This paper examines the numerical properties of the nested fixed-point algorithm (NFP) using Monte Carlo experiments in the estimation of Berry, Levinsohn, and Pakes's (1995) random coefficient logit demand model. We find that in speed, convergence and accuracy, nested fixed-point (NFP) approach using Newton's method performs well like a mathematical programming with equilibrium constraints (MPEC) approach adopted by Dube, Fox, and Su (2012).