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.     

ON DERIVING THE INTERNAL RATE OF RETURN FROM THE ACCOUNTANT'S RATE OF RETURN

L.A. Gordon (J.B.F.A. Vol. 1 No, 3) claims to have derived a method for approximating the IRR using the ARR. This paper demonstrates that the key relationship in Gordon's paper is only valid if the IRR is already known and used to calculate economic depreciation. It is suggested that Gordon has merely derived a means for refining ARR, but not for deriving IRR.
Dans son article paru dam Vol. 1 No 3 de ce journal, L.A. Gordon prétend avoir introduit une méthode qui permet d'évaluer "Internal Rate of Return" au moyen de "Accountant's Rate of Return". Ce papier démontre que le rapport-clé dont Gordon nous fait part n'est vérifiable que si "Internal Rate of Return" est préablement connu et sert a calculer l'amortissement économique. On insinue ainsi que Gordon a simplement présenté un moyen de perfectionner "Accountant's Rate of Return" mais n'en a pas démontré pour autant l'évaluation de "Internal Rate of Return".
L.A. Gordon (J.B.F.A. Band 1, Nr. 3) behauptet, er habe eine Annäherungsmethode abgeleitet, womit der interne Zinsfuss von dem RO1 Kriterium berechnet werden kann. Dieser Beitrag zeright, dass das Schlüsselverhältnis in Gordons Abhandlung nur dann gültig ist wenn der interne Zinsfull schon bekannt ist und als kalkulatorischer Zinssatz für ökonomische Abschreibungsbetrage verwendet wird. Es wird behauptet, dass Gordon keine Methode für die Ableitung des internen Zinsfusses entwickelt hat, sondern nur eine für die Verbesserung des R01 Kriteriums.     

ESTIMATING THE INTERNAL RATE OF RETURN FROM PUBLISHED FINANCIAL STATEMENTS: A REPLY

In estimating the long-range profitability of a business firm two different assumptions have been made on the shape of the distrubtion of contributions from the capital investments making up the firm. Assumptions need not be proved. In a steady-state the two contribution distributions yield equal numerical results. Recent results without the need of different contribution distributions are referred to.     

ESTIMATING THE INTERNAL RATE OF RETURN FROM PUBLISHED FINANCIAL STATEMENTS: A COMMENT

In a recent issue of this journal T. Salmi attempted to estimate the internal rate of return from published financial statements. Two reasons lead to the conclu- sions that his approach is partly in error. The first is a technical one. Also it has been proved that his objective, estimating the IRR in the case that it is approximately equal to the growth rate, can be reached in a much simpler way.     

THE EX-POST INTERNAL RATE OF RETURN: WHO NEEDS IT?*

The relationship between the accounting rate of return and the internal rate of return has been the subject of quite a number of articles. In many of these, it has been assumed that the ex post internal rate of return represents a desirable measure of performance, and efforts have been made to deduce its value from accounting rates of return. The present paper draws attention to some limitations of the ex post internal rate of return and throws doubt on its usefulness as a measure of performance.