It is an important, but at the same time a complicated task to determine the profitability of a firm. This problem can be approached by considering the firm a series of cash inflows and outflows, or, more specificially, a series of capital investment projects. The task of measuring profitability can then be defined as the problem of estimating, from published financial statements, the internal rate of return for the capital investments making up the firm. There are several papers since the mid 1960's considering the problem of deriving the internal rate of return (IRR) from the return on capital invested (ROI), alternatively called the accountant's rate of return (ARR), accountant's rate of profit (ARP), or book-yield. Such research has notably been done by Harcourt (1965), Solomon (1966), Vatter (1966) in a critique on Solomon, Sarnat and Levy (1969), Livingstone and Salamon (1970), Stauffer (1971), Gordon (1974), and Kay (1976), as well as in the consequent notes and replys by McHugh (1976), Livingstone and Breda (1976), Stephen (1976), Wright (1978), and Kay (1978). Whittington (1979) discusses the use of ARR vs. IRR in empirical research. The problem of estimating the internal rate of return simultaneously with the growth rate of the firm from published financial statements has been tackled by Ruuhela (1972) and (1975). His model includes both capital and net working asset investments. (Also Stauffer (1971) includes this feature.) An improved derivation of Ruuhela's model has recently been published by Salmi (1980a) and (1980b) in the English language.
In this paper we shall review and scrutinize some of the results by Kay (1976) and the discussion on Kay's results by Wright (1978) and Kay (1978). We shall test the model first by applying it on simulated financial statements where the true rate of return is known in advance. (A simulation approach has also been used by Livingstone and Salamon (1970), and Bhaskar (1972).) Then, we shall estimate the long-run profitability of a Finnish business firm with the model for a comparison with the estimation results in Salmi (1980).
We shall argue that the applicability of Kay's method on actual published financial statements is more limited than indicated by Kay, one reason being that the accountant's and the economist's valuation of capital stocks is compatible only if the annuity depreciation method is used by the accountant. Our simulations indicate that Kay's transformation between the two valuations would be unstable in business practice, since the direction of the error in Kay's profitability estimate is not well-behaved for the prevalent straight-line depreciation method. Furthermore, as a technical point, we shall demonstrate that initial instead of average capital stocks and discrete instead of continuous discounting should be used in Kay's profitability estimation equation.