Abstract

Accounting measures are traditionally considered not significant from an economic point of view. In particular, accounting rates of return are often regarded economically meaningless or, at very best, poor surrogates for IRR, which is held to be the economic yield. Likewise, residual income does not enjoy, in general, periodic consistency with project NPV, so residual income maximization is not equivalent to NPV maximization. This paper shows that opposition accounting/economic is artificial and, taking a capital budgeting perspective, illustrates strong (formal and conceptual) connections existing between economic measures and accounting measures. In particular, average accounting rate of return is correct economic yield of a project; traditional IRR is (whenever it exists) only a particular case of it. The average accounting rate generates a decision rule which is logically equivalent to NPV rule for both accept/reject decisions and project ranking. The paper also shows that maximization of simple arithmetic mean of residual incomes is equivalent to NPV maximization, owing to its periodic consistency in sense of Egginton (1995). Such an index may then be used for incentive compensation as well. Moreover, asset pricing may be interpreted in accounting terms as process whereby market determines income impact on assets' value. As a result, paper harmonizes notions of accounting rate of return, internal rate of return, residual income, net present value: they are just different ways of cognizing same notion. This conciliation stems in a rather natural way from three sources: (i) a fundamental accounting identity, which links income and cash flow in a comprehensive way, (ii) definition of Chisini mean, (iii) a notion of residual income which takes account of real (comprehensive) cost of capital.

Highlights

  • This paper explores the mathematical relations between accounting measures such as accounting rate of return (ARR) and residual income (RI) on one side, and economic measures such as the internal rate of return (IRR) and the net present value (NPV) on the other side

  • This paper presents a theory of capital budgeting by providing the mathematical relations that connect accounting measures and economic measures

  • The literature has so far focussed on the internal rate of return (IRR) as a privileged index informing about economic profitability, and has judged the accounting rate of return (ARR) in terms of its errors with respect to the IRR

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Summary

Introduction

This paper explores the mathematical relations between accounting measures such as accounting rate of return (ARR) and residual income (RI) on one side, and economic measures such as the internal rate of return (IRR) and the net present value (NPV) on the other side. Are (at the best) overstatements, and the poor status attributed to ARRs is due to (i) a misleading definition of economic yield, according to which it is the constant return rate that makes the discounted-cash-flow function equal to zero, and to (ii) a restrictive notion of residual income, which views the capital charge as the product of the normal rate of profit (NRP) and the capital invested in the project. This average RI, which is invariant under changes in the asset base, coincides with the constant RI associated with a well-determined book value depreciation, where the above-normal capital is constant over time.

The three links and some preliminary results
Some numerical examples
Valuation and asset pricing
Some educational implications
Findings
Concluding remarks
Full Text
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