Business Valuation and the Reduction of Complexity. Wolfgang Ballwieser 16 October 2014

Transcription

1 Business Valuation and the Reduction of Complexity Wolfgang Ballwieser 16 October 2014

2 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and measurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

3 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and mesurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

4 Introduction (1) Valuation is a process of mapping an object s characteristics into a real number, indicating what something is worth for an individual in a specific situation Valuation is a prerequisite for M&A decisions Valuation requires a specification of the valuation object and the valuation subject a decision field of the valuation subject market prices for comparable alternatives within that decision field a preference function of the valuation subject W. Ballwieser Reduction of complexity - 16 October

5 Introduction (2) Market valuation is a fiction, requiring a model which describes the characteristics of the fictive market and its participants Value for a corporation, value for a state or value for society are also fictions, like fair value for financial reporting Value has to be distinguished from price: price is what you pay, value is what you get In contrast to (individual) value, price can be measured in real markets, which does not imply that price measurement is an easy task W. Ballwieser Reduction of complexity - 16 October

6 Introduction (3) Good valuation requires a model which contains all material aspects and which does not lead to false decisions of the individual or a group of individuals For each kind of valuation, complexity of the real world has to be reduced The first question is, what kind of reduction is best for a valuer in a theoretical sense If an optimal reduction cannot be gained, the second question arises, how reductions which can be seen in practice have to be assessed W. Ballwieser Reduction of complexity - 16 October

7 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and measurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

8 Theoretical impossibility of an optimal reduction of complexity (1) In decision theory a decision maker is searching for the optimal decision alternative The one-period decision model usually contains a preference function and a finite set of decision alternatives, states of the world (or nature), their respective probabilities and the (financial) results which have to be expected when a specific alternative meets a specific state of the world The model can be extended to many periods and to active players W. Ballwieser Reduction of complexity - 16 October

9 Theoretical impossibility of an optimal reduction of complexity (2) An optimal reduction of the decision model would balance the marginal benefits of simplification with its marginal costs But, such a calculus runs into problems, since a reduction is unnecessary when the complex model has been solved it is not clear, how the reduction of complexity shall be realised in detail: what elements of the model at first, in what sequence, to what aggregation level, etc.? a meta-model seems to be necessary in order to decide about the usefulness of the reduction of complexity a decision about the reduction of the meta-model seems to be required W. Ballwieser Reduction of complexity - 16 October

10 Theoretical impossibility of an optimal reduction of complexity (3) The above-mentioned decision model neglects group decisions or decisions of a corporation, seen as an agent acting for individual principals It is no easy task to aggregate individual preference functions to a group preference function which guarantees desirable characteristics like completeness of ordering, monotonicity, transitivity, etc. W. Ballwieser Reduction of complexity - 16 October

11 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and measurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

12 Important examples of reduction in practice: a. Stakeholders and stakeholders interests In practice, business valuation usually focuses on (real or potential) owners of a business Owners interests are usually restricted to financial interests Preference functions for an individual owner or a group of owners are usually not explicitly shown The simplification therefore is twofold: with respect to stakeholders with respect to preference function W. Ballwieser Reduction of complexity - 16 October

13 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and measurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

14 Important examples of reduction in practice: b. Definition and measurement of value (1) A German Wirtschaftsprüfer distinguishes between the above-mentioned subjective value and so-called objectified business value The valuation standard IDW S 1, para. 12 says: In the function of a neutral valuer, a Wirtschaftsprüfer acts as an expert who, by means of comprehensible methods, determines a value of the business, independent of the individual ideals of the parties concerned the objectified business value. (Emphasis added, WB.) Consequence is a standardised value, based on certain assumptions W. Ballwieser Reduction of complexity - 16 October

15 Important examples of reduction in practice: b. Definition and measurement of value (2) Important assumptions are the following: Valuation (usually) follows the dividend discount model (DDM) or a discounted cash flow model (DCF) Available market prices are only to be used to assess the plausibility of the value For valuations required under corporate law or required as part of contractual agreements the value is determined taking the perspective of a business owner who is a natural person liable to unlimited domestic taxation Possible, but not yet sufficiently concrete, measures (e.g., investments in expansion/disinvestments) and their resulting cash flows do not count in the cash flow projection W. Ballwieser Reduction of complexity - 16 October

16 Important examples of reduction in practice: b. Definition and measurement of value (3) : Valuation mirrors only so-called pseudo synergy effects, which are characterised by the fact that they can be realised without undertaking the measures underlying the reason for the valuation The decision alternative to owning a business has to be seen in a share portfolio The risk adjusted rate of return is estimated according to the CAPM or Tax-CAPM The risk-free rate of return is determined according to the estimation of the yield curve following the Svensson method No adjustments for size or immobility No total beta W. Ballwieser Reduction of complexity - 16 October

17 Important examples of reduction in practice: b. Definition and measurement of value (4) But, German Wirtschaftsprüfer also use price estimations for establishing fairness opinions Here, so-called market based valuations, like multiples, come into the game W. Ballwieser Reduction of complexity - 16 October

18 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and measurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

19 Important examples of reduction in practice: c. Decision field For Wirtschaftsprüfer the present value approach dominates so-called market based valuations like multiples The decision field for the valuation subject is, as already mentioned, restricted to a share portfolio Motivation for this can be seen in the possibility to get market prices (for shares) from liquid markets For valuers other than Wirtschaftsprüfer market based valuations play a much greater role In that case the decision field for the valuation subject is open for other businesses W. Ballwieser Reduction of complexity - 16 October

20 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and measurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

21 Important examples of reduction in practice: d. Cash flow projection and phase method The present value approach (DDM or DCF) requires the projection of future financial benefits: dividends (flows to equity approach) or free cash flows (WACC or APV approach) Usually a two- or three-period phase method is used for the projection The last phase (representing terminal value) needs simplifying assumptions (like constant growth rates of financial benefits) W. Ballwieser Reduction of complexity - 16 October

22 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and measurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

23 Important examples of reduction in practice: e. Handling of uncertainty (1) Usually, risk is accounted for in the discount rate, not by a deduction from a preliminary present value, which neglects certain kinds of risk Risk adjustments intensively discussed concern: investment or cash flow risk, i.e. irrespective of financing capital structure risk currency risk (cf., e.g., Ruiz de Vargas at this conference) immobility risk size risk country risk non-diversification risk insolvency risk W. Ballwieser Reduction of complexity - 16 October

24 Important examples of reduction in practice: e. Handling of uncertainty (2) Scenario analysis seems to be used only in rare cases, e.g., for banks after the financial market crisis or for companies which seem to be near insolvency W. Ballwieser Reduction of complexity - 16 October

25 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and measurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

26 Important examples of reduction in practice: f. Triangulation of valuation results For acting in the function of a neutral valuer, a German Wirtschaftsprüfer has to use available market prices to assess the plausibility of the value; there is a clear dominance of valuation over pricing This dominance vanishes in fairness opinions by Wirtschaftsprüfer and others In practice of companies and investment banks multiples seem to be dominant W. Ballwieser Reduction of complexity - 16 October

27 Agenda 1. Introduction 2. Theoretical impossibility of an optimal reduction of complexity 3. Important examples of reductions in practice a. Stakeholders and stakeholders interests b. Definition and measurement of value c. Decision field d. Cash flow projection and phase method e. Handling of uncertainty f. Triangulation of valuation results 4. Theoretical pitfalls W. Ballwieser Reduction of complexity - 16 October

28 Theoretical pitfalls (1) 1. Valuation needs an explicit preference function for stakeholders; but even when focusing on owners and DCF it is only an implicit one 2. Future cash flows need to be projected as a sequence of probability functions as a result of an explicit strategy and an explicit estimation of nature s development; but usually deterministic plans of the company s management with implicit strategy and nature s development is taken as a basis for cash flow projection W. Ballwieser Reduction of complexity - 16 October

29 Theoretical pitfalls (2) 3. When using multiples, at the utmost management s deterministic plans for the very near future can be reflected 4. The aggregation of a sequence of probability functions should be done recursively following the principle of dynamic programming; but this is not the way scenario analysis works 5. When insolvency risks shall be handled it is important to project path dependent cash flows; this conflicts with almost all proposed models W. Ballwieser Reduction of complexity - 16 October

30 Theoretical pitfalls (3) 6. CAPM leaves no room for valuation, since all companies are valued by assumption; nevertheless, CAPM is usually used for estimating riskadjusted rates of return 7. DDM and DCF seem to be free from the problem of determining a peer group which is prominent in multiple approaches; but the same problem appears when companies have to be valued which are not listed or do not have liquid shares W. Ballwieser Reduction of complexity - 16 October

31 Theoretical pitfalls (4) 8. It leads to a (logical) contradiction to use CAPM equations for determining total beta which is often recommended for non-diversified investors W. Ballwieser Reduction of complexity - 16 October

32 Is there any positive remark? Let s discuss insolvency risk! Interest and redemption payments are usually assumed to be certain although future cash flows are uncertain In realistic valuation situations, however, insolvency can occur On average, the annual probability of insolvency is low. But it can be significant in individual cases In Germany, insolvency is the dominating cause for bankruptcy W. Ballwieser Reduction of complexity - 16 October

33 Risk of insolvency (1) Increasing leverage has two effects: Trade-off between higher tax shields and higher risk of insolvency (which can cause direct and indirect bankruptcy costs) Insolvency can lead to (partial) liquidation, reorganisation or mergers/acquisitions. In case of liquidation, all future cash flows are limited to zero How to find an adequate reduction of complexity if you want to account for the risk of insolvency? W. Ballwieser Reduction of complexity - 16 October

34 Risk of insolvency (2) Conventional DCF-valuations are frequently extended to positive debt betas, leading to cost of debt that exceed the riskless rate of interest Problems: How to determine the cost of debt? How to account for bankruptcy costs? How to model taxation in the case of insolvency (e.g., tax loss carry-forwards, recapitalisation gains)? Cash flows, tax shields, bankruptcy costs, and cost of capital have to be determined pathdependently W. Ballwieser Reduction of complexity - 16 October

35 Risk of insolvency (3) Ad hoc solution (e.g., Metz 2007; Gleißner 2011): Notation: FCF=free cash flow, g=growth rate, p=probability of insolvency, k=cost of capital Possible extensions (e.g., Saha/Malkiel 2012): Time-dependent probabilities of insolvency instead of constant probability of insolvency Phase model instead of perpetuity model Positive liquidation value instead of zero value Partial liquidation instead of total liquidation Polynomial model instead of binomial model W. Ballwieser Reduction of complexity - 16 October

36 Risk of insolvency (4) Problems of ad hoc solution: How can growth rate be certain when survival is uncertain? How to determine risk-equivalent cost of capital for truncated cash flow distributions (in this approach, cash flows are projected under the condition of survival)? How to determine the probability of insolvency? As the probability of insolvency is exogenous and deterministic, it can not vary over different states of nature. This is visible in polynomial models In real situations, the probabilities of insolvency are path-dependent W. Ballwieser Reduction of complexity - 16 October

37 Risk of insolvency (5) The following approach seems to be promising: Use of polynomial models Use of endogenous default triggers instead of exogenous probabilities of insolvency Implications are: The probability of insolvency varies over different states of nature Path-dependent valuation of cash flows, tax shields and bankruptcy costs is possible Cost of debt can be endogenously determined Concept of risk-neutral probabilities becomes viable W. Ballwieser Reduction of complexity - 16 October

38 Risk of insolvency (6) Kruschwitz/Lodowicks/Löffler (2005) and Kruschwitz/Löffler (2006) have developed such a model, using the following assumptions: 1. Arbitrage-free valuation 2. Recombining binomial model 3. Constant subjective probability function for nature 4. No insolvency costs 5. Simplified assumptions of taxation in case of insolvency More realistic models with respect to # 2 to 4 are in work W. Ballwieser Reduction of complexity - 16 October

39 Literature (1) Ballwieser, W. (2010), Unternehmensbewertung zwischen Individualund stilisiertem Marktkalkül, in: Königsmaier, Heinz/Rabel, Klaus (eds.): Unternehmensbewertung. Theoretische Grundlagen Praktische Anwendung. Festschrift für Gerwald Mandl, (Linde) pp Ballwieser, W. (1990), Unternehmensbewertung und Komplexitätsreduktion, 3 rd ed. (Gabler). Ballwieser, W./Hachmeister, D. (2013), Unternehmensbewertung Prozess, Methoden und Probleme, 4th ed. (Schäffer Poeschel). Friedrich, T. (2015), Unternehmensbewertung bei Insolvenzrisiko (work in progress). Gleißner, W. (2011), Der Einfluss der Insolvenzwahrscheinlichkeit (Rating) auf den Unternehmenswert und die Eigenkapitalkosten, Corporate Finance, Vol. 2, pp Institut der Wirtschaftsprüfer in Deutschland e.v. (2008), IDW Standard: Principles for the Performance of Business Valuations (IDW S 1 (Version 2008)). W. Ballwieser Reduction of complexity - 16 October

40 Literature (2) Kruschwitz, L./Lodowicks, A./Löffler, A. (2005), Zur Bewertung insolvenzbedrohter Unternehmen, Die Betriebswirtschaft, Vol. 65, pp Kruschwitz, L./Löffler, A. (2006), Discounted Cash Flow A Theory of the Valuation of Firms (Wiley). Laux, H./Schabel, M. M. (2009), Subjektive Investitionsbewertung, Marktbewertung und Risikoteilung Grenzpreise aus Sicht börsennotierter Unternehmen und individueller Investoren im Vergleich (Springer). Metz, V. (2007), Der Kapitalisierungszinssatz bei der Unternehmensbewertung: Basiszinssatz und Risikozuschlag aus betriebswirtschaftlicher Sicht und aus Sicht der Rechtsprechung (Gabler). Saha, A./Malkiel, B. G. (2012), Valuation of Cash Flows with Time- Varying Cessation Risk, Journal of Business Valuation and Economic Loss Analysis, Vol. 7 Issue 1, pp W. Ballwieser Reduction of complexity - 16 October