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Salmi, Timo and Ilkka Virtanen (2001). Economic Value Added: A simulation analysis of the trendy, owner-oriented management tool. Acta Wasaensia No. 90, 33 p.
The value-based management performance measure EVA® introduced by Stern Stewart & Co. is an incarnation of the underlying residual income (RI) concept. The concept is evaluated and compared with traditional profitability measures within a controlled simulation framework. It is observed that EVA is very sensitive to its cost of equity component, but it is unexpectedly insensitive to its cost of debt component under regular conditions. EVA and its variability are observed to be strongly affected by the firm's growth policies because of leverage effects. EVA is observed to be much more unstable than the traditional return on investment and directly related to the return on equity measure. Methodologically, the paper demonstrates the advantages of using a controlled simulation approach in financial research.
Timo Salmi, Department of Accounting and Finance, and Ilkka
Virtanen, Department of Mathematics and Statistics, University of
Vaasa, P.O. Box 700, FIN 65101 Vaasa, Finland.
Key words: Simulation; Residual income; Economic Value Added; Return on investment; Return on equity
Acknowledgments: We gratefully acknowledge the financial support from Jenny and Antti Wihuri foundation for the research. Our thanks are due to professors Teemu Aho and Erkki K. Laitinen for useful insights.
The firm has a number of stakeholders with differing, sometimes conflicting goals. The stakeholders include the owners, lenders, management, personnel, customers, suppliers and creditors, government and regulatory agencies. In corporate governance agency theory the managers are regarded as agents of the owners in stockholders' wealth-maximization. Among the management tools EVA, in particular, emphasizes the interests of the owners.
The concept of the economic value added is similar to the traditional accounting concept of Residual Income (RI); see Stark and Thomas (1998:446) and their references. The concept emerges in several variations and incarnations including the trade-marked Stern Stewart & Co's EVA® with its copious accounting adjustments (Stewart 1991, Stewart 1994, Stern, Stewart & Chew 1995, and Stern Stewart & Co. 1997).
In line with the theory of finance the RI derivative EVA is commonly advocated as a management tool because the goal of the firm is to add to the value of the owners' wealth. In other words, the owners expect a maximum compensation over the cost of the capital invested in the firm. A central question concerning EVA is how sensitive this management tool is to the changes in its various components, management policies and external economic factors.
Despite the unambiguous theoretical definition, applying EVA even in its pure, theoretical format is not straight-forward. EVA is defined as the difference between the firm's profit and cost of all capital employed, i.e. the weighted average cost of debt and equity. Measuring the profit of the firm and measuring the components of the cost of capital is problematic both in theory and in practice. In particular, measuring the cost of equity is a highly involved issue. A simulation approach is used in this paper to better facilitate investigating the behavior of EVA under varying management policies and cost conditions.
In the simulation model the capital investments are generated by the following multiplicative process with an exponential trend, a sinusoidal cycle, and an irregular variation made up of a normally-distributed noise component and a potential shock component
The symbols are listed in Appendix 1. Using this capital investment generating process produces financial time series which closely resemble the time series profiles observed on actual business firms. See e.g. the sample of the time series drawn in Salmi et al. (1984:46-48).
The capital investments gt induce subsequent cash inflows which can be defined in terms of a set of contribution coefficients bi. The contribution coefficients fix a capital investment's cash flow pattern. The total contribution ft in year t cumulates from the contributions from the capital investments made in the earlier years
The run of the simulation years t = 1,...,T has been omitted for brevity since Formula (1).
Assuming constant returns of scale and constant profitability in the customary fashion, the contribution coefficients define the profitability of the firm in terms of the internal rate of return
In the numerical simulation a distribution pattern i.e. the shape of the contribution coefficients must be fixed. The negative binomial distribution corresponding to a typical product life cycle is used (see Salmi & Virtanen, 1997)
(4) bi = s(i+1) q2 (1-q)i , i = 1,...,N.
Other distribution patterns, such as a uniform pattern or a steadily declining pattern could also be adopted. Such alternatives are not, however, presented in this paper, since we observed that they do not substantially affect the nature of the numerical results.
The profit of the accounting period is defined by a simple income statement as the cash inflows less depreciation less the interest on loans
(5) pt = ft - dt - ht.
The common straight-line depreciation method is applied by the simulated firm. Hence the depreciation, assuming a life-span of N years, is defined by
The same goes for the alternative depreciation methods as goes for alternative contribution patterns. They can be omitted from the presentation, since they are not crucial from point of view of the nature of the numerical results. The interest payments in (5) are defined later by Formula (9).
The simplified balance sheet of the simulated firm is depicted by Figure 1.
Ever since Salamon (1982:294) in defining the long-run profitability of the firm it has been conventional to regard the firm as a series of repetitive capital investments with a fixed life-span and a fixed cash-flow pattern. Furthermore, it is customary to assume that the working capital of the firm has the same profitability level as the firm's capital investments. Hence, we combine the simulated firm's plant assets and its working capital under the same caption. We define
(7) Pt = Pt-1 + gt - dt.
Debt on the ending balance sheet of a year is defined by the beginning debt balance less the amortization on the old loans plus the new loans
(8) Bt = Bt-1 - at + lt.
The interest payments on a year's outstanding initial debt are calculated using the loan interest rate
(9) ht = j·Bt-1.
The amortization is made in equal installments until the loans' maturity
The capital investment schedule of the simulated firm is defined by (1). The necessary funding for the capital investments, interest payments, and amortization comes from cash inflows, and, when not sufficient, from the new loans
If the firm generates enough funds internally, no new loans are taken. Instead, the potential extra funds are paid out as dividends
The retained earnings are defined by
(13) Rt = Rt-1 + pt - ot.
The level of common stock is kept constant in the simulation, i.e. no new stock issues are included in the model
(14) St = St-1.
The book value of the firm at the end of each year is calculated from the liabilities plus the equity side of the balance sheet as
(15) Vt = Bt + St + Rt.
In general terms EVA is defined in this paper in a manner similar to the RI (residual income) as (see e.g. Biddle et al., 1997:305-306)
(16) EVA = NOPAT - WACC · Capital
where NOPAT is the net operating profit after taxes and WACC is the weighted average cost of capital. The trade-marked Stern Stewart & Co's EVAO includes accounting adjustments both in NOPAT and the capital. The adjustments are too proprietary to be carried out in this paper. Fortunately, it is not to be expected that this has a bearing on the nature of the results (see e.g. Biddle et al. 1997 and Chen & Dodd 1997). Furthermore, we do not include taxation in our model. Our NOPAT will be the accounting profit before the interest on loans. This will not affect the general pattern of the results.
In terms of our simulation model the EVA is the profit before interest payments net of a charge for the cost of all debt and equity capital employed
(17) EVAt = (pt + ht) - ct Vt-1
where the weighted average cost of capital for the year under observation is calculated from the cost j of debt and cost e of equity
(18) ct = j·Bt-1/ Vt-1 + e·(St-1 + Rt-1)/ Vt-1.
An alternative format of (18) that emphasizes the effect of leverage on the average cost of capital can be written as
(18a) ct = e - (Bt-1/ Vt-1)·(e-j).
In the above we have chosen to use the initial balances instead of e.g. annual averages of the balance sheets.
In the finance literature one of the most involved issues is the assessment of the cost of capital. In particular, assessing the cost of equity is a difficult question both in practice and theory. In our simulation two alternative ways of defining the cost of equity will be used. In the above formulas it is given as an external parameter. However, the cost of equity can also be defined as the firm's internal rate of return (see Fama and French, 1999). Here we can utilize an important advantage of our simulation approach. The IRR is accurately known in the simulation.
It is possible to define a theoretical version of the EVA using the economic profit on the assets net of a charge for the cost of all debt and equity capital employed.
where the average weighted cost of capital is defined by the rate of interest and the firm's profitability
The question naturally arises whether the practical EVA (17) vs. the theoretical EVA (19) will lead to substantially differing results.
The model calculates also traditional financial ratios for profitability. Return on (the capital) investments is defined by
(21) ROIt = (pt + ht) / Vt-1.
Return on equity is
(22) ROEt = pt / (St-1 + Rt-1).
The firm's financial standing is reflected in its leverage defined by
(23) LEVt = Bt / Vt.
EVA is a measure that is expressed in absolute, monetary terms. Nevertheless, it will be interesting to compare the behavior of a relative EVA to the firm's ROE and ROI. The latter is left for the simulation, but the former relation is easily assessed analytically. Define the relative EVA as
(24) EVARt = EVAt / (St-1 + Rt-1).
Using EVA definition (17), the definition of the weighted average cost of capital (18), and the formula for the interest payments (9), it is readily seen that the relative EVA is just the return on equity less the cost of equity
(25) EVARt = ROEt - e.
The selected combinations of the different input sets will become evident below in discussing the results for the research questions posed.
The cost of loans can be considered an external variable determined by the interest rate on the markets. In the simulation runs the loan interest rate is varied all the way up from 0% (to see one end of an extreme case) to the long-run profitability of the firm's capital investments (the internal rate of return). Interest rates beyond the IRR are not considered, because a firm would not be viable under such circumstances.
The measurement of the cost of equity is an involved issue both in practice and theory. One relevant way of looking at the concept, especially in connection with EVA, is regarding the cost of equity as the owners' required return on the capital they invest in the firm. In the simulation runs the cost of equity is varied from the extreme case of 0% up to a maximum of 12%. In particular, in line with Fama & French (1999), the case where the cost of equity is made equal to the IRR is interesting as a benchmark. The special strength of the simulation approach, as compared to empirical data from actual business observations, is that the true IRR will be available without any bias.
The first question before it is conductive to observe EVA's behavior is to see under what loan costs the firm can stay generally viable. In a rudimentary framework one can observe what happens to the firm's leverage as a function of the load interest rate and the firm's profitability. Figure 2 delineates the mean leverage for the observation period (years 22-34 in the simulation, c.f. Appendix 2). As is to be expected, if the firm's growth rate constantly exceeds its profitability, the firm's situation is not tenable in the long run. In Figure 2, when the profitability of the firm is 4% and it tries to grow at a rate of 8%, not even practically costless loans can keep the firm afloat. On the other hand, when the profitability (12%) clearly exceeds the firm's growth rate (8%), the leverage curve is very flat until a sudden, steep upwards slope at the growth level. At normal profitability figures (6%, 8%) the leverage increases smoothly along the cost of loans.
Next consider the behavior of EVA for the different levels of cost of loans under different levels of cost of equity, i.e. the shareholders' requirement of return. Figure 3 delineates the results for the case of balanced growth and profitability.
When the required rate of return, i.e. the cost of equity equals the firm's true profitability (e = r = 8% in the figure) in line with Fama and French, it is evident from all our simulation results that the cost of loans has very little effect on the EVA of a viable firm.
The theoretically correct cost of equity is not necessarily available to the stakeholders. In actual practice the cost of equity / required rate of return is determined on an ad hoc basis or estimated from market based data. This situation is exemplified in Figure 3 by the case of e = 5%. It is readily seen that on the other hand EVA stays insensitive to the cost of loans, but on the other hand the absolute level of EVA is significantly affected.
It is also evident from the figure, that if the required rate of return is set unrealistically by the shareholders (e = 12% or e = 0% in Figure 3), EVA's behavior becomes more drastic.
By definition, a comparison of the practical EVA (17) and theoretical TEVA (19) is relevant only when the required rate of return is set at the (true, but in practice unknown) profitability of the firm. Under these circumstances the EVA and TEVA figures are very close. This result is similar to the results concerning the economist's vs. accountant's valuation of the firm's profits. For a further discussion and references see e.g. Salmi & Virtanen (1997:21).
The results in this section indicate, somewhat contrary to the intuitive expectations, that (as long loans can be secured at viable rates), EVA is almost unaffected by the cost of loans. To summarize, we draw the following conclusion
Figure 4 shows that the more aggressive the growth policy the more sensitive the EVA. This goes both for the level and the variability of the annual EVA figures.
The mechanism that causes this behavior is rather obvious. At higher growth rates (with respect to the firm's profitability) more and more financial leverage is needed to keep the firm and the growth going. The increase in EVA and its variability comes through two effects. As a physical phenomenon, the growth increases the level of the earnings component as such. As a financial phenomenon, the increasing financial leverage gears upwards the returns earned on the shareholder's equity and thus adds economic value to the shareholders.
It should be noted that the results in Figure 4 are obtained in a Modigliani-Miller type of setting. In other words, the calculations are performed under unchanging risk, fixed return requirements and non-increasing loan costs for the different growth levels.
In business practice EVA is a measure that is applied in absolute, monetary terms. Nevertheless, it is interesting to compare the behavior of a relative EVA to ROE and ROI. It was already shown in (25) that there is a one-to-one correspondence between the relative EVA and the firm's ROE, which are only separated by the firm's cost of equity. This fact may be a good explanation for the empirical results such as Biddle, Bowen & Wallace (1997) and Chen & Dodd (1997) not finding evidence of an EVA supremacy over net income in explaining the firms' stock returns.
Figure 5 delineates the behavior of the relative EVA at the different growth strategies in comparison with ROI.
The behavior of the relative EVA shows both similar and different features as the absolute EVA. Again, the variability is significant. The more aggressive the growth policy the more sensitive the EVA. Despite the variability, the mean levels of the relative EVAs stay fairly constant. The mean levels are determined by the growth strategies.
ROI behaves differently. It is a very good approximation of the profitability of the firm's capital investments, i.e. the firm's IRR. There is very little fluctuation in the ROI figure. ROI is a highly robust measure. This result is in line with the results in Salmi & Virtanen (1997).
Furthermore, the results show that on an annual level the EVA figures are affected by cyclical business fluctuations (and irregular events). On the other hand, the further, unreported simulation experiments done in the project, show that average nature of the EVA results are not affected by the cycles.
Figure 3 indicates that, as is expected, if the firm is unable to earn profits in excess of the required return, EVA will go negative. However, the behavior under increasing loan interest rates is counter-intuitive. The answer would thus seem to be at most a qualified yes for EVA acting as a financial distress warning, as far as the economic value distress definition is used. The key issue is whether the owners have set a reasonable required return. If not, a perfectly sound firm will falsely appear to be in distress.
Consider legal bankruptcy in the light of Figure 4. In practice, firms that develop an extremely high leverage will in many cases either go bankrupt, or at could be taken over for a restructuring. At least if risk premiums are not included, strongly leveraged (growth) firms will have higher and higher EVAs. Hence, the absolute EVA measure could be dangerously susceptible as a distress warning device.
The central idea of EVA is subtracting the cost of capital from the firm's profits to measure, as the term indicates, the economic additional value produced by the firm to its owners over the weighted cost of the capital employed. This raised the question of the effect of the debt and equity cost components on the behavior of EVA. It was observed that under realistic (with respect to the firm's profitability) required returns (cost of equity) the loan interest rate has little effect on the EVA's behavior until the cost of loans approaches the firm's profitability. This insensitivity can be considered a somewhat unforeseen result with respect to the intuitive expectations of EVA's behavior. On the other hand, as is expected, EVA behaves in a linear fashion with respect to the cost of equity.
Business firms may and do adopt different growth strategies in relation to their profitability levels, ranging from conservative to aggressive. A interesting current example of the aggressive growth strategy choices have been the new information technology companies. It was confirmed in this paper that EVA and its variability are strongly affected by the firm's growth policy choices. This result is in line with expectations because the consequent increasing financial leverage gears up the return earned on the shareholders equity.
The results have also a bearing on the debate of the relative merits of the value-based measures against the properties of traditional accounting measures. It was observed that even under regular economic circumstances (the relative) EVA is much more unstable than the traditional return on investment (ROI) measure. Furthermore, as was shown in the mathematical derivations, there is one-to-one correspondence between (the relative) EVA and the traditional return on equity (ROE). These findings subject to doubt the potential claims on EVA's supremacy over the more traditional accounting measures.
Traditional financial ratios are commonly used also for distress prediction. It was observed that EVA does not have incremental value in the predicting.
Besides the results arrived at concerning EVA and its relation to the traditional accounting profitability measures, this paper goes to demonstrate the good applicability of the controlled simulation approach in financial research. The major advantages of the simulation approach are the ability to emulate different business situations at will and to facilitate a plausible ceteris paribus scrutiny of the relevant cases.
|EVAt||=||economic value added in year t|
|TEVAt||=||economic value added in year t based on the internal rate of return|
|EVARt||=||relative economic value added in year t|
|ROIt||=||return on investments|
|ROEt||=||return on equity|
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