This paper applies the binary tree classifier and discriminant analysis methods to predicting failures of banks and insurance companies. In this study, discriminant analysis is generally better than the binary tree classifier in the classification of bank defaults; the binary tree is generally better than discriminant analysis in the classification of insurance company defaults. This situation can be explained that the performance of a classifier depends on the characteristics of the data. If the data are dispersed appropriately for the classifier, the classifier will show a good performance. Otherwise, it may show a poor performance. The two data sets (bank and insurance) are analyzed to explain the better performance of the binary tree in insurance and the worse performance in bank; the better performance of discriminant analysis in bank and the worse performance in insurance.