Problems in measuring the cash recovery rate and measurement error in estimates of the firm IRR

Abstract

This paper considers the impact on estimates of the IRR derived from the cash recovery rate approach to the estimation of economic performance of an inability to observe the conceptually defined CRR from accounting data. In particular, it considers a typical proxy used in empirical applications of the CRR approach and asks the question — under what circumstances will this proxy fail to measure the true CRR? Two circumstances are identified. First, the empirical CRR will not measure the true CRR when advertising and research expenditures exist which should be treated as part of the composite investment (and, hence, as investment expenditures) but are expensed in the accounting records -referred to as the capitalize/expense case. Second, the empirical CRR will not measure the true CRR when the composite investment is made up of projects with different lives — referred to as the retirement case. For these two cases, relationships are developed between the proxy and the true CRR. From these relationships the impact of errors in measuring the CRR on estimates of the IRR are deduced. Analytically, it is demonstrated that, in the capitalize/expense case, the inability to measure the CRR produces measurement error in the IRR estimate that is monotonically and negatively related to the rate of investment growth. Further, as the proportion of expensed investment expenditures increases, measurement error increases if the investment growth rate is less than the IRR and decreases if the investment growth rate is greater than the IRR. In the retirement case, it is identified analytically that measurement error also will be monotonically and negatively related to the investment growth rate. This is the case even though the analyst is able to specify the basic relationship between investment outflows and subsequent cash inflows (the inability to spec ify this basic relationship is a problem considered in many papers on the CRR approach). Numerical examples suggest that these effects are not insignificant in size a priori.