Essay 4: On the General Equivalence of Company Valuation Models



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Essay 4:
On the General Equivalence

of Company Valuation Models

- Free Cash Flow, Economic Value Added, Abnormal Earnings,

Dividends, and the Adjusted Present Value Model

in Equity Valuation



March, 1998

Joakim Levin


Stockholm School of Economics

The Managerial Economics Section

Box 6501, S-113 83 Stockholm, Sweden

E-mail: CJL@HHS.SE

Telefax: - 46 - 8 34 81 61


Abstract. This essay analyses the relations between prominent valuation concepts and models for company valuation in the traditional constant discount rate setting as well as in settings where the cost of capital is adjusted according to anticipated changes in the capital structure. The essay provides a company valuation framework with corporate taxes where the valuation result is independent of the choice of valuation model, and discusses the usefulness of the different concepts and models. The implementation of the valuation framework is described in the Eldon AB case study.

______________________________

The author wishes to thank Peter Jennergren, Kenth Skogsvik, and Niklas Ekvall for clarifying comments and inspiring suggestions, Per Olsson for many fruitful discussions regarding the issues covered in this essay, and participants at the 21st meeting of the Euro Working Group on Financial Modelling (Venice, Italy, 1997) for valuable comments. Financial support from the Bank Research Institute, Sweden (Bankforskningsinstitutet) is gratefully acknowledged.

1. Introduction

Several different discounting based models have been suggested as the way to proceed when performing a company valuation. The most prominent examples are perhaps







  • the free cash flow (FCF) model, where total company value (i.e., debt plus equity) is calculated as the present value of all future free cash flows,




  • the economic value added (EVA) model2, where total company value is calculated as the present value of all future economic value added plus the existing capital,




  • the abnormal earnings (AE) model3, where equity value is calculated as the present value of all future abnormal earnings plus the book value of equity, and




  • the adjusted present value (APV) model,4 where total company value is calculated as the (unlevered) value of the company’s operations plus the value of financing (interest tax shields in particular).

One problem is that when these models are implemented for company valuation under guidance of textbooks in the area (e.g., Copeland, Koller & Murrin (1994), Stewart (1991), and Copeland & Weston (1988)), the different models may give different results, even though they are theoretically equivalent. An implication of the findings in Essay 2 is that a valuation using the Copeland, Koller & Murrin (1994) (CKM)5 version of the FCF model will not generally be equal to a valuation using the DIV model (in a world with corporate taxes). But Essay 2 shows that the equivalence can be achieved if the changing capital structure in market terms is taken into consideration by the discounting procedure. This result is further elaborated upon in Essay 3 where it is shown how the discounting procedure can also handle a non-constant cost of equity capital with respect to varying leverage over time in accordance with several different cost of capital models, e.g., the Miles & Ezzell (1980) model.


The main purpose of this essay is to analyse the factual relations between the different valuation concepts and models, and to provide an implementable company valuation framework (with corporate taxes) where the valuation result is independent of the choice of valuation model. Further, the essay will discuss the link between the expected future characteristics of the company and different cost of capital concepts, and show how this link can be incorporated in the valuation models through the discounting procedure.
This essay is developed in a discounting framework where all risk- and time-preferences are reflected in the discount rate function. This approach is supported by, e.g., CKM for FCF valuation and by Stewart (1991) for EVA valuation. Alternative approaches are capitalisation (as opposed to discounting) techniques, approaches using an assumption of risk neutrality, or approaches where risk-adjustments are carried out in the numerator (as opposed to risk-adjusted discount rates), i.e., where the expected values are risk-adjusted following Rubinstein (1976).6 The approach following Rubinstein is theoretically very interesting, since the valuation expressions are of an appealing, transparent form. However, the risk-adjustment of the valuation attribute tends to be a very complex issue in practice, involving complicated contingent probability measures,7 and this makes this approach hard to implement.
It should be recognised that equivalence results have been established by other authors, but in different settings. Feltham & Ohlson (1995) show that the DIV, FCF, EVA and AE models are equivalent in infinite valuations of going concerns. In their framework there is no taxes and investors are risk-neutral, which together means that all discounting operations are carried out at the risk-free rate. Their model can be extended to the (more general) approach with risk-adjusted expectations following Rubinstein (1976), but as mentioned above this approach may be complicated to implement. Penman (1997) shows that the AE, FCF and EVA models (in a finite valuation context)8 can be “recast” as the DIV model, given appropriate terminal value calculations. But the Penman (1997) analysis is explicitly demarcated from the specifications of costs of capital: The cost of equity is assumed to be non-stochastic and flat.9 The free cash flows are discounted at the weighted average cost of capital such that the value for operations “consistent with [Modigliani & Miller] (1958) is independent of the level of financial assets (or debt)”(p. 10).10 But this implies that the cost of equity is a function of leverage, and for the cost of equity to be flat the leverage ratio must be (expected to be) constant over time.
An important contribution of this essay is to translate the equivalence results of Feltham & Ohlson (1995) and Penman (1997) into an implementable context 1) where all risk-adjustments are done through the discount rates (i.e., the appropriate costs of capital), 2) where corporate taxation (including tax deferrals) can be handled, 3) where the specifications of the costs of capital are explicitly considered and linked to the anticipated future development of the company (i.e., cost of equity, cost of debt, and weighted average cost of capital allowed to be non-flat), and 4) where the valuation concepts are defined in terms of explicitly forecasted financial statements of the same type as in annual reports. The equivalence is also extended to the APV model. Moreover, the equivalence is shown to hold on a year-to-year basis (and not only when considering infinite valuations or finite valuations over specific horizons), thus revealing that the models can be combined in any way. Further, advantages and disadvantages of the models as well as implementation related issues are discussed. The implementations of the different valuation models are visualised through valuations of the Swedish firm Eldon AB.
The basic foundation of the framework in this essay is that explicit forecasts of future financial statements are made, as proposed by CKM. The question of how these forecasts can be made is discussed in CKM and Essay 2. Here, only the structure of the forecasted financial statements and the relations between the items in these statements are modelled. The whole approach is suited for implementation in a spreadsheet model where one typically assigns a column to each year and a row for each accounting item. An implementation is exemplified by the Eldon AB case (see Appendix 4 for the forecasted financial statements). The usefulness of explicitly forecasting the future development of the company’s balance sheets and income statements is that it makes it possible to undertake explicit account analyses of many different types.11




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