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

*Carlo Alberto Magni*

*Journal of Mathematical Economics*, 2016, vol. 67, issue C, 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.

**Keywords:** Rate of return; Depreciation; Capital; NPV; AIRR; Mean (search for similar items in EconPapers)

**Date:** 2016

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** View citations in EconPapers (8)

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0304406816301501

Full text for ScienceDirect subscribers only

**Related works:**

Working Paper: Capital depreciation and the underdetermination of rate of return: A unifying perspective (2016)

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:67:y:2016:i:c:p:54-79

**DOI:** 10.1016/j.jmateco.2016.09.007

Access Statistics for this article

Journal of Mathematical Economics is currently edited by *Atsushi (A.) Kajii*

More articles in Journal of Mathematical Economics from Elsevier

Bibliographic data for series maintained by Catherine Liu ().