4.4 Evaluation of Ruuhela's Method

Also Ruuhela's IRR estimation method differs from Kay's in the financial statement data that it uses. Like Ijiri-Salamon method an estimate of the life-span of the capital investments is needed. Furthermore, Ruuhela's method needs the estimate of the growth rate of the firm. On the other hand, and very importantly, Ruuhela's method does not need the time series of depreciation. Ruuhela's IRR estimation method is independent of the depreciation method that the firm chooses.

4.4.1 Effect of Regular Business Cycles

We begin the simulation evaluation of Ruuhela's IRR estimation method by considering our first research question which concerns the effect of business cycles. Tables 15 and 16 present the IRR estimates for the Anton contribution distribution. The derivation of Ruuhela's method assumes the Anton contribution distribution. The noise component is omitted in this section. We make these two choices in order to minimize the number of concurrent issues that need to be taken into account at this stage. The estimates in the tables are displayed for the different growth vs. profitability combinations, the alternative cycle amplitudes and the alternative estimates of the life-span of the investments.

Ruuhela's method needs an estimate of the firm's growth rate. This growth rate is estimated in Ruuhela's method by OLS regression from the time series of the funds from operations corresponding to f t, i.e. the simulated cash inflows. The OLS-estimated growth rates are given within the parentheses in Table 15. For comparison, Table 16 presents Ruuhela's IRR estimates with exactly the correct growth (k = 8%).

Image: Table
15. Estimation of IRR (and growth) with Ruuhela's method, Anton
contribution distribution, true growth rate k = 8%, true life-span N
= 20, no noise, no shock.

Image: Table
16. Comparison estimation of IRR with Ruuhela's method knowing the
true growth k = 8%, Anton contribution distribution, true life-span
N = 20, no noise, no shock.

It is readily seen that unlike in Kay's and Ijiri-Salamon methods Ruuhela's method is sensitive to the business cycles. It is also seen in Table 15 that when there are no cycles (A = 0.00), when the life-span estimate is equal to the true life-span (20 years) of the capital investments and when the capital investments contribute according to the Anton distribution that Ruuhela's method produces exactly the correct IRR estimates. Like Kay's method Ruuhela's method has under its own assumptions a direct linkage to the income (and depreciation) theory. Furthermore, it is obvious both from the formulas of Ruuhela's method (especially Formula (30)) and the empirical results presented (see Table 16, columns with cycles for the 20-year life-span estimate) that Ruuhela's constant-growth assumption is crucial for his method. The business cycles causes a deviation under even perfect growth estimates and correctly estimated life-spans of the capital investments. Given the methods assumptions of constant-growth and its observed sensitivity to business cycles it is not surprising that the worst cases in the tables appear with strong business cycles (A = 1.00) and with misestimated life-spans.

4.4.2 Effect of Noise

To observe the effect of noise on Ruuhela's method we present the IRR estimates of Table 15 anew in Table 17 this time with the noise component included.

Image: Table
17. Estimation of IRR (and growth) with Ruuhela's method, Anton
contribution distribution, true growth rate k = 8%, true life-span N
= 20, noise = 20%, no shock.

Two observations can be made by comparing Tables 15 and 17. First the noise obviously affects the growth OLS estimates. On the other hand the profitability estimates do not change much. Hence the sensitivity of Ruuhela's method to noise is mild. This corroborates the importance of the effect of the cyclical component on Ruuhela's IRR estimation results.

4.4.3 Effect of Contribution Patterns and Growth-Profitability Relationship and Other Factors

Our second research question concerns the effect of the cash contribution patterns of the capital investments available to the firm. Our third question concerns the effect of disparities between the firms growth rate and profitability. Tables 18 and 19 respectively give the IRR estimates for the different growth-profitability combinations under the uniform contribution distribution and the negative binomial distribution. Table 17 in the previous section contains the IRR estimates under the Anton contribution distribution for the firm's capital investments.

Image: Table
18. Estimation of IRR (and growth) with Ruuhela's method, Uniform
contribution distribution, true growth rate k = 8%, true life-span N
= 20, noise = 20%, no shock.

Image: Table
19. Estimation of IRR (and growth) with Ruuhela's method, Negative
binomial contribution distribution, true growth rate k = 8%, true
life-span N = 20, noise = 20%, no shock.

The contribution pattern of the capital investments has an effect, but the effect is a joint effect with the other parameters of the IRR estimation situation. As discussed, in the case of Ruuhela's method the Anton distribution has a special role since it is used as an assumption in the derivation of the method. This is also seen in the tables. The best IRR estimates are gained under the Anton contribution distribution.

The comparison of the tables for the case when growth equals profitability produces near-correct but not perfect estimates under no business cycles. A discrepancy between growth and profitability has a considerable effect on the quality of Ruuhela's IRR estimates. The effect of the fluctuations in the capital investments caused by business cycles is overriding in Ruuhela's method. With the increase of the cyclical fluctuations the growth vs. profitability equality loses its effect in Ruuhela's method.

Our fourth question concerns the effect of the firm's choice of the depreciation method on the quality of the IRR estimates. In Ruuhela's method this question does not rise since the method is independent of the firm's depreciation choices.

4.4.4 Effect of Major Capital Investment Shocks

Our last research question concerns the effect of major capital investment shocks on the reliability of the IRR estimation methods. Table 20 gives the OLS growth estimates k^, Ruuhela's IRR estimates with the estimated growth and the IRR estimates with the true growth (k = 8%).

Image: Table
20. Estimation of IRR (and growth) with Ruuhela's method, Negative
binomial contribution distribution, true growth rate k = 8%, true
life-span N = 20, realistic shock S = 5.309.

It is readily seen from the table that with the introduction of major capital investment shocks the OLS growth estimation procedure is derailed. In conclusion, if there are major capital investment shocks, Ruuhela's method should not be applied on a the time period including such a structure-changing shock. (At the very least another method of growth estimation, like LAD estimation should be considers.) This observation is in line with Ruuhela's own observations about IRR estimation being valid only for periods of stable business culture.

4.4.5 Analysis of the Estimation Error in Ruuhela's Method

Tables 21 and 22 decompose the IRR estimation error in Tables 19 and 17, respectively, into its components for Ruuhela's method. The results are presented for our benchmark contribution distributions, the negative binomial distribution, and for Anton distribution which features in the derivation of Ruuhela's method. The components of the total error are attributable to deviation in the OLS growth estimate ("Grwt esti") and the error in the capital investments' life-span estimate ("Life span esti"). The third component is the remainder of the total error. The remainder is attributed to the IRR estimation formula ("Formula"). The errors can either strengthen or dampen each other.

Image: Table
21. Decomposition of the estimation error in Ruuhela's method. An
example with negative binomial contribution distribution, growth

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4.4.6 Conclusions about Ruuhela's Method

The main findings about Ruuhela's IRR estimation method are the following. Like Kay's method Ruuhela's method has a strong theoretical background in the linkage to the income determination theories of accounting and economics. The formal requirements of Ruuhela's method are more restrictive than Kay's. The constant-growth assumption is essential in Ruuhela's method. It explains the method's considerable sensitivity to business cycles and noise. Shocks should be excluded. They usually are involved with a change of business culture. An assumption of a unique IRR would be contested in applying Ruuhela's approach under the circumstances.

A disparity between the firm's growth and profitability generally increased the deviation of Ruuhela's IRR estimate from the true IRR. This feature is common with Kay's method.

The quality of the growth estimate affects Ruuhela's IRR estimate. The effect, however, is a joint effect with the other potential sources of error.

Ruuhela's method is independent of the depreciation method that the firm uses. Thus the accounting choices of the firm with regard to depreciation policies do not affect Ruuhela's IRR estimation method unlike the other methods.


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Departments of Accounting and Mathematics, University of Vaasa,
Finland

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