A consortium led by billionaire Johann Rupert agreed to buy Mediclinic International Plc in a deal that values the South African hospital operator at 3.7 billion pounds ($4.5 billion) after a series of improved offers. Rupert’s investment group Remgro Ltd., already Mediclinic’s biggest shareholder, and MSC Mediterranean Shipping Company SA will pay 504 pence a share for the stock it doesn’t already own, according to a statement on Thursday. That’s up from the 463 pence that was rejected in June. The group followed up with the higher bid in July. Mediclinic closed Wednesday at 487 pence. Remgro is a long-term investor with a near 45% stake.