SOME ANALYTICS OF WHY CONDITIONAL IRRs CAN CONTAIN GROWTH RATE RELATED MEASUREMENT ERROR

This paper investigates the consequences of incorrectly modelling the investment outflow/benefit inflow relationship on estimates of the internal rate of return (IRR) prepared by using cash recovery rates (CRRs). The main result of this paper is that CRR-based estimates of the IRR will contain such bias if and only if either the duration of the assumed shape of the investment outflow/benefit inflow relationship is less than the duration of the true investment outflow/benefit inflow relationship for all rates of interest or the duration of the assumed shape of the investment outflowlbenefit inflow relationship is greater than the duration of the true investment outflowlbenefit inflow relationship for all rates of interest. This result is then applied to the case where both the true and the assumed shape of the investment outflow/benefit inflow relationships have benefit inflows that change exponentially over time. It is shown that if the exponential rate of change is mis-specified the resulting CRR-based estimate of the IRR will contain systematic bias monotonically related to the rate of growth.