BIBLIOGRAPHY AND REFERENCES
2. Simpler valuation models work much better than complex ones
5.4 CALCULATING THE WEIGHTED AVERAGE COST OF CAPITAL
where x equals the period under forecast and the range is from 1 to 8 (3 years’ actual sales figures plus another 4 years of estimates plus an extra year we want to forecast). So the sales for 2018 equal:
Sales 2018= 2,406.8 * 82− 34,206*8 + 215,424 = €95,811k and the EBITDA2018
2018
€2,262k
€95,811k €2,348k.
€93,915k
EBITDA = × =
Moreover the working capital (WC) for 2018 is derived by the following equation:
WC2018= WC2018 as a % of Sales × Sales2018
The WC as a percentage of sales, as we calculated it in Chapter 4, for the fiscal years 2011 to 2013 was 49%, 50%, and 52% respectively. We can see that it followed an increas-ing trend. Nevertheless this trend seems to have been reversed in the forecastincreas-ing period 2014 to 2017. The WC as a percentage of sales for this period is 36%, 33%, 30%, and 30%
respectively. We discussed in Chapter 4 whether this is a plausible assumption or not. More-over we discussed how we could forecast this ratio for 1 more year. The ratio was found to be 27% (see Section 4.6). Suffice it to say for the time being that this ratio for 2018 will be 26%. We will discuss the consequences of the ratio being 27% further towards the end of this chapter. So:
WC2018 = 26% × €95,811k = €24,911k
Since we are interested not in the working capital per se but in working capital increases or decreases across the years the ΔWC2018 is:
ΔWC2018-2017= WC2018 − WC2017= €24,911k − €25,570k = − €2,659k
The negative number declares a decrease in working capital and thus cash inflow. That is why we add it to the operating cash of the company.
Finally, the CAPEX for 2018 has been chosen as equal to that of 2017, which is €300k (instead of the figure of €997k estimated in section 4.5.1).
The free cash flow for 2018, then, is:
FCF2018= EBITDA2018− ΔWC2018-2017− CAPEX2018 =
€2,348k − (− €2,659k) − €300k = €2,348k + €2,659k − €300k = €4,707k.
Having finished with the derivation of the free cash flows for the explicit forecast period, next we proceed to the estimation of the weighted average cost of capital.
rate of return. The WACC equation is the cost of each capital component multiplied by its proportional weight and then summing:
WACC D
D EK T D
D EK
d e
= + − +
(1 ) + where
Ke: Cost of equity Kd: Cost of debt
E: Market value of equity D: Market value of debt T: Tax rate.
Gearing (G = D/(D + E))
This is the company’s capital structure, that is, the ratio of its debt to the market value of its equity.
Cost of debt (Kd)
The cost of debt reflects the cost that a company has to bear in order to get access to short- and long-term loans. For each company the cost of debt is estimated as the projected interest (cost) on its loans.
Tax rate (T)
The tax rate reflects the effective tax rate for a company operating in a certain country.
Cost of equity (Ke)
The cost of equity can be defined as the minimum return that an investor will require in order to purchase shares of the company. This return has been calculated according to the CAPM based on the following formula:
Ke = Rf + [Rm – Rf] × ß where
Ke: Cost of equity
Rf: Risk-free rate. This is the amount an investor could expect from investing in securities considered free from credit risk, such as government bonds.
Rm – Rf: Market risk premium or the expected return on the market portfolio minus the risk-free rate. The market portfolio is a portfolio consisting of all the securities available in the market where the proportion invested in each security corresponds to its relative market value. The expected return of a market portfolio, since it is completely diversified, is identical to the expected return of the market as a whole.
ß: This is the so-called beta (also known as levered beta) of a stock that measures the risk associated with that particular stock, i.e. how sensitive is the particular stock to move-ments of the whole market portfolio.
The CAPM was developed back in the fifties by Sharpe and Lintner and assumes 2 types of return for the investor of a particular stock: the risk-free return (e.g. of government bonds) and beta times the return on the market portfolio. The first type of return (risk-free) relates to
the time value of money concept (see Section 5.1) and the second type of return relates to the risk associated to the particular stock.
Depending on the continent in which the valuation is taking place, a good proxy for the risk-free rate is the 10-year US Treasury Bill or the Euro Area’s 10-year Government Bond2 or the UK 10 Year Gilt, details of which are available on Bloomberg3 or similar financial sites.
The market risk premium denoted by [Rm – Rf] is the premium required above the risk-free rate that an investor would require in order to bear the additional risk inherent in equity returns on a risky asset. Values for this parameter are published by the Stern School of Busi-ness (see Professor Damodaran’s1 website). Moreover, if you are interested in the approach to computing the market risk premium, you can download his latest paper (“Equity Risk Pre-miums: Determinants, Estimation and Implications”) from the following web address: http://
papers.ssrn.com/sol3/papers.cfm?abstract_id=2238064.
Beta is a measure of the risk of a specific asset relative to the market risk and reflects the extent to which possible future returns are expected to co-vary with the expected returns of the market as a whole. A beta value greater than 1 declares that the investment entails more risk than the market as a whole. On the other hand a beta value less than 1 corresponds to a lower risk investment. For a listed company it is easy to estimate its beta and it is a function of its average monthly returns, over let us say a couple of years, against the general index returns (market return) of the country in which the company is listed.
ß=Covariance of General Index (Market Return) with Stock (LListed Company) Return Variance of General Index (Market Reeturn)
Although we will not elaborate on the formulae of covariance and variance, since on the one hand Excel provides both the COVAR () and the VAR () functions and on the other this would be beyond the scope of this chapter, it will suffice to mention Investopedia’s4 definition of covariance. Covariance is a measure of the degree to which returns on 2 risky assets move in tandem. A positive covariance means that asset returns move together. A negative covari-ance means returns move inversely. Moreover the varicovari-ance of the general index let us say the S&P 500, is a measure of its volatility. The higher the volatility, the more risky is the index.
Recall from your mathematics class that the variance of a variable is a measure of how dis-persed its values are from its expected values as expressed by its mean.
So the calculation of beta is simply the covariance of the 2 arrays of returns (that of a par-ticular stock and that of the index) divided by the variance of the array of returns of the index.
If we apply the above relationship to the sample general index and stock data of November 2013 of a stock exchange as shown in Exhibit 5.5 then the beta of the stock would be 1.7. The returns are calculated as the closing stock or index price minus the opening stock or index price divided by the opening stock or index price.
Beta = COVAR (C2:C26, E2:E26) / VAR (E2:E26) = 0.256 × 10−3/ 0.149 × 10−3 = 1.7 Calculating beta is a bit more complicated in the case of a non-listed company, that is, a private company. Price information is not available for a private company and its beta is usu-ally found by identifying either a listed company with a similar business risk profile and using its beta or a group of companies that are part of the sector the private company participates in and estimating the average betas for the listed companies of this sector. However, when selecting an appropriate beta from a similar company, we have to take into consideration the
gearing ratio (financial risk) involved. And we have to do so because the beta factor of a company reflects both its business risk (resulting from its business model) and its finance risk (resulting from its level of gearing). So in order to be able to use a beta of company A (which is listed) to value company B (which is private) we have to unlever or degear the beta of company A and relever or regear it using the so-called Modigliani-Miller formulae, presented below:
ßprivate company = ßungeared * (1 + (1 − tax rate) (private company’s Debt/Equity)), where ßungeared = ßlisted company * 1 /(1 + (1 − tax rate) (listed company’s Debt/Equity)).
Sometimes the ßungeared is called Asset beta, ßa, and reflects the business risk of the sector.
Moreover the ßprivate company or the beta of a listed company calculated in Exhibit 5.5 is called equity or geared beta or levered beta, ße, and reflects both the industry risk of the company and the company-specific risk because of its financial gearing.
If we want to summarize how to estimate beta from the raw data of a publicly traded com-pany provided from the stock market on which it is listed, we would follow the steps below (steps 6 and 7 apply to beta estimation of private companies):