This paper analyzes optimal monetary policy under zero lower bound in the presence of cost channel. Cost channel introduces trade-off between output and inflation when economy is out of ZLB. As a result, exit time both under discretion and commitment is endogenous in the presence of cost channel. We also find that commitment outperforms discretion by promising future boom and inflation and a T-only policy closely replicates commitment both under presence and absence of cost channel. Moreover, the exit date (from ZLB) under discretion, commitment and T-only policy rises with the magnitude of demand shock given the degree of interest rate pass-through irrespective if the cost channel is present. We also show that, while exit date both under discretion and T-only policy rises with the degree of interest rate pass-through/credit market imperfection, it falls under commitment given demand shock.