Required Rate of Return on Equity

The required rate of return on equity is the return equity holders expect to receive from investing in company shares. The most common way to calculate the cost of equity is through the Capital Asset Pricing Model (CAPM) (Koller, Goedhart and Wessels, 2010).

The basic idea of CAPM is that shareholders only pay the price for risks that cannot be diversified away (Petersen and Plenborg, 2012). These risks are the company specific systematic risks and the CAPM adjusts for these risks by including beta (Koller, Goedhart and Wessels, 2010). Alternatively, the Fama-French three factor model or the Arbitrage Pricing Theory (APT) can be applied to calculate the required rate of return on equity. However, we think that CAPM is the best model because it is based on solid theory about risk and return and not just historical, empirical data (Koller, Goedhart and Wessels, 2010). Additionally, several statistical tests have proven the strong relationship between beta and return (Kothari, Shanken and Sloan, 1995).

The CAPM defines the shareholder’s required rate of return as

>_L = >_K+ ß ∗ y.(>_z) − >_K{

41 Calculation of the capital structure in the appendix 44

Where

Rf = Risk-free rate

ß = Stock’s sensitivity to the market E(rm) = Expected return of the market E(rm)-rf = Market risk premium

In the following, we will discuss and estimate the different input factors of the CAPM.

Beta

Beta illustrates the company-specific risk adjustment. It measures the stock’s co-movement with the aggregate stock market and thereby represents the extent to which a stock may diversify the investor’s portfolio. A company with a beta of one moves exactly with the market. If products are independent of stock market’s value, the beta is low (<1). The lower the beta the more independent the stock (e.g. basic consumer foods). On the other hand, companies with a high beta (>1) are very sensitive to the market development and react even stronger than the market. Therefore, the beta drives the stock’s expected return: If the beta is low, i.e. there is a protection against economic downturn, investors are willing to pay for it and the return on equity is lower. On the other hand, stocks with high beta and consequently high company-specific risk demand for a high return on equity (Koller, Goedhart and Wessels, 2010).

The beta used in the CAPM is called systematic risk, equity beta, or more commonly known, levered beta. Other than the unlevered beta it illustrates the risk investing in equity compared to the market portfolio. The unlevered beta or asset beta on the other side illustrates the company’s operating risk (Petersen & Plenborg, 2012; Koller, Goedhart and Wessels, 2010).

The equity beta has to be estimated since it cannot be observed. To estimate a company’s beta, the raw beta can be measured through a regression analysis (Koller, Goedhart and Wessels, 2010). A regression of returns on the Carlsberg stock against the return on a wide equity market index is performed to receive an estimation of beta (Damodaran, 2018B).

As an index for market returns we use the Morgan Stanley Capital International (MSCI) ACWI Index, because it represents the performance of large- and mid-cap stocks across 47 countries and is thus well-diversified. Other than for example the MSCI World Index which is recommended by Koller, Goedhart and Wessels (2010) the MSCI ACWI includes developed as well as emerging markets and thus represent the markets Carlsberg operates in well. At the moment, the index includes over 2,400 index constituents which cover approximately 85 percent of the free float-adjusted market

capitalization in each market (MSCI, 2017). We choose not to use a local market index such as OMX Copenhagen 20 because it is weighted in only 12 industries and thus is not an appropriate index for measuring systematic risk.

We use monthly returns from the last 5 years. In sum, this gives us 57 data points which we think is a good amount to receive a statistically relevant result. We use monthly and not weekly or daily data because too frequent data points could lead to systematic biases (Koller, Goedhart and Wessels, 2010). The monthly stock prices are derived from Bloomberg’s database.

When calculating the return of Carlsberg stock and the MSCI Index we include the change in stock price as well as dividends paid by Carlsberg (Damodaran, 2018B).

Figure 20: Regression analysis to estimate beta; own creation based on data from Bloomberg (2018)

Our raw beta which is the slope of the line in figure 20 is 0,94. However, this beta is not very precise as the regression’s R-square is only 23 percent. This means that only 23 percent of Carlsberg’s stock’s variance can be explained by the variance in the market. Additionally, the standard error of the estimated beta is 0,23. Therefore, we assume that the true value of beta is between 0,48 and 1,4 and need to make some adjustments to get a more exact estimate of the value (Damodaran, 2018B).

We improve our results by deriving an unlevered industry beta and then levering it to the company’s capital structure. The use of industry rather than company-specific beta improves the precision of our estimated beta. Companies in the same industry face similar operating risk and over- or underestimates tend to level out. Damodaran (2018C) calculates an average unlevered beta in the alcoholic beverage industry of 0,64. We use this industry beta and convert it into a Carlsberg-specific

levered beta. Basis for this calculation is Modigliani and Miller’s theorem on capital structure (Koller, Goedhart and Wessels, 2010):

ß_L = ß_J+ (ß_J− ß_w) ∗GDUd

|r.

Since the debt-holders’ claim has priority, the beta of debt is usually very low. We thus assume in the following that the beta of debt is zero which leads us to the following formula (Koller, Goedhart and Wessels, 2010):

ß_L = ß_J(1 +GDUd

|r.) Our calculation results in an adjusted beta of 0,81.

However, there is a high chance that the unlevered industry beta is biased since it includes mainly but not only breweries. Companies that produce other alcoholic beverages are taken into account in Damodaran’s calculation of the unlevered beta. Additionally, indirect competitors of Carlsberg who have a very different geographic reach or size are included as well (Damodaran, 2018C).

Another approach to improve our estimate is to smoothen beta through the following formula:

1F}:2+3F 73+6 = 0,33 + 0,67 ∗ H6Ç 73+6

This formula smoothens the regression estimate towards the overall average of 1 to reduce extreme observations and adjust them towards the overall average companies are moving towards to (Koller, Goedhart and Wessels, 2010; Damodaran, 1999) Our adjusted beta is now 0,94⁴². The result of a beta very close to 1 means that Carlsberg is sensitive to the market development.

Since we based our estimation on historical data, our beta is backward looking and might be noisy (Damodaran, 2010).

Risk-free rate

The risk-free rate illustrates the return on a portfolio that has no covariance with the market. This means that economic downturns do not present a risk. The returns are guaranteed and thus the expected return is the actual return. The best estimate for the risk-free rate is a portfolio where beta is zero because then the stock is not co-moving with the market at all (Damodaran, 2010; Koller, Goedhart and Wessels, 2010).

The best way to estimate the risk-free rate would be to construct a zero-beta portfolio which is very complex and time-consuming to design (Koller, Goedhart and Wessels, 2010). Therefore, the most common way to estimate the risk-free rate is through a highly liquid, long-term government bond

42 Calculation of beta in appendix 47

assuming that governments cannot default and will always pay their obligations (Damodaran, 2010).

These bonds are not always risk-free but mostly have very low betas. The longer the time horizon of the bond, the better it matches the underlying cash flow stream. However, for example for a 30-year government bond the yield can be impacted by illiquidity issues (Petersen and Plenborg, 2012).

Since the bond has to be denominated in the same currency as its cash-flows to exclude deviations from inflation we choose a 10-year zero-coupon Danish government bond (Koller, Goedhart and Wessels, 2010).

The bond we used (GDGB10YR) yields 0,48 percent in December 2017. However, as the figure in appendix 45⁴³ illustrates the bonds’ returns are very volatile and especially at the end of 2017, the returns were at a very low level. Based on empirical evidence we assume that the return will not stay at this level but rather move back to an average. Therefore, we calculate the average monthly return of the government bond during the last 10 years. This gives us an average risk-free rate of 1,94 percent (Bloomberg, 2018)⁴⁴.

Market risk premium

The market premium is the market portfolio’s expected return less the return of risk-free bonds. It illustrates the premium investors demand for investing in risky assets instead of saver bonds, e.g.

with a risk-free rate (Damodaran, 2010; Koller, Goedhart and Wessels, 2010).

Past market risk premiums are easily calculated as actual data from the past can be used. To estimate the future market risk premium however, is more difficult since the market’s expected future returns are very unpredictable (Koller, Goedhart and Wessels, 2010; Mayfield, 2004).

Several analysts and professors have estimated the market risk premium through historical or forecasted data. Their results differ significantly. Until today, there is no certainty about the right determination approach or the true level of risk premium (Petersen and Plenborg, 2012). Therefore, we compare the values from several professors or authors.

Jorion and Goetzmann (1999) find a global risk premium of 4 percent. Fama and French (2002) calculate an equity premium from data of the years between 1951-2002. Their calculation results in an estimated global risk premium of 4,32 percent. Petersen and Plenborg (2012) collect the market risk premium from 884 professors and come up with an average of 5,3 percent in Europe. Dimson,

43 Development of 10-year Danish government bond in appendix 45

44 Calculation of risk-free rate in appendix 46

Marsh and Staunton (2002) use historical data from 1990-2008 and calculate a risk premium of 4,6 percent for Denmark. Brealey, Myers and Allen (2010) update this study and come up with an average market risk premium in Denmark of 4,3 percent. Koller et al. (2010) define that an appropriate risk premium lies between 4,5 and 5,5 percent. Damodaran’s (2018D) estimated market risk premium in Denmark is 5,08 percent. Fernandez et al. (2017) update their statistics on the average market risk premium in every of our considered years. They always use a high number of references including among others Ibbotson/Morningstar, Damodaran, Bloomberg, Fernandez, Duff

& Phelps, DMS, Brealey and Myers, McKinsey, Fama and French and Siegel who again use data from several different professors, analysts, companies or databases. In 2017 their survey estimate an average market risk premium of 6,1 percent in Denmark (Fernandez et al., 2017). Because of the broad variety of high-quality statistics they include, Fernandez et al.’s estimates seem to be a good summary of the above mentioned authors.

All these assumptions and sub-calculations result in a return on equity of 7,7 percent.