Anil Agarwal supercharged his rise from scrap metals trader to billionaire commodities magnate by embracing bold acquisitions and lots of debt. But that decades-long playbook is now being put to the test as rising borrowing costs complicate Agarwal’s efforts to clinch a buyout of the publicly traded crown jewel of his globe-spanning empire. His battle for control over Vedanta Ltd. is highlighting the risks for indebted tycoons in India and around the world as interest rates climb from historic lows and family businesses grapple with complicated holding structures. The stakes are high for London-based Agarwal, whose personal holding company has amassed about $7 billion of debt and faces a far less receptive bond market than it did in early 2020. Winning full control of Vedanta’s cash-rich balance sheet would help Agarwal meet those liabilities.