In the traditional literature of engineering and managerial economics, a variety of different and not generally consistent indices have been proposed for deciding whether a given capital investment project should be undertaken. Using mathematical programming, it is shown herein that in an unconstrained situation under certainty, with complete freedom to borrow or lend at one rate of interest, the present worth index and its equivalents are correct while indices inconsistent with present worth are wrong. However, in the presence of further constraints, e.g., on allowed borrowing or on available scarce material, even the present worth index is unsatisfactory, and, in general, a complete mathematical programming solution is required.