This research analyzes four internal rate of return (IRR) estimation methods from literature for assessing the long-term profitability of a business firm from its published financial statements. The IRR estimation methods considered are Kay's, the Ijiri-Salamon, Ruuhela's and the average ARR methods. A realistic simulation approach is developed to evaluate and compare the methods. A simulation approach with a known internal rate of return makes it possible to study the ability of the various methods to estimate the firm's true IRR. The research contributes by evaluating the performance of selected IRR estimation methods under more general conditions than the earlier literature. This is facilitated by including cyclical fluctuations, noise and the possibility of major capital investment shocks into the simulated financial data. Most importantly the research contributes in literature's long-standing dispute about the validity of accountant's rate of return ARR as a proxy for the IRR.
Five research questions are posed concerning Kay's, Ijiri-Salamon, Ruuhela's and the average ARR methods. The questions cover how the methods are affected by business cycles and irregularities in the capital investments, the methods' sensitivity to capital investments' payback patterns, their sensitivity to disparity between growth and profitability, and their sensitivity to the accounting choices made by the firms.
First, the effect of business cycles and orginary noise around the growth-trend of the firm's capital investments is of interest in evaluating the performance of the IRR estimation methods. The simulation model includes capital investment cycles in generating the simulated financial data. It is observed that three of the four methods are insensitive to cyclical fluctuations. The exception is Ruuhela's method which relies heavily on its constant-growth assumption. In the case of Kay's, Ijiri-Salamon and the average ARR method the insensitivity to business cycles is an important result because it confirms the applicability of the methods beyond the common steady-state assumptions. Furthermore, it is observed that ordinary noise in the capital investment time-series does not have a marked effect on the IRR estimates.
Second, the sensitivity of the IRR estimation methods to the capital investment's payback patterns is of interest. The true pattern of contributions from the firm's capital investments is not known for actual business firms. Therefore, alternative contribution distributions are considered. It is observed that all the methods can be sensitive to the contribution distribution. The effect of the shape of the contribution distribution on the IRR estimates is interactively dependent on the depreciation methods applied by the firm and the relationship between growth and profitability. The conclusion is that contribution distribution of the firm's capital investments can have an effect of the quality of the IRR estimates given by the analyzed IRR estimation methods. Furthermore, contrary to the other two IRR estimation methods, Ijiri-Salamon and Ruuhela's methods require an estimate of the life-span of the firm's capital investments. The reliability of the IRR estimates by Ijiri-Salamon and Ruuhela's method depends on the quality of the life-span estimate.
Third, it is to expected from theory that a disparity between the firm's growth rate and its long-term profitability affects the quality of the IRR estimates. It is observed that the reliability of the IRR estimates of all the methods is very sensitive to the relationship between the underlying true profitability and the firm's growth rate. In accordance to the simulation results the discrepancy between the true growth and profitability is the dominating source of the error in the IRR estimates in all the methods analyzed. In addition, the other sources of errors in the IRR estimates interact with the growth-profitability discrepancy. The errors can be aggravated by the discrepancy. This indicates that for better IRR estimation methods a correction for growth-profitability discrepancy should be an integral part.
Fourth, the depreciation method applied by the firm in its financial statements can affect the IRR estimation result in concert with the contribution distribution of the capital investments. Also this effect is strongly related to the growth-profitability discrepancy. For example, for Kay's and the average ARR method a worst case of the interactive effect appears under the following circumstances: The firm grows fast, it has low profitability and the firm applies an accelerated depreciation method in a situation where the contribution from the capital investments happens to follow the uniform distribution. In this respect Ruuhela's method has an advantage over the other methods since it is unaffected by the firm's depreciation choice.
Fifth, the simulations mostly indicate an unexpectedly good tolerance of the analyzed IRR estimation methods to major capital investment shocks. Ruuhela's method is the exception in this respect since its growth estimation is disrupted by such shocks. However, as discussed, in corporate practice a major capital investment shock is likely to coincide with a change in business culture. It is the literature's standard assumption of a constant IRR for the firm that comes to doubt under such circumstances.
To conclude, the simulation comparison of the selected IRR estimation methods shows that none of the analyzed sophisticated methods performs consistently better than the average ARR method. Thus, considering the various facets discussed in this paper, the accounting-practice-based average ARR method can be recommended as the best choice for the long-term profitability estimation. However, none of the methods, including the average ARR, is an unbiased estimator of the firm's IRR. For fast growing firms with low profitability and for slow-growth firms with good profitability the long-term profitability estimates should be interpreted with much caution. On the other hand, the average ARR method can be safely used when a firm has comparable growth and profitability even when there are ordinary fluctuations and noise in the capital investment intensity.