Business Activity Tax Simplification Act of 2013 - Expands the federal prohibition against state taxation of interstate commerce to: (1) include taxation of out-of-state transactions involving all forms of property, including intangible personal property and services (currently, only sales of tangible personal property are protected); and (2) prohibit state taxation of an out-of-state entity unless such entity has a physical presence in the taxing state. Sets forth criteria for: (1) determining that a person has a physical presence in a state, and (2) the computation of the tax liability of affiliated businesses operating in a state.