Circularity problem – Wikipedia

The Circularity problem means that when it comes to the company valuation, individual parameters such as the degree of debt depend on the evaluation result.

The circularity problem with the equity method can be formally presented as follows: ^[first]

The evaluation result (EK) must already be known to determine the level of debt on the market value basis (FK/EK), which is required to calculate the capital costs. In other words, the result of the assessment has already been determined in order to be able to determine the return of the equity provider for the indebted company R (EK) V. However, the company value cannot be determined without the return on the return of equity providers.

The circularity problem in the Weighted Average Cost of Capital (WACC) approach can be formally presented as follows: ^[first]

There are two circularities in the WACC aproach. On the one hand, the degree of debt on the market value basis (FK/EK) is necessary for determining the return request of the equity provider for the indebted company. On the other hand, the weighting factors in determining the weighed average capital cost rate (WACC) depend on the evaluation result to be searched. However, the degree of debt on market value is specified, such as: B. in the event of a breathing or company value-dependent financing policy, the WACC procedure leads to the evaluation result with progressively and circulatoryity. The circularity problem therefore only results in the WACC procedure in the event of autonomous financing policy.

The Adjusted Present-Value (APV) approach leads to the evaluation result with autonomous financing policy progressively and without circularity. On the other hand, if there is a breathing or company value-dependent financing policy, there is also a circulatory problem when using the APV procedure. In this case, the future borrowed capital for calculating the tax shields must be derived from the future market values ​​of total capital, which at the same time represent the result of the assessment.

If you choose a recursive calculation, it is possible for both autonomous and corporate value-oriented financing policy to calculate the company value with all varieties of the DCF procedures. One speaks of recursive calculation if the company value is backed up from the company value in the eternal retirement period for period to the valuation date. One also speaks of a “successive reverse bill” or a “gradual-retrograde calculation”. The recursive company value determination can be carried out using the following procedures:

• Roll-Back process: In the case of roll back processes, the company value based on the value of the eternal pension with formal transformation of the evaluation equations is determined backwards to the time of evaluation. The circularity problem is dissolved by formal equivalent formations of the evaluation equations.

• Iteration procedure: The circulatory problem resulting from the company value determination is through mathematical iteration, i.e. H. ultimately solved by a “trial process”.

• Gerwald Mandl/Klaus Rabel: Company valuation – a practice -oriented introduction . Interpreters, Graz 1997; ISBN 3-7064-0163-0.
• Alexander Enzinger/Peter Kofler: The roll back procedure for corporate evaluation-circularity-free corporate assessment for autonomous financing policy based on the equity method In: Evaluation practitioner No. 4, 2011, pp. 2-10. [first]
• Christoph Kuhner/Helmut Maltry: Corporate evaluation . Springer, Berlin Heidelberg New York 2006; ISBN 3-540-28412-5.
• Heinz Königsmaier/Klaus Rabel [ed.]: Company valuation – theoretical basics – practical application. Commemorative publication for Gerwald Mandl on his 70th birthday . Linde, Vienna 2010; ISBN 978-3-7073-1606-3.
• Volker H. Peemöller: Practice manual of the company valuation . 5th edition, NWB, Herne 2004; ISBN 978-3-482-51185-1.

1. ↑ ^{a b} See Alexander Enzinger/Peter Kofler: The roll back procedure for corporate evaluation – Circularity-free corporate assessment for autonomous financing policy using the equity method In: Evaluation practitioner No. 4, 2011, p. 3.