Opportunity Costs, Linear Programming, Cost allocation

Abstract Reviews the book "Economic Analysis," by Kenneth E. Boulding.

Richard H. Bernhard, Risk-Adjusted Values, Timing of Uncertainty Resolution, and the Measurement of Project Worth, The Journal of Financial and Quantitative Analysis, Vol. 19, No. 1 (Mar., 1984), pp. 83-99

Richard H. Bernhard, A Simplification and an Extension of the Bernhard-deFARO Sufficient Condition for a Unique Non-Negative Internal Rate of Return, The Journal of Financial and Quantitative Analysis, Vol. 15, No. 1 (Mar., 1980), pp. 201-209

In a past issue of the Journal of Financial and Quantitative Analysis, Norstrπm [7] has presented a very simple sufficient condition for detecting whether a given pattern of cash flows over time has a unique nonnegative internal rate of return. Nor strum's condition is now widely cited in the literature and included in stock computer routines for analyses using the internal rate of return. See, e.g., de Faro [5] and Newnan [6].

In this issue of the Journal of Financial and Quantitative Analysis, Beranek [2] has presented a clever but cumbersome analysis showing that, for a simple multiperiod situation, computing a project's net present worth by discounting its cash flows at particular “costs of capital” and accepting the project if that net present worth is positive is completely consistent with raising the net present wealth of stockholders, initial investment from whom provides partial funding for the project.

Consider a productive investment project (or financial security), which would yield a stream of cash flows, positive and negative, over time. A major index of the acceptability of such a project is its internal rate of return, i.e., that rate of interest which discounts all the cash flows from the project to a present worth of zero. Soper [8] has developed a sufficient condition for the internal rate to be unique in the interval, (−1, ∞), along the real line. Then, if the project requires an initial outlay, if Soper's condition holds, and if the unique internal rate exceeds the market rate of interest in each period of the project's life, the project's present worth is positive, and hence, other things being equal, it is worth undertaking.

Until very recently, in most work on normative models for capital investment planning, it has been assumed that availability of capital is unconstrained; i.e., that money may be freely borrowed or lent at a single market rate of interest, and that no other constraints affect the proper choice of available productive investment projects to be undertaken. Since practical situations almost universally do involve such constraints, the traditional theories have, for the most part, been an unsatisfactory guide to achievement of optimal capital investment behavior in the real world.

Richard H. Bernhard, Carl J. Norstrom, A Further Note on Unrecovered Investment, Uniqueness of the Internal Rate, and the Question of Project Acceptability, The Journal of Financial and Quantitative Analysis, Vol. 15, No. 2 (Jun., 1980), pp. 421-423