Debt beta is the result of the ratio of credit spread and market risk premium. If it is taken into account, the company value usually increases.

## What is the discount rate?

In the context of a company valuation using the DCF process or the income value method, the discount interest rate is used to assign a present value to future income or cash flows. The discount rate is therefore used to calculate the present value of future payments, with future payments being discounted to the current value. Among other things, exchange rate fluctuations, the current interest rate level, the risk of payments and expectations of future inflation are taken into account. In general, the higher the discount rate, the lower the present value of future payments and vice versa. On the one hand, this article addresses the underlying theoretical concepts. In addition, the most important aspects of determining capital costs from the practice of company valuation are addressed.

### Cost of capital as an expected return

Many company valuers are familiar with the term cost of capital, so the term is only briefly outlined below and the theoretical foundations are discussed.

Equity costs include dividend payments and increases in the value of an investment, while borrowing costs include interest payments; users generally agree on this. The answer to the question of perspective is often less clear. Are capital costs the actual returns achieved in the past or is it the returns agreed between investors and companies?

Looking to the future and from the perspective of a rational investor, capital costs are neither one nor the other. Capital costs are the expected returns of an investment, taking into account the agreed conditions and weighing up the opportunities and risks of the investment.

However, it is precisely because of this interpretation that the cost of capital is well suited as an expected return as a discount interest rate in DCF valuation, as a valuation interest rate in impairment tests or as a decision criterion in economic efficiency calculations. Capital costs as an expected return are the opportunity costs of the next best investment of invested capital. (Opportunity costs are the costs of alternatives that are not taken when making an economic decision. They represent the lost benefit (or return) and support the decision-making process.)

## Method for calculating the discount rate

The calculation of capital costs as an expectation of return is methodically based on portfolio theory, a branch of capital market theory. **Modern portfolio theory** was founded on the work of Harry M. Markowitz (1952). It describes certain assumptions about the investment behavior of investors, in particular their risk aversion. For an optimal balance of return and risk, the central recommendation to investors is therefore to diversify their investments

In the following years, Markowitz's investor-oriented perspective was converted into a market equilibrium model, which **Capital asset pricing model** (1962, William F. Sharpe, John Lintner and Jan Mossin). The CAPM offered the opportunity to explain the expected return on securities.

Price and yield-relevant risks, so-called systematic risks, and price-irrelevant risks, so-called unsystematic risks, were differentiated for the first time. Arbitrage pricing theory (1962, Stephen Ross) took a less approach-intensive and at the same time intuitive approach. Instead of a central risk factor, such as a market index, arbitage pricing theory postulates several, albeit unspecified, factors to describe the return expectation on the capital market.

In valuation practice, the CAPM or the Tax CAPM has ultimately established itself as the standard model for determining capital costs. Many company valuers are familiar with the application and the required parameters can be determined with reasonable effort.

#### Requirements of the IDW/IASB standard setters

With the adoption of the Business Valuation Standard (IDW S1) for the first time in 2000, IDW replaced the previous opinion HFA 2/1993 and made the calculation of capital costs on the basis of CAPM mandatory for the auditor profession. This was achieved through the revision of **IDW S1** further specified in 2008.

Capital costs have also found their way into accounting requirements and case law, including for the valuation of companies and business combinations, through the requirements of the IASB (standard setter IFRS) and not least as a result of the decisions of the Federal Court of Justice (Federal Court of Justice).

The IDW draft to take account of the special features of company valuation to determine claims in family and inheritance law also requires the application of the tax CAPM in principle (see IDW S 13).

#### Cost of capital in company valuation

To value a company, future financial payment surpluses must be discounted to the valuation date at an appropriate interest rate. The capitalization interest rate used corresponds to the expected return on an adequate alternative use of capital compared to the valuation object. It therefore states what minimum interest rate must be achieved in order not to be worse off than when investing in the next best alternative.

An investment on the capital market is generally an alternative investment for equity and debt providers. This is available to all potential investors. The price information on the capital markets is also characterized by a high degree of transparency. They ensure that the selected alternative investment is optimally coordinated with the character of the valuation object in terms of maturity, risk and taxation.

At the same time, however, this makes it clear that cash surpluses to be assessed and the discount interest rate must methodically match. Returns to equity providers require discounting at the cost of equity. Cash surpluses, which are available to all investors, must be discounted at a total cost of capital rate.

The WACC approach, a total cost of capital approach, is referenced throughout and in accordance with valuation practice. There are other alternative capitalization concepts in valuation theory and also in the IDW guidelines (cf. Tz. 136 — 139). In the end, however, the WACC concept proved to be the most practicable method.

#### Eigenkapitalkosten im CAPM berechnen

The cost of equity, also known as return on equity, indicates what return a company must make available to its equity providers in order to adequately remunerate their invested capital.

In capital market theory, it is common to present the expected return on an equity investment as the sum of a risk-free investment and a premium for the entrepreneurial uncertainty that has been incurred. Investors can discount the assumption of this uncertainty and the associated opportunities and risks in the form of a risk premium. This asymmetrical treatment of opportunities and risks is generally accepted in theory and practice and is the result of investors' risk aversion.

The most commonly used model to explain the cost of equity and the risk premium for assuming entrepreneurial risks is the Capital Asset Pricing Model (CAPM). Even though CAPM is not without controversy among theorists and practitioners, it is considered the standard model for determining the return on equity. In IDW S1, reference is made explicitly to the CAPM to determine the cost of equity (see Tz. IDW S1 118 ff.).

This approach uses the following formula to calculate the cost of equity:

Here, the risk-free interest rate stands for the interest rate of a risk-free investment, such as government bonds. The beta measure indicates how strongly the company's share prices react to fluctuations in the entire market. A beta number of 1 means that the company's shares are just as unstable as the overall market. A number greater than 1 indicates that the company is more solid than the overall market.

The market interest rate is the expected return that investors expect from investing in the overall market. To determine the cost of equity, it is therefore essential to know the risk-free interest rate, the beta rate and the market interest rate. However, these values may be subject to fluctuations and must be updated regularly for a more precise calculation. With the **SmartZebra Valuation Pro module** company valuers determine all required parameters.

## The return on equity and its interpretation

The return on equity (also known as return on equity) determines how much profit a company generates in relation to the equity invested.

The interpretation of return on equity depends on the company's sector and the current economic climate. In general, a higher return on equity is better than a lower return on equity. Finally, it shows that the company is successful and able to generate a reasonable return for its investors.

However, there can also be positive reasons for a low return on equity if, for example, the company invests in a long-term growth strategy and accepts higher costs and lower profits in return.

## Equity risk premium

According to the standard CAPM, the return on equity corresponds to the risk-free interest rate plus the equity risk premium. The latter is the product of the beta factor and the market risk premium. The beta factor is a company-specific measure of the amount of risk, while the market risk premium corresponds to the “traded price” of risk on the capital market.

## Peer Group

Sometimes no capital market data is available for the purpose of determining a company's cost of capital. This happens regularly due to a lack of stock exchange listing. Alternatively, the weighted beta factors of a comparison group or peer group can be used here. Care must be taken to ensure that the companies included in the peer group are comparable with the company to be valued in terms of their systematic risk.

“Systematic comparability” with regard to the selection of suitable comparative companies basically means a comparison with companies in the same sector or companies with a similar product or market structure. As a rule, there will be no absolute equality of coverage between companies, but this is also not necessary from a methodological point of view. Ultimately, it is essential that the selected companies have an economic and macroeconomic cyclicality of business activity and profit and cash flow generation similar to the target company.

## Market risk premium

The market risk premium represents the difference between the expected return of an equity portfolio comparable to the overall market and a risk-free investment. There were recent studies and publications on this by the FAUB (Technical Committee for Business Valuation and Business Administration of the IDW — Institute of Auditors in Germany e.V.) in September 2012. These lead to new recommendations, also in view of the changed risk tolerance caused by the financial market crisis: Accordingly, it is recommended to use a range of 5.50% to 7.00% for the appropriate measurement of market risk premiums using the CAPM. When using the Tax CAPM, a range of 5.0% to 6.0% applies.

#### Calculate borrowing costs

In order to calculate borrowing costs, the alternative investment concept is usually also used. According to the calculation of equity costs, the expected return of borrowers is calculated additively as the sum of the risk-free interest rate and a risk premium for lenders commensurate with the company's level of indebtedness.

The risk-free interest rate is set in accordance with the derivation of the risk-free interest rate for determining the cost of equity. The credit premium is regularly derived from the credit rating and credit premium of comparable listed bonds/issuers. For this purpose, traded credit premiums, measured as the difference between current return and risk-free interest rate, are assigned to the rating classes AAA, AA, A, BBB, BB, B and C and averaged.

Corresponding data on loan premiums for normal market loan interest rates is provided by **SmartZebra Credit Spreads Pro module**: