Timo Salmi
Professor of Accounting and Business Finance
University of Vaasa, Finland
Email: ts@uwasa.fi  WWW: http://www.uwasa.fi/~ts/

Ilkka Virtanen
Professor of Operations Research and Management Science
University of Vaasa, Finland
Email: itv@uwasa.fi  WWW: http://www.uwasa.fi/~itv/

Proceedings of the University of Vaasa, Finland, No. 201, 1995.

Deriving the Internal Rate of Return from the Accountant's Rate of
Return: A Simulation Testbench


ABSTRACT

This paper presents a realistic simulation testbench for evaluating
the various methods for estimating the long-term profitability of
business firms in terms of the internal rate of return (IRR) of
their capital investments. The simulation model extends the earlier,
rigid approaches by incorporating business cycles and capital
investment shocks. Kay's IRR estimation method is used to
demonstrate the usage of the improved simulation approach. When the
growth rate and profitability are near each other, Kay's method
yields accurate estimates as expected by theory. The more growth and
profitability differ the less accurate will the estimates be. The
magnitude (and even the direction) of the error depends on the
depreciation method applied and the capital investments'
contribution distribution. It is also seen that Kay's method is
insensitive to full business cycles, but disrupted by excessive
capital investment shocks.

Keywords: Long-term profitability, accountant's rate of
return, internal rate of return, Kay's IRR estimation model,
simulation.


CONTENTS

Abstract

1. Introduction
   1.1 Background
   1.2 Research Problem and Methodology

2. Simulation Model
   2.1 The Firm as a Capital Investment Process
   2.2 Discussion on IRR Uniformity, and on the Role of Financing
   2.3 Profits and Valuation
   2.4 Depreciation Methods
   2.5 Further Considerations on the Simulation Model
   2.6 Kay's IRR Estimation Model

3. Simulation Design
   3.1 The Outline of Data Generation
   3.2 Contribution Distribution
   3.3 Depreciation
   3.4 Capital Investment Variation
   3.5 Capital Investment Shocks

4. Empirical Results to Evaluate Kay's IRR Estimation Model
   4.1 Research Questions for the Empirical Estimation
   4.2 Results with Regular Business Cycles and Uniform
       Contributions
   4.3 Results with Regular Business Cycles and Non-Symmetric
       Contributions
   4.4 Results with Inclusion of Shocks

5. Conclusions and Directions for Further Research

References

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This paper is the first research paper in the simulation project to
evaluate different long-term profitability estimation methods based
on IRR estimation of the firm's capital investments. At the time of
updating this file the program sources for the second paper are
available as ftp://garbo.uwasa.fi/pc/research/simarr10.zip.
