Evaluating investments by discounting anticipated future benefits at an exogenously determined risk-adjusted discount rate (hereafter referred to as the RADR approach) is well accepted in the canon of finance. If benefits (Dt) are to be received for T periods and if k, the discount rate, is constant over each of the t periods, then the discrete time net present value (NPV) is defined as:

A positive NPV characterizes a desirable investment.

In a recent article appearing in this journal [2] Jonathan Ingersoll developed a normative multidimensional security pricing model for the individual investor in which he corrected errors in an earlier attempt by William Jean [3] [4] [5] at developing such a model. The purpose of this correction is to clarify and correct certain parts of Ingersoll's correction of Jean's work.

The dynamic behavior of the corporation has been examined in recent literature by a number of authors. These efforts, however, although attempting to characterize the firm's optimal financing program have neglected to incorporate the threat of bankruptcy associated with these decisions. When the threat of default is appropriately considered, the investment and financing strategies are inexorably joined over time so that determination of an optimal policy becomes a multiperiod problem. The thrust of this paper is to address the problem of determining the firm's dynamic investment-financing program explicitly recognizing the uncertainty of financial ruin attributable to the firm's choice of capital structure.

There are seven academic finance associations in the United States; two are considered to be national and five are identified as regional. The national organizations are the American Finance Association (AFA) and the Financial Management Association (FMA), and the regional associations are the Eastern Finance Association (EFA), Midwest Finance Association (MFA), Southern Finance Association (SFA), Southwestern Finance Association (SWFA), and the Western Finance Association (WFA).

In a recent article in this Journal Joy and Tollefson [10] (hereafter J&T) critically analyzed discriminant analysis and its application to bankruptcy analysis. The authors make several interesting points and provide a useful discussion of the application of this statistical technique in finance. There are, however, three aspects of their presentation which need further elaboration. These relate to their discussions of (1) the difference between the stability of the discriminant model and its predictive ability, (2) the alternative methods of making inferences about the relative discriminatory power of variables, and (3) the reference statistics to use in assessing classification efficiency. In commenting on these points we will make use of the data from the Altman [1] study as did J&T.

In response to the many issues raised by Altman and Eisenbeis (A&E) [2], we will use their three-part outline. Before turning to their comments, however, we would like to take this opportunity to correct a typo in footnote 10 from our original paper [4]. The denominator of the formula is incorrect as shown, and should be .

In a timely, comprehensive article in this journal, Joy and Tollefson (J & T hereafter) treated design and interpretation problems for linear multiple discriminant analysis (LMDA). Although the article is generally correct in treating a complex topic, it has two problems:

1. The (widely-used) split-sample validation technique that J & T used is an inappropriate method for establishing the efficacy of the estimated discriminant function.

2. J & T reach erroneous conclusions on the correctness of two methods for assessing the discriminatory power of individual variables.

This comment addresses these two problems.