A Simplification and an Extension of the Bernhard-deFARO Sufficient Condition for a Unique Non-Negative Internal Rate of Return

Bernhard, Richard H.

doi:10.2307/2979027

Cited by 21 publications

(12 citation statements)

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“…For the proof of the Cases (a), (b) and (c), see [6]. In this case r=O is unique in the interval [0,+00) and moreover, from (58) it follows that the last nonzero term of the sequence (35) will be negative.…”

Section: A Unified Presentation Of Extended Uni~ueness Criteria Of Thmentioning

confidence: 95%

“…Also, g(x) > 0 for x € (0,1) and g(x) < 0 k=O for x > 1. Hence, due to (6) in [16], f(x) < 0 for nonnegative x~l and consequently reO is unique and multiple in the interval (-1,+00). If g(l) < 0, then also g(x) < 0 for x > 1 and f(x) does not have a root in the interval (+1,+00).…”

Section: Z=o 'mentioning

confidence: 95%

“…This is therefore significant, because it allows us, for an arbitrary finite CFP, to create uniqueness conditions for the IRR in the interval (-1,+00), knowing uniqueness conditions for the IRR for this CPr in one of the subintervals (0,+00), or (-1,0]. We will use this to determine uniqueness conditions for the nonnegative IRR in the interval (_1,+00) for the three following criteria: the Norstrom Condition (16], the de Faro s-Test [10] and the Bernhard Proposition II (6]. De Faro (10] has done it already, for the positive IRR only, in the case of the fourth criterion under consideration, while defining his version of the Bernhard-de Faro Condition on the basis of the VT (22].…”

mentioning

confidence: 97%

See 2 more Smart Citations

Complete Method for Separation of Internal Rates of Return

Hajdasiński

1983

The Engineering Economist

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Section: A Unified Presentation Of Extended Uni~ueness Criteria Of Thmentioning

confidence: 95%

Section: Z=o 'mentioning

confidence: 95%

mentioning

confidence: 97%

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Complete Method for Separation of Internal Rates of Return

Hajdasiński

1983

The Engineering Economist

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“…Proposition 4 (Norstrøm 1972 The class of projects described by Norstrøm was in turn extended in the following years by several scholars, including the following result provided by Bernhard (1979Bernhard ( , 1980. Proposition 5 (Bernhard 1979, 1980, Gronchi 1987 (See also Aucamp and Eckardt 1976, De Faro 1978, Pratt and Hammond 1977, 1979.…”

Section: Irr Acceptability Criterion Rule (I) An Investment Is Accementioning

confidence: 99%

“…Proposition 5 (Bernhard 1979, 1980, Gronchi 1987 (See also Aucamp and Eckardt 1976, De Faro 1978, Pratt and Hammond 1977, 1979.…”

Section: Irr Acceptability Criterion Rule (I) An Investment Is Accementioning

confidence: 99%

Capital depreciation and the underdetermination of rate of return: A unifying perspective

Magni

2016

Journal of Mathematical Economics

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Abstract. This paper shows that the notion of rate of return is best understood through the lens of the average-internal-rate-of-return (AIRR) model, first introduced in Magni (2010a). It is an NPVconsistent approach based on a coherent definition of rate of return and on the notion of Chisini mean, it is capable of solving the conundrums originated by the rate-of-return notion and represents a unifying theoretical paradigm under which every existing measure of wealth creation can be subsumed. We show that a rate of return is underdetermined by the project's cash-flow stream; in particular, a unique return function (not a unique rate of return) exists for every project which maps depreciation classes into rates of return. The various shapes a rate of return can take on (internal rate of return, average accounting rate of return, modified internal rate of return etc.) derive from the (implicit or explicit) selection of different depreciation patterns. To single out the appropriate rate of return for a project, auxiliary assumptions are needed regarding the project's capital depreciation. This involves value judgment. On one side, this finding opens terrain for a capital valuation theory yet to be developed; on the other side, it triggers the creation of a toolkit of domainspecific and purpose-specific metrics that can be used, jointly or in isolation, for analyzing the economic profitability of a given project. We also show that the AIRR perspective has a high explanatory power that enables connecting seemingly unrelated notions and linking various disciplines such as economics, finance, and accounting. Some guidelines for practitioners are also provided.

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Aspetti matematici nella ricerca di condizioni di unicita' per il tasso interno di rendimento

Lonzi

1986

Rivista di Matematica per le Scienze Economiche e Sociali

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A Simplification and an Extension of the Bernhard-deFARO Sufficient Condition for a Unique Non-Negative Internal Rate of Return

Cited by 21 publications

References 8 publications

Complete Method for Separation of Internal Rates of Return

Complete Method for Separation of Internal Rates of Return

Capital depreciation and the underdetermination of rate of return: A unifying perspective

Aspetti matematici nella ricerca di condizioni di unicita' per il tasso interno di rendimento

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