The purpose of this paper is to consider some problems arising in several applications of the theory of portfolio analysis pioneered by Markowitz [8] and Tobin [13]. This theory of asset choice under uncertainty has been applied to a large and growing set of problems beyond the original application to the selection of the investor's optimal portfolio, e.g., the capital budgeting decision of the firm (Lintner [7]), international capital flows (Grubel [5]), the choice of an export mix for a country (Brainard and Cooper [1] and the flow of direct investment (Stevens [12] and Prachowny [10]). In all applications a common element is the set of efficient portfolios which, in turn, is determined. by the set of moments—means, variances, and covariances—of the returns from the different assets that are. Considered for inclusion in the portfolio.

As has been demonstrated, the process of deciding whether or not to produce beyond the split-off point is not as simple as set forth in most managerial accounting books. Linear programming can be used in these situations as long as the production relationships remain relatively constant. However, in applying linear programming it is necessary to allow for inventories of unused intermediate outputs or optimality may not be truly found. It is not possible to construct a general model, but a wide variety of assumptions have been discussed in this paper with the goal of establishing a methodology of formulating decision models when joint products are involved.

Recently, Cohen and Gujarati [2] have suggested that when multicollinearity is present there is “ …danger involved in mechanically dropping variables from multiple regression equations by t tests because t values of the regression coefficients may not be significantly different from zero when the true (population) values of these coefficients are in fact not zero…” The problem they discuss is not a new one and has been extensively treated in the existing literature. However, their approach is straightforward and will certainly aid the practitioner in his understanding of the problems associated with multicollinearity.

This article aims to examine how relative differences in key financial variables among buyers and sellers affect the valuation of aggregate and hence the benefits arising from the merger to buyer's and seller's stockholders as well as the implications for merger strategy which buyer and seller might adopt. It also aims to carry out the foregoing analyses as of the time the merger transaction takes place and also over a specified planning horizon. A major conclusion of this article is that when two firms, experiencing unequal growth rates, merge on the basis of an exchange of shares, their combined value in the market will be less than the sum of the market values of the individual companies, as a result of a bias in the valuation models commonly used in security analysis. The specific source of this bias is the underestimate of the growth rate in combined earnings that results from typical forecasting methods. Another major conclusion is that although there is a valuation loss in total, the stockholders of the firm with the smaller of the two growth rates can experience valuation gains over a period of time at the expense of the other firm's stockholders. It would follow from this that a firm will always find it to the advantage of its stockholders to acquire or merge with firms experiencing higher growth rates than its own, provided these stockholders are willing to hold their stocks for a period of time, the minimum length of which would depend upon the relative sizes and growth rates of the merging firms.