Circularity problem

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The circularity problem means that individual parameters such as the level of indebtedness depend on the valuation result sought in the company valuation.

Equity method

The circularity problem with the equity method can be formally presented as follows:

RTD approach

In order to determine the level of indebtedness on the basis of market value (FC / EK), which is required to calculate the cost of capital , the valuation result (EK) must already be known. In other words, the result of the valuation sought must already be determined in order to be able to determine the return requirement of the equity providers for the indebted company r (EK) v. Without the equity provider claiming a return, however, the company value cannot be determined.

WACC approach

The circularity problem with the Weighted Average Cost of Capital ( WACC ) approach can be formally presented as follows:

WACC approach

There are two circularities in the WACC approach. On the one hand, the level of indebtedness on the basis of market value (FC / EK) is again required to determine the return requirement of the equity providers for the indebted company. On the other hand, the weighting factors when determining the weighted average cost of capital (WACC) depend on the valuation result to be sought. However, if the gearing is given on the basis of market value, such as B. With a breathing or company value-dependent financing policy, the WACC procedure leads progressively and circularity-free to the valuation result. The circularity problem therefore only arises in the WACC procedure with an autonomous financing policy.

APV approach

With an autonomous financing policy, the adjusted present value ( APV ) approach leads to the evaluation result progressively and without circularity. If, on the other hand, there is a breathing or company value-dependent financing policy, a circularity problem also arises when the APV procedure is used. In this case, the future debt capital stocks for calculating the tax shields are to be derived from the future market values ​​of the total capital, which, however, also represent the result of the valuation sought.

Solving the circularity problem

If you choose a recursive calculation, it is possible to calculate the company value using all types of the DCF method, both with autonomous and company value-oriented financing policies. One speaks of a recursive calculation when the company value is calculated backwards based on the company value in the perpetual annuity period for period up to the valuation date. One also speaks of a "successive backward calculation" or a "successive retrograde calculation". The recursive determination of company value can be carried out using the following methods:

  • Roll-back procedure : In the roll-back procedure, the company value is determined based on the value of the perpetual annuity with formal transformations of the valuation equations, periodically backwards to the valuation point. The circularity problem is solved by formal equivalence transformations of the evaluation equations.
  • Iteration method: The circularity problem resulting from the determination of the company value is solved by mathematical iteration, i. H. ultimately solved by a "trial process".

literature

  • Gerwald Mandl / Klaus Rabel: Company Valuation - A Practice-Oriented Introduction . Überreuter, Graz 1997; ISBN 3-7064-0163-0 .
  • Alexander Enzinger / Peter Kofler: The Roll Back Procedure for Company Valuation - Circularity-Free Company Valuation with Autonomous Financing Policy Using the Equity Method In: Valuation Practitioner No. 4, 2011, pp. 2-10. [1]
  • Christoph Kuhner / Helmut Maltry: Company valuation . Springer, Berlin Heidelberg New York 2006; ISBN 3-540-28412-5 .
  • Heinz Königsmaier / Klaus Rabel [Hrsg.]: Company valuation - theoretical basics - practical application. Festschrift for Gerwald Mandl on his 70th birthday . Linde, Vienna 2010; ISBN 978-3-7073-1606-3 .
  • Volker H. Peemöller: Praxishandbuch of business valuation . 5th edition, NWB, Herne 2004; ISBN 978-3-482-51185-1 .

Individual evidence

  1. ↑ a b cf. Alexander Enzinger / Peter Kofler: The Roll Back Procedure for Company Valuation - Circularity-Free Company Valuation with Autonomous Financing Policy Using the Equity Method In: Valuation Practitioner No. 4, 2011, p. 3.