; and making Petrobras the only principal operator in Brazil’s vast offshore pré-sal (“beneath the salt”) fields.

Ms Foster’s successor, who had yet to be chosen as we went to press, faces a sea of challenges. At current world oil prices, much of the pré-sal output barely makes money. Despite debt-fuelled investment of $40 billion a year, production has flatlined at 2m barrels a day (b/d) for the past four years and is set to nudge up by just 4.5% in 2015. A goal set last year, of producing 4.2m b/d by 2020, looks fanciful.

Then there is the spectre of corruption. It first reared its head last March, with the arrest on money-laundering charges of Paulo Roberto Costa, who ran the firm’s refining arm from 2004 to 2012. In a plea bargain Mr Costa confessed to channelling 3% of the value of his division’s contracts with suppliers to slush funds for politicians. The public prosecutor has identified at least 2.1 billion reais of suspicious payments. Aggrieved foreign investors have filed lawsuits against Petrobras in New York, where some of its shares are traded.

Petrobras was expected to take a bribery-related write-down on its third-quarter earnings. It was supposed to publish these figures in November but has twice postponed them as it struggles to work out what the write-down should be. So far it has come up with two vastly differing figures. Applying Mr Costa’s 3% cut to the value of those contracts it suspects, Petrobras comes up with a figure of 4 billion reais. But revaluing the assets created as a result of those contracts (mostly refineries), at the prices they might fetch in current market conditions, it reckons they may be worth 89 billion reais less than their book value.

The lower figure probably understates the write-down that will be needed, because the problem with dubious contracts may extend beyond Mr Costa’s former fief. The higher figure is probably an exaggeration, because valuing each asset separately fails to account for economies of scale. What is more, all sorts of other factors, from currency moves to the weak oil price, may explain much of the impairment to the assets’ values.

Without a credible write-down number, the firm’s auditor, PwC, refused to sign off the accounts. Last week Petrobras published them anyway. It had to do so before March to avoid triggering a technical default. Should it fail to release an audited full-year statement by July, creditors may demand early repayment of up to $54 billion of debt. With just $25 billion in the kitty, $16 billion-18 billion in debt and dividend payments due this year, and limited access to new financing because of the lack of audited books, meeting those obligations may require a government bail-out.

Tackling these troubles will require inordinate skills. Yet the hardest task for the new boss will be to resist interference from the state. Government intervention has made it the least profitable big oil firm, according to a report by Credit Suisse. But the bank also found that where meddling is minimal, such as in finding oil and getting it out of the ground, Petrobras is one of the best. Sadly, Brazil’s government is unlikely to pay that much heed.