Unobservable parameters and conditional estimates of internal rate of return

INTRODUCTION Even though evaluating the past investment decisions of commercial entities is critical to the success of investors, creditors, government agencies, and managers, identifying an appropriate measure upon which to base the evaluation remains difficult in several important contexts. The internal rate of return (IRR) generated by the firm's portfolio of investments represents the theoretical ideal for some ex post performance evaluations, but this measure is unobservable in most cases. The firm's stock return has limited usefulness as a substitute for IRR because it is not well suited to evaluating long-term profitability and asset returns (Schwert 1981). Moreover, those interested in evaluating privately held firms and sub-units of publicly held firms will not have access to stock returns. Often the only means by which investment performance may be assessed is through the use of profitability measures based on the firm's external accounting reports. Those who use accounting-based measures of profitability face a difficult choice. The most widely discussed and best understood profitability measure, the accounting rate of return (ARR), is relatively easy to calculate, but analytical research indicates that it exhibits sensitivity to accounting valuation bases and allocation methods, inflation, cash flow patterns, real growth rates, and length of asset lives in some models. (The literature investigating the relationship between ARR and IRR includes contributions by Harcourt (1965), Solomon (1966), Livingstone and Salamon (1970), Stauffer (1971), van Breda (1981), Fisher and McGowan (1983), and others. Jensen (1986) and Luckett (1984) provide reviews of this literature.) The conditional estimate of internal rate of return (CIRR), a profitability measure developed more recently by Salamon (1982 and 1985), addresses some of the ARR's conceptual deficiencies by incorporating several of these factors. Building on the work of Ijiri (1978, 1979 and 1980), Salamon modeled the firm's IRR as a function of inflation, investment growth rate, life of the firm's composite project, the firm's cash recovery rate (CRR), and the cash flow profile of the firm's composite project. Nevertheless, researchers have expressed concern about the CIRR's reliance on assumptions of a fixed real investment growth rate (Brief, 1985; and Stark 1989), an assumed constant cash flow profile (Brief, 1985; and Griner and Stark, 1991), assumed project lives (Brief, 1985; and Hubbard and Jensen, 1991), and a definition of cash from operations based on working capital (Lee and Stark, 1987; and Griner and Stark, 1988). In short, the CIRR possesses greater construct validity than ARR as an estimate of IRR, but several practical difficulties, especially the need to assume a project life and cash flow profile, have prevented it from being adopted as an unqualified successor to the ARR. The inherent limitations of research approaches used to date have prevented researchers from being able to determine whether erroneous assumptions about project lives and cash flow profiles result in significant measurement error in the observed value of CIRR. The extant analytical research has greatly increased our understanding of the relationships between CIRR and IRR, including the manner in which systematic and random error can affect CIRR. However, analytical models do not generally include sufficient information about the magnitudes of the variables involved to support inferences about the practical or statistical significance of identified sources of error. Empirical studies have investigated the relationships suggested by analytical research, but because IRR is not observable, the findings generally are based on an indirect empirical approach. Researchers using an indirect empirical approach have tried to draw inferences about the relationship between accounting-based profitability measures and IRR, based on the relationship between accounting-based profitability measures and variables believed to be related to IRR (e. …