Tax element in Cost of Equity

I often see two different formulas for CoE in practice: CoE = Rf + MP * beta where either MP is defined as: 1) MP = Rm - Rf or 2) MP = Rm - Rf * (1-t) Questions: - What is the rationale for tax adjusting Rf in formula 2? - Should Rf be tax adjusted when calulating MP? - Does anyone know of an article discussing the issue?

Could this have been relating to a certain type of investor? Say, a tax exempt one?