# What is market valuation

## Company valuation

### Table of Contents

- overview
- Theoretical foundations
- Assessment process in practice
- Capital market anomalies as a problem of the theoretical evaluation of finance
- Alternative evaluation methods and approaches

Procedure and process for determining the value of a company as a whole or the value of its equity (company value).

### overview

The valuation of a company as a whole must be distinguished from the valuation of company shares (e.g. shares) and the estimate of a possible purchase and sale price, since the value and the price achievable in a transaction generally differ from one another (and only under restrictive assumptions, e.g. a perfect one The capital market). So-called multiplier methods are more likely to be understood as price estimation methods because they are based on known prices from other companies (comparison method).

Company valuations are carried out, for example, for value-oriented corporate management (e.g. for strategy evaluation to prepare decisions), for external accounting in accordance with HGB and IFRS (investment book values, impairment test for goodwill) and for determining severance payments for minority shareholders (Section 305 AktG).

From the specific purpose of the company valuation, the appropriate valuation procedures and the valuation principles to be observed are to be derived (“functional valuation theory” by Münstermann, Busse from Colbe, Sieben, Matschke). The main functions of the evaluation are, for example, the decision function (decision value), the expert function (objectified value) and the argumentation function. Such a differentiated view can not be found in US valuation theory with its pronounced capital market orientation (Penman, 2016).

### Theoretical foundations

A distinction can be made between different theoretical structures for company valuation (for the principles of company valuation, see Moxter, 1983).

When determining the company value as a marginal price, one can assume the uncertain payments that the company (as valuation object) generates for its owner (as an individual valuation subject) and a utility function of the valuation subject (see Schosser / Grottke for use-based valuation as an "individual calculation") , 2013).

The investment-theoretical company valuation is also based on the individual calculation of the valuation subject, which determines the value of a company taking into account individual alternative investment options (by means of linear optimization) (Matschke / Brösel, 2013 and Hering, 2014).

The alternative is capital market-oriented valuation, especially corporate valuation based on finance theory. It is not based on the individual calculation of a valuation subject and therefore does not require any knowledge of the individually realizable alternative investment options or their utility functions. This requires specific assumptions about the capital market. Valuation procedures based on the assumption of a complete capital market assume, for example, that a perfect "replica" of a payment flow with securities traded on the market (with known prices) is possible (duplication, complete replication). Assumptions such as market completeness and completeness are, however, not fulfilled in reality because, for example, information is distributed differently among market participants, transaction costs occur and not every payment flow can be completely "replicated" by securities traded on the market.

The Capital Asset Pricing Model (CAPM) also assumes a perfect capital market. It does not require completeness, but is based on restrictive assumptions (see also 3. and 4.). Instead of using CAPM, discount rates for company valuation can also be derived using alternative models to explain the stock return, such as the three-factor model by Fama and French, 1993, or their five-factor model from 2015, which are used as variants of the arbitrage Pricing theory (APT) by Ross (1976) can be understood.

When assessing a company using the risk-value model and “incomplete replication”, restrictive assumptions with regard to the capital market are not required. basis

The valuation is the expected value of a company's cash flows and their risk content (expressed by a risk measure, such as standard deviation or value at risk).

Evaluation equations are derived under the assumption that two payments at the same point in time have the same value if and only if the expected value and the selected risk measure

are identical (Dorfleitner / Gleißner, 2018).

### Assessment process in practice

Company valuation methods that are frequently used in practice and are based on the capital value calculation are the income value method and the discounted cash flow method (DCF method); often in connection with the CAPM to derive discount interest rates (Henselmann / Barth, 2009). In valuation practice, the DCF valuation is often based on free cash flows (FCF) that are discounted (WACC method). The value of the borrowed capital must be deducted from the total value calculated in this way in order to obtain the value of the equity capital (with the liquidation value as the lower limit). With the discounted earnings method, the excess payments to which the owners are entitled (flow-to-equity) are used directly as the basis for the valuation (see Ballwieser / Hachmeister, 2016). Other variants of the DCF process can be seen in the figure "DCF variants".

In all of these methods, the expected value of a payment Z at time t (E (Z)) is discounted using a discount rate or cost of capital k that is regarded as certain (often assumed to be constant for the sake of simplicity) in order to calculate the value W:

formula 1

With this so-called risk surcharge method, the interest rate of a risk-free investment to a risk surcharge increased so that . This risk surcharge is with a

market-oriented assessment depending on the scope of risk of the series of payments and a "market price for risk" and thus on the market risk premium. The latter is a market size that depends on the

Risk aversion of market participants and thus the risk-return profile of the alternative investment options (e.g. equity portfolio) depends (opportunity costs). The value W of a company results from the capitalized earnings method as the sum of all future expected payments E (Z), discounted with the risk-adequate cost of capital rates k, that flow to the owners.

Formula 2

Numerator and denominator are to be calculated consistently, i.e. in particular either before or after taxes (corporate taxes and, if necessary, personal taxes of the owners). In the earnings value

opportunities and dangers (risks) of the company are to be recorded, i.e. a planning that is not true to expectations, which may have been created initially for the purpose of corporate management, must be

Expected values are transferred. In the assessment, it is often assumed that from a period T that is representative of the future, the company structure no longer changes and the payments Z only grow at the constant, secure rate w (continuation phase).

The most common way to determine the cost of capital, especially the cost of equity, is to use the Capital Asset Pricing Model (CAPM); mostly based on stock return fluctuations rather than earnings risks (volatility of payments). However, the CAPM does not prove itself in empirical capital market research (see 4.). The risk-based requirement for the return on equity is the cost of equity, which is to be used as the discount rate for the discounted earnings method. The total cost of capital of a company in the WACC method results from the weighted equity and borrowing costs. There is, however, the “circularity problem” because the value of the equity capital required for the weighting is precisely to be determined. This problem does not arise with the Adjusted Present Value method (APV), in which the value of the non-indebted company is calculated first, to which the tax shield is added and the debt is subtracted. The suitability of the respective process depends on various assumptions, e.g. the company's financing policy.

### Capital market anomalies as a problem of the theoretical evaluation of finance

Numerous empirical studies of capital market research illustrate the low or even lack of capability of the CAPM, stock returns and various other capital market imperfections

that have raised doubts about the suitability of the model for deriving discount rates.

The study by Banz (1981) showed the “size effect” (above-average returns for small companies) and Basu (1977) found that stocks with a low valuation level

(low P / E ratio) allow us to expect above-average returns. Both cannot be explained by the CAPM. Fama and French (1993) have established a multi-factor model that can be viewed as an alternative to CAPM and that better explains empirical stock returns. It relates the book value-price ratio (valuation level) and the company size (logarithm

Market capitalization) as explanatory factors for the stock returns. The four-factor model by Carhart (1997) also takes into account momentum (relative strength of the price increase of a share), a factor for which there is no rational explanation (Jegadeesh / Titman, 1993). In the five-factor model by Fama and French (2015), profitability and investment intensity (growth) are also recorded.

### Alternative evaluation methods and approaches

When valuing a company, the risks are usually recorded in the cost of capital k (“risk premium method”). Instead, the company risk can also be taken into account by applying a risk discount to the expected value. An uncertain payment at time t is transformed to a security equivalent and this with the risk-free interest rate

discounted. In risk-value models, the risk discount depends on the scope of the payment risk, expressed by a risk measure R (Z) and a parameter (), which records the risk-return ratio of the alternatively available investments (see e.g. also the security equivalent variant of the CAPM in Robichek / Myers, 1966, with covariance as a risk measure):

Formula 3

By using a measure R (Z) for the risks of a company's payments, the results from risk analysis and risk aggregation can be used for company valuation

can be used (e.g. in a "simulation-based company valuation"). The expected value of the payment and the risk measure of the payments can be consistently derived from a "multi-valued planning"

be derived. By solving the above equation for k, risk-adjusted discount rates can also be calculated and used in the company valuation according to formula 2

become.

In the case of the investment-theoretical evaluation approaches, possible future scenarios (risks) of the company (its risks) are also considered and also taken into account

the valuation subject's alternative individual investment opportunities. The objective is to determine an optimal program of investment and financing options, what

implicitly enables the derivation of the enterprise value as a decision value (as well as the cost of capital). Restrictive assumptions about the capital market are not necessary.

There are special challenges in company valuation, e.g. when considering country risks that are not recorded as a surcharge on capital costs calculated using CAPM

allowed and at risk of bankruptcy. The latter covers the fact that the probability of insolvency (credit rating) and insolvency costs influence the expected value of cash flows and earnings as well as their development over time. Contrary to a common assumption about the continuation phase, companies do not exist forever.

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