MULTIPLE INTERNAL RATES OF RETURN: A REVISITATION

This paper investigates the utility of certain existing rules for the identification of non-imaginary internal rates of return in the capital budgeting process. More specifically, the paper demonstrates the applicability of Descartes' Rule of Signs, Budan's Theorem, and Sturm's Theorem from the theory of equations and rules developed in the business literature by Teichroew, Robichek, and Montalbano (1965a, 1965b), Mao (1969), Jean (1968, 1969), and Pratt and Hammond (1979). In so doing, the paper provides a framework that accounting, economic, and finance practitioners may use while grappling with the increasing possibility of multiple solutions in contemporary capital budgeting decisions.     

AN ANALYSIS OF REGULATED RATES OF RETURN FOR WHOLLY OWNED SUBSIDIARIES

Two methods are used by public utility regulators to set the allowed rate of return to a wholly owned subsidiary: the “independent firm” approach and the “double leverage” approach. Neither approach is consistent with any existing theory of firm valuation. The contribution of this paper is to derive from standard valuation theory a “divisional cost of capital” specification of the allowed rate of return to a wholly owned subsidiary. On the basis of this specification it is shown that the independent firm approach allows shareholders to capture the value created by the interest tax savings on parent debt. It is also reconfirmed that the double leverage approach induces cross-subsidization since it allows each subsidiary to earn the same rate of return on equity regardless of the level of risk specific to the subsidiary.     

AN ALGORITHM FOR DETERMINING UNIQUE NONNEGATIVE INTERNAL RATES OF RETURN

The problem of determining an internal rate of return of a given sequence of cash flows is equivalent to solving a polynomial equation. Although Sturm's theorem determines the exact number of roots of a polynomial in a given interval, its application can be long and tedious. For this reason it has not been particularly popular with non-mathematical practitioners. Recently, considerable effort has been devoted to finding tests or algorithms which are easier to apply. This paper introduces an old but useful theorem on the location of roots of a polynomial, elucidates recent results due to Clarke and others, and also offers some improvements.