Anglo American AAL.LN -0.04% PLC is finally shipping iron ore from its troubled Minas-Rio operation in southeastern Brazil, after years of delays and cost overruns that tripled the project’s initial budget and brought turmoil to the mining company.

The timing, however, couldn’t be worse: Iron-ore prices have plummeted in recent months to their lowest levels in five years, and analysts are increasingly pessimistic about the prospects for a recovery. While Minas-Rio’s operating costs are low enough to be competitive in such an environment, the same can’t be said for the $8.8 billion it cost to build.

“Really it’s not going to be very easy to get a return on the capital we invested in Minas-Rio,” said Paulo Castellari, head of Anglo American’s Brazilian iron-ore division, at a news conference Monday.

London-based Anglo American put 80,000 tons of Brazilian iron ore on a vessel bound for China on Oct. 25, in what Chief Executive Mark Cutifani described as a “great victory for our team.” Two more similar-sized shipments are expected to go out in December, and the company plans to gradually bring the mine to its full capacity of 26.5 million tons a year over the next 18 to 20 months.

Conceived at the height of the last decade’s commodity boom, Minas-Rio became emblematic of the way tantalizingly high prices can leave mining companies temporarily blinded to risks.

The project was supposed to give Anglo American a bigger slice of the lucrative global market for iron ore, where it lagged behind other mining majors. Prices for the steelmaking ingredient soared in the early 2000s as China’s fast-growing economy started importing vast amounts of raw materials for new buildings and infrastructure.

Former Chief Executive Cynthia Carroll traveled to Brazil and met with billionaire Eike Batista, who became the country’s richest person before his business empire collapsed in bankruptcy last year. Ms. Carroll agreed in 2008 to pay Mr. Batista’s mining company, MMX, $5.5 billion for Minas-Rio and another, smaller, iron-ore operation in northern Brazil that Anglo American sold last year. The company told shareholders that the Minas-Rio project would cost $2.7 billion to develop.

But rising costs for labor and equipment, environmental lawsuits and a thicket of red tape drove up that bill. Anglo American had to obtain a total of nearly 460 different licenses, Mr. Castellari said.

Including the acquisition, which analysts now consider hugely overpriced, the company spent some $539 per annual ton of iron-ore production capacity at Minas-Rio. That is more than double the $220 that Brazilian mining giant Vale SA VALE5.BR -0.28% is spending to open a comparable new mine in northern Brazil. And it is more than four times what London-based Rio Tinto RIO.LN -0.08% PLC is investing to expand its comparable operations in Western Australia.

“The project has personified Anglo American’s wider issues of poor management strategy, bad capital management and weak operational performance,” said Paul Gait, an analyst at Bernstein Research, in a recent report.

Ms. Carroll stepped down in 2012. Mr. Gait gives high marks to her replacement, Mr. Cutifani, who met the timeline and budget he set for getting Minas-Rio up and running.

Even with the recent drop in iron-ore prices, the operation should generate earnings for Anglo American going forward. It will cost the company $33 to $35 a ton to put ore from Minas-Rio on a ship in Brazil, where the commodity currently fetches between $65 and $67 a ton, according to IronOreTeam, a data provider.

“Our mission now is to prove that we will be able to deliver value in the operational phase,” Mr. Castellari said.