1. INTRODUCTION

1.1. Background

The firm's ability to find and implement successful capital investment opportunities decides its long-run profitability and financial position. There is no doubt that the questions of profitability measurement and the valuation of the firm's financial assets are the most important questions in financial accounting research. The question of a theoretically sound and pragmatic profitability measurement is of crucial importance not only to the firm but also to an economy's overall welfare. The allocation of resources in an economy is directly affected by the validity and reliability of the decision makers' measures of the firms' performance (profitability) and financial position. For example, in loan and credit decisions the creditors are not only interested in the applicant's short-term situation but in the firm's long-term ability to generate income.

The firm's profitability is crucially reflected in the financial statements of the firm. The stakeholders of the firm need the profitability information for their decision making both for the short and for the long run. In the economics literature the internal rate of return (IRR) is the widely used theoretical long-run profitability concept. A recent survey by Pike (1996) in the area capital budgeting confirms that IRR is a well-established measure also among practitioners. Furthermore, the investment theory of finance recognizes IRR as a profitability measure, albeit under restrictive assumptions.

Strictly speaking the theory of finance states that, for example, under capital rationing only the net present value method is uniquely consistent with maximizing the value of the stockholders' wealth. See any good text-book of finance such as Copeland and Weston (1979), Levy and Sarnat (1986), Brealey and Myers (1991) for a discussion. However, under ordinary practical conditions of investment opportunities in the same size categories and conventional cash-flow patterns the internal rate of return method can in most cases be expected to give conforming evaluation for the capital investment evaluation. In this paper we accept IRR as the valid long-run profitability measure for the firm. The focus of the paper is on the theoretical consistency and numerical accuracy of the methods presented in earlier literature for estimating the IRR from financial statements.

The accountant traditionally measures profitability as the ratio between the firm's annual income and the book value of its assets. This ratio is often called the accountant's rate of return (ARR) in literature. Other common terms for it are the return on the capital invested (ROI) and the book yield. This measure looks at profitability after the fact. The economist has a different definition of income. It is based on the changes in the market value of the firm defined as its discounted future cash flows. The economist's definition is based on expectations about the future. The internal rate of return (IRR) is consistent with the economist's concept of income. The internal rate of return also is prominent in the capital investment theory.

One traditional way of looking at the firm is to regard it as a series of capital investments. As discussed, the IRR of the capital investments making up the firm is the well-accepted, theoretically valid measure of the firm's profitability. The problem with this theoretical notion is, however, that the IRR of the firms is not readily measurable in actual business and financial analysis practice, while the annual values of the ARR are calculated routinely for business firms. There is a considerable body of literature that discusses the possibility of analytically deriving or empirically estimating the firm's IRR. Since the mid 1960's there is a long-standing controversy, both conceptual and technical, whether it is possible successfully to estimate the firm's IRR. The discussion is too extensive to review in the presentation at hand. For the references see the review article by Salmi and Martikainen (1994), Butler, Holland and Tippet (1994) and Stark (1994).

The approaches in literature to the IRR estimation can be classified into several, partly overlapping categories. The first approach is trying to establish a link from ARR to IRR. This approach is exemplified by Kay (1976) and later by Peasnell (1982a, 1982b). Kay's method has been evaluated for example by Whittington (1979), Salmi and Luoma (1981), Brief and Lawson (1992) and Salmi and Virtanen (1995). A second approach is to derive the IRR by utilizing an auxiliary estimate such as CRR (the cash recovery rate). This approach has been suggested by Ijiri (1979 and 1980), extended and tested by Salamon (1982) and Gordon and Hamer (1988). The Ijiri-Salamon method has been further tested by Shinnar, Dressler, Feng and Avidan (1989) and Stark, Thomas and Watson (1992). A third approach seeks to establish the IRR directly from the published financial statements. This category is represented by Ruuhela (1972) and its mathematically streamlined rederivation in Salmi (1982). The assumptions of Ruuhela's model and the consequences of relaxing them have theoretically been considered by Tamminen (1976). Another direct IRR estimation method has been presented in Finland by Laitinen (1980). Furthermore, Kay (1976: 455) presented how his IRR estimate could be improved if the ratio of the accountant's valuation of the firms assets and the economist's valuation of the firms assets were available. Steele (1986) suggested the use of market values from the stock market to represent the economist's valuation of the firm's assets needed in Kay's correction. Lawson (1980) presented an approach based on cash flows and market values. Artto (1980) advocates a cash-flow-based profitability estimation.

Which of the various methods put forward in literature should one select? For the business practitioner, as well as for an academic researcher, facing the number of the various long-run profitability estimation methods, and the theoretical controversy of their correctness, the question becomes the following. What methods are reliable and applicable for evaluating the long-run profitability of a business firm? In other words which method or methods work both in practice and in theory? In particular, might it be, after all, that the practice of calculating a straight-forward average of the annual ARRs would be at par with the more theoretical IRR estimation methods?

1.2 Overview of Research Problem and Methodology

As pointed out, the outcome of the discussion in literature on the possibility of estimating the firm's IRR has been inconclusive. There is no unique consensus on the merits of the different methods presented. The controversy has concerned both the generality of the theoretical derivations and the empirical applicability.

Under the circumstances, it is our view that the various methods are best evaluated in their empirical context. Empirical investigation is not unproblematic, either. The following difficulty arises. The empirical estimates of the IRR given by the various methods have been compared in the earlier literature. However, the earlier, empirical approach does not resolve the absolute reliability of the methods compared. The reason is the following. The true IRRs of the firms under observation are needed as benchmarks for the reliability evaluation. But the true IRRs are not available when actual financial statement data are used. This dilemma can be solved by using a simulation approach. A simulation approach with a known IRR facilitates evaluating the ability of the various methods to estimate the firm's true IRR.

Our paper evaluates the three financial-statement-based methods by Kay, Ijiri-Salamon and Ruuhela. In addition, we compare these IRR estimation methods to the simple practice of using the average of the annual accountant's rate of returns as the estimate of the firm's IRR. The market-value-based methods of Lawson and Steele are excluded in the present paper, since their evaluation is not readily amenable to our simulation approach. An attempt at a consistent simulation of the stock market values of the firms is beyond the present scope.

The IRR estimation methods of Kay, Ijiri-Salamon and Ruuhela all are mathematically non-trivial. They are not straight-forward to apply in practice on actual financial data. The practitioner's obvious alternative would be to use the averaged accountant's rate of return as a surrogate of the IRR estimate. However, in earlier literature there are reservations on using the average ARR as the estimate. The reservations can be traced as far back as to Vatter (1966). Later e.g. Fisher and McGovan (1983: 82) stated that "accounting rates of return provide almost no information about economic rates of return". On the other hand, as pointed out by Pike (1996: 83-84) in connection with capital budgeting, the technically simple methods such as the payback period and the average ARR has been condoned by several authors starting from Weingartner (1969).

We intend to revisit the question of the usefulness of the average ARR as an ex-post long-term profitability measure, since it has not been unequivocally demonstrated that the average ARR method would necessarily be markedly inferior to the more complicated IRR estimation methods presented in literature. Given the obvious fact that the business firms continuously use accounting measurement we would find it rather surprising if ARR would not be a useful concept also for the firm's long-run profitability (IRR) measurement. Hence we will consider the average ARR method together with the more complicated methods in this paper.

In the literature on IRR estimation some general assumptions have become conventions. We use these same conventions. An important, established convention in the long-run profitability research is to consider the firm as a series of repetitive capital investments. Stating this research convention in Salamon's (1982: 294) words "... the firm is a collection of projects that have the same useful life, same cash-flow pattern, and same IRR". See, however, the critique of this standard assumption by Kelly and Tippet (1991). The assumption of the constant cash-flow pattern has usually been presented as a necessary, technical simplification of the business reality. However, this restriction is not an unrealistic, technical assumption. It can be posed that the assumption is in line with observing often long periods of stable business culture in individual firms. The business culture of the firm is above all created by its CEO-level management and their ability to generate and utilize capital investment opportunities.

Another strong convention is the firm's access to the financial markets freely to obtain the funding for the capital investments. In other words the implied capital markets in this area of research conventionally are perfect and complete. There is no capital rationing. Therefore, the question of financing of the simulated capital investments need not be considered in this paper.

1.3 Problem Statement

In the current paper we are interested, in general terms, in evaluating the accuracy of the selected long-term profitability estimation methods under different economic circumstances, under different capital investment payback profiles and under different accounting decisions on depreciation. More specifically, the following research questions will be considered.

In the earlier research a constant growth approach to the capital investments has been fairly common. This restriction has meant the absence of business cycles and noise. A priori one would expect that the cycles can have a drastic effect on the ability of the methods to estimate the correct IRR. We relax the steady-state restriction. Therefore, our first research question is

1) Are the methods sensitive to business cycles in the capital investment activities? Are the methods sensitive to ordinary irregularities in the capital investments?
Second, an outside stakeholder has to base the profitability estimates on the financial data provided by the firm. In the financial statement data the capital investments and their cash flows are totally mixed. It is not possible to know the contribution pattern of the capital investments based on the external data. The question of the effect of the different contribution patterns arises as in Salamon (1982) and Gordon and Hamer (1988). Hence, our second research question is
2) Are the methods sensitive to the underlying, alternative cash contribution patterns and life-span of the firm's capital investments?
Third, it has been put forward in the earlier literature that there are some particular instances where the profitability estimates given by the accountant's rate of return theoretically become close or equivalent to the underlying, true profitability of the capital investments making up the firm. These include the case where growth equals profitability as presented by Solomon (1966: 115) and the case where the theoretical annuity method of depreciation is postulated as presented in e.g. Salmi and Luoma (1981: 28) and Peasnell (1982a: 364). The annuity depreciation is the economist's depreciation in defining the concept of economic income discussed e.g. in Bromwich (1992: 31-51). Hence, our third research question is
3) Are the methods sensitive to disparities between the firms growth and profitability?
Fourth, in accounting practice the choice between the depreciation methods such as the prevalent straight-line and the declining- balance methods affects the reported annual income figure. Our fourth question is
4) Are the methods sensitive to the depreciation choice that the firm has used in producing its financial statements?
Fifth, the IRR estimation methods are largely based on the idea of regular development uninterrupted by structural changes or other major one-time events causing exceptional capital investment peaks. Our fifth question relates to this aspect:
5) Are the methods sensitive to major capital investment shocks?
An economic time series is made up by several constituents. These are the growth trend, the business cycle, the seasonal variation and the noise. Furthermore, there can be regular or irregular shocks. The growth trend and the business cycle are relevant in this paper. Seasonal variations are intra-year. Thus they do not arise in our research questions. It is true that the economic activities of the firm are continuous in nature. However, the financial data used for the profitability estimation in the methods under observation use discontinuous observations from the annual statements.


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