This paper develops a new factor-analysis-based (FAB) approach for choosing the optimal direction in a directional distance function (DDF) analysis. It has the combined merits of factor analysis and slacks-based measure (SBM) and incorporates the relative ease with which various input-output could be adjusted. This development relieves the dependency of price information that is normally unavailable in the provision of public goods. This new FAB-DDF model has been applied on a dataset containing all public hospitals in New Zealand (NZ) observed during 2011-2017. The empirical results indicate that the average reduction across different labor is in the range of 3-10 percent, and the corresponding figure for capital input is 25.7 percent. The case-adjusted inpatient-discharge and price-adjusted outpatient-visit are used as measures of desirable output, the average efficiencies are 92.7 percent and 99 percent respectively. Hospital readmission within 28 days of discharge is used as a measure for undesirable output, and the average efficiency score is 90 percent. These evidence support the suspicion that perverse incentives might exist under the National Health Targets abolished in 2018, which was a set of six indicators used in the last decade to evaluate the performance of local District Health Boards.