Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one-step regression function m. In the literature, estimators for the three parameters of m, that is, the breakpoint θ and the levels a and b, are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non-i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one-factor model for the input X and a Bernoulli mixture model for the output Y. The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic.