7. VALUATION
7.1 Required Rate of Return on Equity
For calculating the required rate of return on equity (re) the Capital Asset Pricing Model (CAPM) is applied. According to CAPM, re can be calculated as follows:
€
re =rf +βe(rm−rf)
Equation 1 Required rate of return on equity, re
Where rf represents the risk‐free interest rate, rm the return on the market portfolio, and βe the systematic risk on equity. In the following subsections, inputs for the model are found and discussed. Note that I have chosen to find an explicit measure of the differ‐
ence between rm and rf, better known as the risk premium.
7.1.1 Risk‐free Interest Rate
Estimating the risk‐free interest rate (rf) is straightforward. Seeing as the time horizon in this case is infinite, applying a zero‐coupon rate based on a local, i.e. Danish, 10 or 30‐
year government bond.106 In this case I have chosen the 10‐year bond, as I believe it is the most commonly applied. Data extractions from the Danish national bank show that the rate is 1) fluctuating and 2) very low.107 For this reason I have chosen to calculate a simple average based on the period from October 2010 to and November 2011.
Hence the measure of the riskfree interest rate is estimated to be 2,885%
7.1.2 Market Risk Premium
Estimating the market risk premium is not an easy task. First, one must choose from either calculating, reasoning or conducting a survey.
Calculations can be either based on historical events (co‐variability between market portfolio returns and returns on risk‐free investments) or based on current situation and expectations of the future using Gordon’s Dividend Model.108 There are advantages and disadvantages connected to both methods. Jyske Bank has attempted to rate the quality of four different methods in estimating the risk‐free interest rate and the market
106 Petersen, C. V., & Plenborg, T. (2010). Financial Statement Analysis, p 309.
107 Appendix V, Table A V‐I.
108 Petersen, C. V., & Plenborg, T. (2010). Financial Statement Analysis, p 322.
risk premium – i.e. since both can be estimated using either historical data or actual cur‐
rent level and/or outlook, there are four different optional combinations. The highest rated was the one, in which actual levels are used for estimating both inputs. Since the risk‐free interest rate applied is based on actual levels, I have to choose between this combination and the middle rated combination.109
While reliability of using the ex‐post method is clearly high, however the validity of es‐
timates calculated on historical events suffer the underlying assumption, that historical events are good indicators of future events. In addition, there are a number of methodo‐
logical issues to consider, when calculating. First, the time period chosen for calculations naturally affects the results to a great extent, i.e. calculations in a study made by the Danish national bank showed levels of 2,1%, 7,2%, and 5,2% for the periods of 1970‐
1982, 1983‐2002, and 1970‐2002 respectively.110 Secondly are mainly two different cal‐
culation techniques, i.e. arithmetic and geometric average. Cooper(1996) argues, that when the purpose of calculating past returns is to estimate capital costs for use in capital budgets, the arithmetic is seemingly more correct. The point is that the discount rate used in capital budgeting is used to discount the expected cash flow, where the expecta‐
tion involved is arithmetic. Thus an arithmetic estimate of the discount rate involved is consistent with the procedure, whereas a geometric estimate is not.
Basing the estimate on a survey is naturally does not score very high on the reliability scale, one positive side to this method is, that it is forward looking.
Given all these different methods of estimating the market risk premium experts’ claims, empirical studies, surveys etc are not few, and moreover, there is no prevailing consen‐
sus about what the appropriate level is. Hence, a survey conducted by PwC in 2010 showed that respondents were allegedly were calculating with market risk premiums ranging from 4% to 7,2%, yet with 82% of respondents having their answer between 4% and 5%; and the average risk premium was 4,9%.111 This is also supported by an‐
109 Møller, R., & Jørgensen, A. (2010). Estimation af danske aktiers risikopræmie. Jyske Bank.
110 Danmarks Nationalbank. (2003). Kvartalsoversigt 1 kvartal 2003. Danmarks Nationalbank.
111 PricewaterhouseCoopers. (2010). Prisfastsaettelsen på aktiemarkedet, p 2.
other empirical study, in which it is argued, that historically based estimates should be adjusted for transitory items.112
Based on extensive empirical research, Claus Parum (2004) has found, that based on historical period from 1925 up to date (i.e. 2004), the market risk premium in Denmark of stocks held against government bonds was 3 percent points. Ole Risager (2005) found estimates of 4,2% and 5,7% based on a historical approach (1950‐2004) and a forward P/E approach.
I have chosen to apply the average risk premium found in the survey of PwC. Knowing that many of the respondents in the survey are basing their estimates on historical data, seemingly it is not completely future oriented. However, I do believe, that it actually is a long way – simply because it is difficult to imagine that anyone would calculate a cost of capital in neglect of the economic turmoil. Also, the level is way above that found by Pa‐
rum, and well in‐between Risagers estimates. The level is also within the recommenda‐
tions from the Danish Tax and Customs Administration (2009), as it falls in the interval between 4 and 5.
The market risk premium is estimated to be 4,9%
7.1.3 Beta
Beta (βe) is a reflection of the systematic risk of a stock, i.e. the non‐diversifiable risk. In other words it measures the co‐variation between returns on the market portfolio and returns on a specific stock. A beta value above one indicates that the stock bares less systematic risk, while a beta value above indicates more systematic risk. The ‘e’ denotes that it is the systematic risk on equity; we are dealing with the levered beta.
Seeing as an empirical approach is infeasible in this case, I must chose from a number of other options. One option is to estimate the beta value based on reasoning. Another op‐
tion is to simply use a beta value from one of the stock analysis of TDC and/or competi‐
tors. A third and last option is to use a pre‐calculated average value based on industry.
I have chosen to approach the problem using the third method, i.e. an average industry measure. Aswath Damodaran a professor of Finance provides these numbers on a suffi‐
ciently detailed level, i.e. the beta used is based on 5 years data, i.e. the period from
112 Dimson, E., Marsh, P., & Mike, S. (Fall 2003). Global Evidence on the Equity Risk Premium, p. 27‐38.
2006‐2010, on EU companies operating in ‘Telecommunication Services’ with a market capitalization above $5 million held against the locally most followed stock index.113 The advantage of using this measure is, that it will be completely unbiased, as it based on empirical data, which I hypothetically could have extracted myself. Seeing as underly‐
ing data tables are available, I am presented with the option of calculating a different average – i.e. perhaps leaving out companies of certain countries, which seem to be more than just different or perhaps leaving out those which can not really be compared to TDC in terms of size or business model. However, as it is based on EU companies, and the Danish economy was found highly correlated to EU in terms of GDP per capita, I see no reason to do so.
The beta is estimated to be 1,10114 7.1.4 Calculating re
Putting the found inputs into Equation 1, the required rate of return on equity is found to be:
re = 8,275%115
113 Damodaran, A. (January 2011).
114 Damodaran, A. (January 2011).
115 2,89%+1.1*4,9%