But how high might BP shares go? Currently 19 analysts have ratings on BP shares. That's also lower than the 24.5% gain BP shares have delivered over the past 12 months. Yet that 11%+ predicted return would still turn £9,999 today into an impressive £11,128 by 12 August next year. While analysts believe BP shares will keep soaring, they're split over whether the FTSE 100 company's shares are a Buy.