LONDON—The world’s biggest oil companies have vowed to bring down the costs of big projects in the face of slumping oil prices, but the unrelenting price weakness—with crude below $50 a barrel—suggests they could have to dig deeper still. In the past year, as oil prices plunged 60% from highs of $114 in 2014, U.K. energy giant BP PLC began testing new projects for profitability around $60 a barrel, down from $80 a barrel last year. Its Anglo-Dutch rival Royal Dutch Shell is testing projects at prices as low as $50 a barrel, though its overall price outlook is between $70 and $110 a barrel.