We consider networks of banks with assets and liabilities. Some banks may be insolvent, and a central bank can decide which insolvent banks, if any, to bail out. We view bailouts as an optimization problem where the central bank has given resources at its disposal and an objective it wants to maximize. We show that under various assumptions and for various natural objectives this optimization problem is NP-hard, and in some cases even hard to approximate. Furthermore, we also show that given a fixed central bank bailout objective, banks in the network can make new debt contracts to increase their own market value in the event of a bailout (at the expense of the central bank).