PE firms have recently begun to negotiate smaller equity contributions as borrowings increase, reports Matthew Sheahan at Mergers & Acquisitions.   LBO activity came to a screeching halt last summer; there were $19.7 billion issued via 34 deals to back buyouts for all of 2011, but so far this year, nine high-yield bond deals totaling $8.3 billion have been issued to back LBOs. Banks and other creditors are sticking more of their necks out when funding private-equity players’ leveraged buyouts. Equity contributions to leveraged buyouts have generally remained in the 30 percent to 40 percent area for a couple of…