A German financier, Hypo Real Estate, agreed to buy Depfa Bank of Dublin in a cash and stock transaction that values the business at $7.9 billion, the companies said. Hypo Real Estate, which is based in Munich, said it would pay Depfa shareholders 6.80 euros ($9.38) a share in cash and 0.189 new share. That is the equivalent of 16.14 euros ($22.27) a share, a 17 percent premium over Depfa’s closing price on Friday. Depfa, which specializes in public-sector finance, will become a wholly owned subsidiary of Hypo but keep its name, headquarters and brand identity. Hypo Real Estate said the acquisition would create one of the world’s leading providers of financing for commercial real estate, the public sector and infrastructure projects.