Cost of equity

Generally speaking, there are several methods to calculate the cost of equity for a company such as Capital Asset Pricing Model (CAPM), Three-Factor Fama-French Model, Single-Stage Discounted Cash Flow etc.

Although CAPM method is most favoured by investment specialists, this thesis applies the modified CAPM method to determine the cost of equity for ECCO. In modified CAPM model, as investors need to be compensated for time value of money and risk, the cost of equity consists of risk-free rate, beta, market risk premium, size premium and company-specific risk factor. Firstly, the modified model is built on the results of many empirical studies that find the realised total returns on smaller companies to be substantially greater over a long period of time compared to what the pure CAPM would have predicted. (Grabowski & Pratt, 2014) Secondly, the pure CAPM assumes that the systematic risk is based on the notion that all the investors in the market hold a perfectly diversified portfolio of risky assets, whereas the modified version incorporates risk factors that have not yet been captured by the equity risk premium as modified by beta. (Grabowski & Pratt, 2014)

Equation 13 below explains the relation of these variables in which the expected return of equity equals the risk-free rate plus the equity’s beta times the market risk premium, plus risk premium for small size and company risk factor. (Grabowski & Pratt, 2014)

Equation 13 – Cost of equity by modified CAPM

𝐸(𝑅_𝑖) = 𝑟_𝑓+ 𝛽 × (𝑟𝑝_𝑚) + 𝑟𝑝_𝑠± 𝑟𝑝_𝑐

The following sub-sections discuss the determination of cost of equity variables pointed out in Equation 13. It is important to note that the company-specific premium is assumed to be zero, because its calculation is highly subjective. In summary, the cost of equity will be determined in the iteration process of determining the market equity value of ECCO, because size premium is directly associated with the market capitalisation of the company.

8.1.1 Risk-free rate

8.1.1.1 Risk-free rate applicable to ECCO

The risk-free interest rate expresses how much an investor can earn without incurring any risk. In most cases, a government bond is used as a proxy for the risk-free rate. (Petersen & Plenborg, 2012)

Source: Petersen & Plenborg (2012)

Source: Grabowski & Pratt (2014)

Ideally, each cash flow should be discounted using a government bond with the same maturity, but in reality, very few practitioners discount each cash flow using a matched maturity. For simplicity, the most common approach is applied – a single yield to maturity government bond that best matches the entire cash flow stream being valued. (Koller et al., 2010)

As there are several government bonds to choose from, the 10-year zero-coupon government bonds are preferred. This is mostly, because their maturity is better established and the reinvestment risk is avoided compared to alternative bonds. (Petersen & Plenborg, 2012) Government’s bond yield must be denominated in the same currency as the company’s underlying cash flows, because in this way, inflation will be modelled consistently between cash flow and the discount rate. (Koller et al., 2010)

As ECCO’s cash flows are denominated in Danish kroner, the Danish government’s 10-year zero-coupon bond yield will be used as the risk-free rate. As of 30.04.2014, the yield was 1,54%. (Investing, 2014)

8.1.1.2 Peer group companies

For the purpose of comparative comparison under financial and profitability analysis, it is also important determine the risk-free rates of ECCO’s peer group companies. The companies fall into two categories: US based, and Europe based.

Firstly, Crocs, Deckers and Wolverine World Wide are based in the US, and their cash flow is denominated in US dollars. Therefore, the risk-free rate applicable to these companies is the yield of a 10-year zero-coupon government bond of United States, which was 2,66% as of 30.04.2014. (Investing, 2014)

Secondly, Geox and Tod’s are located in Europe, and their cash flows are denominated in euros. Although both of the companies are headquartered in Italy, (Koller et al., 2010) argues that European companies should be valued by using the 10-year German government bond, because they have higher liquidity and lower credit risk than other European bonds. The yield of this bond was 1,47% as of 30.04.2014. (Investing, 2014)

8.1.2 Beta estimation

In accordance with CAPM theory, a stock’s expected return is driven by beta, which measures how much the stock and entire market move together. (Koller et al., 2010) This is true due to one of the fundamental principles of the theory, which assumes that investors pay only for the risk that cannot be diversified, i.e. the systematic risk.

In most cases, a company’s levered equity beta is estimated by regressing the company’s stock return against the market’s return with the following formula (Koller et al., 2010):

Equation 14 – Regression of raw beta

𝑅_𝑖 = 𝛼 + 𝛽 × 𝑅_𝑚+ 𝜀

The outcome of this regression, levered equity beta, measures the co-variation between the company-specific returns and the market portfolio’s stock returns. (Petersen & Plenborg, 2012) The implications of the beta measure are the following:

 β = 0 Risk-free investment

 β < 1 Equity investment with comparatively less systematic risk

 β > 1 Equity investment with comparatively higher systematic risk

 β = 1 Equity investment with equal systematic risk as the market

Source: Koller et al. (2010)

However in ECCO’s case, there are evident beta measurement problems since it is a private company with no price observations. Therefore, it is necessary to use alternative methods in measuring the systematic risk of the company. An appropriate method to estimate a beta for ECCO is from comparable companies in the same industry. To begin with, it is first necessary to identify comparable listed companies, and then to find their respective betas and leverage in order to determine their unlevered beta.

Based on the data from Bloomberg, Appendix 104 shows the relevant information concerning ECCO’s peer group companies. The unlevered beta for these companies is calculated by using the simplified formula in which the beta of debt is assumed zero, and the capital structure remains constant:

Equation 15 – Equity beta

𝛽_𝑒= 𝛽_𝑢× (1 +𝐷 𝐸)

As there are many standards of beta measurement practices, this thesis applies the method used by Bloomberg in which the betas are measured by using two years of weekly historical data. Furthermore, the adjusted beta is smoothed by the following formula, which relieves extreme observations toward the overall average:

Equation 16 – Adjusted beta

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑏𝑒𝑡𝑎 = 0,33 + 0,67 × 𝑅𝑎𝑤 𝑏𝑒𝑡𝑎

In order to estimate the company’s levered unleveraged equity beta, it is necessary to determine its applicable debt to equity ratio. In doing so, (Damodaran) suggests that industry’s average market debt to equity or management’s targeted debt ratio should be used. As the target debt ratio is currently not available, the average debt ratio of ECCO’s peer group companies’ will be applied. The respective values for the median unlevered beta and the average debt to equity ratio are 0,63 and 0,33, which can also be seen in Appendix 104. As a result, by substituting these values into Equation 15, the formula returns a value of 0,84, which will be applied as the leveraged beta of ECCO.

8.1.3 Market risk premium

As an important variable in cost of equity calculation in modified CAPM model, the market risk premium is the difference between the market’s expected return and the return of a risk-free investment. As (Petersen &

Plenborg, 2012) explains, there are two main ways to determine the market risk premium: post and ex-ante approach. In ex-post approach, the focus is on the historical differences between the returns of stock market and risk-free investments, and the mean of these variations is expected to serve as an indicator for the future. Ex-ante approach, on the other hand, attempts to estimate the future premium by relying on earnings forecasts stated by investment professionals.

This thesis applies the ex-post method, which is also the most commonly used approach in practice. More specifically, the determination of the market risk premium is based on the work of Aswath Damodaran, a respected professor and researcher in the field of corporate finance and equity valuation. He proposes a basic equation to determine the risk premium in any equity market:

Source: Koller et al. (2010)

Source: Koller et al. (2010)

Equation 17 – Equity risk premium

𝐸𝑞𝑢𝑖𝑡𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝐵𝑎𝑠𝑒 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑓𝑜𝑟 𝑚𝑎𝑡𝑢𝑟𝑒 𝑒𝑞𝑢𝑖𝑡𝑦 𝑚𝑎𝑟𝑘𝑒𝑡 + 𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑝𝑟𝑒𝑚𝑖𝑢𝑚

In his proposition, he assumes that the US equity market is a mature market, because it has sufficiently long history of returns, and large and well-diversified equity market. The country risk, however, reflects the additional risk an investor has to bear by investing in a specific market.

In determining the base premium for the US market, he examines the returns of S&P 500 index and treasury bonds. The general notion is, as (Koller et al., 2010) suggests, to use the longest time period available in order to reduce the estimation error. To be consistent with the latter argument, Damodaran has analysed the returns of two distinct time periods by using the geometric averages, and found that the average market premium for period 1926-2000 was 5,59%, and 4,20% for 1928-2012. (Damodaran, 2013) Therefore, as of 1 January 2014, he suggests using 5,00% as the forward looking base premium for mature equity market. (Damodaran) In order to find the country risk for a specific country, Damodaran uses the local currency sovereign ratings from Moody’s, and estimates the default spread over risk-free government bond rate. (Damodaran) As Denmark has the highest Moody’s sovereign rating of Aaa similar to the US, there will be no country risk premium applied.

In addition, (Fernandez, Linares, & Acin, 2014) performed a comprehensive international survey in summer 2014, where they asked professors, analysts and business managers their applied market risk premiums. The median result of the survey for Denmark indicated a 5,00% market risk premium, which is also consistent with Damodaran’s suggestions.

In conclusion, the applied market risk premium in ECCO’s cost of equity calculation is 5,00%.

8.1.4 Size premium

The size effect is based on the empirical observations that companies of smaller size are associated with greater risk and, therefore, have a greater cost of capital. (Grabowski & Pratt, 2014) The risk characteristics of smaller companies may differ from larger companies due to several reasons, for example, smaller companies may have less resources to adjust to competition or avoid distress during the crisis, and have fewer analysts following them, which restricts the information available to the public. (Grabowski & Pratt, 2014)

This thesis applies the size premium suggested by (Duff & Phelps, 2012), which is measured by market capitalisation. An important criteria for the analysis is that it uses CRSP return data and S&P Compustat database, and excludes start-up companies and companies with high financial risk. They determine the size of the premium by comparing the realised excess returns to the returns that CAPM would have estimated. In addition, (Duff & Phelps, 2012) smooth out the raw size premiums by various regression techniques due to the scattered nature of their findings.

Appendix 105 summarises their findings of smoothed size premiums for companies with different market capitalisations. As the applicable size premium for ECCO requires market equity value, it will be determined in the iteration process in valuation section.