CASE STUDIES IN FINACE
CASE STUDY 3: ESTIMATING THE COST OF CAPITAL
The Capital Assets Price Model (CAPM) is used to describe the relationship between risk and expected return and is often used to estimate a cost of equity (Investopedia, 2009). The cost of equity(COE) of the discount rate is: R = Rf + β*(E - Rf)
Rf = Risk free rate of return, usually U.S. treasury bonds β = Beta for a company
E = Expected return of the market (commercial airlines market) (E - Rf) = Sometimes referred to as the risk premium The following table shows the average annual arithmetic returns investors earned on various asset classes over the period 1900 to 2003. (Source: Table 7.1 in Brealey/Myers/Allen)
| Nominal Return
| Real Return
Long- term Government Bonds
Short-term Government Bonds
Consumer Price Index (Inflation)
Equity Risk Premium = Stocks – Long Bonds = 11.7% - 5.2% = 6.5% use with long Rf Equity Risk Premium = Stocks – T-Bills = 11.7% - 4.1% = 7.6% use with short Rf The following table shows the average annual arithmetic and geometric nominal returns investors earned on various asset classes over the period 1926 to 2002. (Source: 2003 Ibbotson Associates, Inc.)2 The data assumes reinvestment of all interest and dividend income and does not account for taxes or transaction costs. The average return represents an arithmetic average annual return.
| Arithmetic Return
| Geometric Return
Long-Term Corporate Bonds
Long-Term Government Bonds
Short-Term Government Bills
Consumer Price Index (Inflation)
At the time of the case, four main equity market risk premiums (EMRP) were used:
Arithmetic Equity Risk Premium = Stocks – Long Bonds = 12.2% - 5.8% = 6.4% Geometric Equity Risk Premium = Stocks – Long Bonds = 10.2% - 5.5% = 4.7% Arithmetic Equity Risk Premium = Stocks – T-Bills = 12.2% - 3.8% = 8.4% Geometric Equity Risk Premium = Stocks – T-Bills = 10.2% - 3.8% = 6.4% The 74-year equity market risk premium (EMRP) was estimated to be 6.4%. Based on the Exhibit 8 (Bruner, p. 247-250, 2007)3, Boeing forecast sales and free cash flows of Boeing 7E7 for the next 30 years, this is the reason for choosing the Beta calculated over the longer period of time. And the project of building airplanes is a long-term gamble with the life period more than five years, out of the three Betas calculated over the period of time five years: 1.05, 0.8 and 1.00 (Exhibit 10, Bruner, p. 252, 2007), we can take the largest figure, 1.05. It provides the largest discount rate for the project evaluation thus it will provide the most pessimistic scenario. According to the weight average rule: Total Beta = (% of commercial business)*Commercial Beta + (% of defense Business)* Defense Beta.
(2) From the Exhibit 10, we used the 60 trading days betas (0.37 and 0.30) calculated against the NYSE composite index because it consisted of the most data in comparison with the New York Stock Exchange Composite Index. The average Beta for defense business = ([(Beta of Lockheed Martin)/[1+(1-tc)*(D/E of Lockheed Martin)] + (Beta of Northrop Grumman)/[1+(1-tc)*(D/E of Northrop Grumman)])/2 The average Beta for defense business
= (0.37/(1+(1-0.35)*0.410 + 0.30/(1+(1-0.35)*0.640)/2 = 0.25 In 2002, commercial business generated $28,387 million in revenue and the defense systems segment generated $24,957 in revenue. In total, the weight of commercial business is 54% and the weight of defense systems business is 46%. From (2), we obtain:
1.05 = 0.54*Commercial Beta + 0.46*0.25
Commercial Beta = (1.05 – 0.46*0.25)/0.54 = 1.73 For the CAPM the risk free rate of return for a given period is taken to be the return on government bonds over the period. Because a government cannot run on its own...
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