Build America Bonds Act of 2013 - Amends the Internal Revenue Code to: (1) make permanent the issuance authority for Build America Bonds and the authority for payments to issuers of such bonds, (2) make phased reductions in the credit percentage to bondholders and the percentage of payments to issuers of such bonds, (3) allow refundings of currently issued bonds, and (4) allow the use of Build America bonds to fund capital expenditures for levees and flood control projects.

Provides for an increase in payments to issuers of Build America bonds to compensate for reductions in the amount of such payments due to sequestration.