A Comparison of Accounting and Internal Rates of Return for the Firm in A Dynamic Setting
Volkert, James Francis
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Permalink
https://hdl.handle.net/2142/68274
Description
Title
A Comparison of Accounting and Internal Rates of Return for the Firm in A Dynamic Setting
Author(s)
Volkert, James Francis
Issue Date
1981
Department of Study
Accountancy
Discipline
Accountancy
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Business Administration, Accounting
Language
eng
Abstract
This study is an exploration of the relationship between Accounting Rate of Return (ARR) and a Weighted-average Internal Rate of Return (WIRR) in a discrete flow model of the firm in some simple dynamic situations. The model parameters are the IRRs, durations, and cash flow profiles of the capital projects which constitute the firm, and the investment growth rate and accounting depreciation methods for the firm. The study is divided into two parts, each part using a different methodology and studying the firm in a different kind of dynamic situation.
The first part of the study examines the behavior of the difference between ARR and WIRR during transitions between steady states. The transitions are caused by the change in a model parameter from some initial steady-state value to a new, different final steady-state value. Mathematical expressions are derived for ARR and WIRR, in terms of the basic model parameters during the transitions. The behavior of the difference between the two measures is analyzed in terms of a comparison with the steady-state differences.
The second part of the study is a probabilistic simulation in which the project parameters are treated as random variables. The simulation was repeated for various distributions of the random variables in combination with various values for the other parameters to provide a sensitivity analysis framework. The means and standard deviations of the return measures and their difference were calculated for each simulation run.
The results of the first part of the study indicate that the behavior of the difference between ARR and WIRR during a transition between steady states is not accurately predictable from knowledge about steady-state differences. During the transition, the difference may be larger or smaller than the related steady-state differences, and may be of the opposite sign.
The results of the simulation study indicate that when one of the model parameters is a random variable, the average difference between ARR and WIRR is approximated by the difference in an appropriate steady state. The relative size of the standard deviations of the differences indicate that year-to-year fluctuations in the difference may be quite large in comparison to the steady-state differences.
The results of earlier research, done using a steady-state model, indicated that the discrepancy between ARR and WIRR varied widely under different conditions. The conclusion to be drawn from the present work is that the steady-state research probably mis-estimates the size of the discrepancy. In the dynamic case even more than in steady state, ARR is a poor estimation of the true economic rate of return on investment in the firm, as measured by WIRR.
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