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

Magni, Carlo Alberto (2016): Capital depreciation and the underdetermination of rate of return: A unifying perspective. Published in: Journal of Mathematical Economics , Vol. 67, (December 2016): pp. 54-79.

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 NPV-consistent 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 domain-specific 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Investment decision, project appraisal, rate of return, depreciation, capital, net present value, AIRR, mean.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; G - Financial Economics > G0 - General; G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G2 - Financial Institutions and Services > G22 - Insurance ; Insurance Companies ; Actuarial Studies; G - Financial Economics > G3 - Corporate Finance and Governance; G - Financial Economics > G3 - Corporate Finance and Governance > G31 - Capital Budgeting ; Fixed Investment and Inventory Studies ; Capacity; G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill; G - Financial Economics > G3 - Corporate Finance and Governance > G35 - Payout Policy; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M2 - Business Economics; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M4 - Accounting and Auditing > M41 - Accounting; N - Economic History > N0 - General

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