Lack of robustness and systematic bias in cash recovery rate methods of deriving internal (Economic) rates of return for business firms

Advances in CRR cash recovery rate methods of deriving a conditional internal (economic) rate of return (IRR) are receiving increased attention in theory and application as “a new way of evaluating corporate profitability” (Ijiri, 1979, p. 261). Implicit in the CRR methods are assumptions that: (i) the firm can be represented as a composite asset in a steady state useful life of recurring reinvestments, and (ii) the recurring economic life of this asset can be estimated with sufficient accuracy for deriving meaningful IRRs. This paper casts doubts on the robustness of IRRs to error of estimating economic life of a firm's composite asset. In particular, it is shown that IRRs are not robust to this estimation error and are systematically biased in ways that change over both the economic life and CRR estimates. For example, the robustness is quite bad for most firms but improves for outlier firms such as IBM, having very high CRR average annual cash recovery rates. However, IBM's robustness hopes are dashed by having a very low (8.74 year) composite asset life estimate. The worst case scenario is for a firm having a very low cash recovery rate coupled with a very low composite asset life. This changes to the best case scenario, however, if the CRR and the composite asset life are both very high. If steady-state assumptions are reasonable (as posited by Professor Ijiri), then results of this paper will be useful in determining what composite asset life estimates are in the relevant range. Ijiri has advocated the preparation of financial reports based upon cash-flow data in order to make the reports more consistent with capital budgeting decision criteria and to make the content of the reports less influenced by the accounting method choices of the firm. Another important feature of the cash-flow-based financial reports is that they emphasize the calculation of the firm's cash recovery rate... The firm's cash recovery rate is important, because Ijiri has shown that under certain conditions a firm's cash recovery rate converges to a constant which is related to a firm's internal or discounted cash-flow rate of return... This means that if the specified conditions are met, then an estimate of the firm's IRR can be obtained from knowledge of its cash recovery rate (Salamon, 1982, p. 293).