Chisini Mean and a Unified Approach to Capital Budgeting Criteria

Capital budgeting decisions are of paramount importance in production economics and, in particular, in manufacturing: investors direct their funds towards firms that create value and withdraw funds from companies which destroy value. Unfortunately, a disparate class of metrics and criteria is available to managers and shareholders for making decisions and assess performance: Net Present Value, Internal Rate of Return, Modified Internal Rate of Return, Profitability Index, Average Accounting Rate of Return, Project Investment Rate. These metrics are originated from different perspectives and are usually conceptualized as leading to non-equivalent evaluations and decisions. Building upon Magni's (2010, 2013) AIRR approach, we show that all the above-mentioned criteria can be encompassed into a unifying framework, which stems from two intuitive concepts: the notion of Chisini mean and the notion of coherent rate of return. The former, introduced by Chisini (1929), is a general method for constructing a synthetic measure of a set of observations taking into account the rationale of the problem; the latter is the ratio of return to capital, which expresses the amount of return per unit of invested capital. By mingling the two concepts, we show that the traditional metrics provide reciprocally consistent pieces of information. We also unearth a surprising network of relations and present new metrics which correctly capture a project's economic profitability