In comparing the different methods for estimating the internal rate of return of the firm's capital investments the following aspects are relevant: numerical performance, theoretical foundations and practical applicability. In this section we summarize the results in general terms.
First, consider numerical performance. In our simulations the relevant parameters are given such values as should put them in a realistic range with regard to actual business firms. Within the observed range none of the methods unequivocally outperforms the others in the simulation. The deviations in Kay's and the average ARR method are more regular and predictable than the deviations in Ijiri-Salamon and Ruuhela's methods. The number of potential sources of errors in Ijiri-Salamon and Ruuhela's method is greater than the other two methods. Since the errors of these methods partly compensate for each other, the resulting total error, while less predictable, is no worse for Ijiri-Salamon method than for the other methods. Ruuhela's method is the most dependent of the methods on its internal assumptions. Under its restrictive assumptions it works perfectly, but in a general situation it also produces the worst of the overestimation errors if there are strong business cycles and if the firm's profitability exceeds its growth considerably.
No common, generalizable pattern of errors emerged for the observed, different parameter combinations, with one tentative exception. Kay's method, Ruuhela's method and the average ARR method all have a tendency to overestimate rather than underestimate the true profitability when the firm's profitability exceeds its profitability considerably.
In the simulations of the present paper each of the boxes in the different tables can be considered "equally weighted". One potential direction of further research would be to adopt a numerical index to compare the numerical performance of the methods with each other. For this purpose it would be necessary to estimate from factual business observations the relative frequencies of the different combinations of the key parameters. (Some indication of the relative frequencies of the different cases are provided by the data in Figures 6 and 7.) In simulation a Monte-Carlo approach could be considered.
Second, consider the methods' theoretical robustness in the light of the simulation results. Kay's method came out as the theoretically most generic, with the average ARR method very close by. The ARR equality to IRR when the growth rate and the IRR agree, the theoretical annuity depreciation method's IRR-conformance, and the posed relationship of the annuity and straight-line depreciation methods under Anton contribution distribution all were confirmed in the simulations with Kay's method. Ruuhela's method is theoretically very sound, but its constant-growth and Anton contribution distribution assumptions make it empirically more vulnerable than Kay's and the average ARR method. Ijiri-Salamon method does not conform empirically to any of the expected theoretical propositions. This fact casts serious doubts on the theoretical validity of the method despite its relative reliability in the numerical simulation. The conclusion for the Ijiri-Salamon method is that it can be regarded as an elaborate, good rule of thumb. The other methods have deep roots within income theories of accounting and economics.
Last, consider practical applicability. In this area the average ARR method has the outstanding merit of being directly based on established accounting practice of performance measurement. It would be trivial to use computers to calculate Kay's IRR elaborate weighted-average estimates in business practice. However, the marginal improvement compared to the average ARR method does not compensate the obvious disadvantages of having to "sell" an iterative method to the users of financial information over the suggestion of using an average return on investment (ROI = ARR) for long-term profitability measurement. Ijiri-Salamon and Ruuhela's method are at a considerable disadvantage compared to the average ARR method since they require a fairly involved estimation process. In this light, for the practitioner it is our recommendation to choose for long-term profitability estimation the average ARR method over the more sophisticated IRR estimation methods. Knowing and understanding the analyzed, more sophisticated methods is not wasted, however. On the contrary, the practitioner should be aware of and familiar with the foundations of the methods s/he applies in order to make sound decisions.