Weighted Average Cost of Capital --Calculating cost of equity in practice ll The equity risk premium is the average annual return of the market expected by investors over and above riskless debt How to estimate the risk premium-E(km-kf) --1 Look up a value in Dimson,Marsh Staunton (2003) --2 Arithmetic or geometric average? --3 Estimate it-using same choices as when estimating b
The equity risk premium is the average annual return of the market expected by investors over and above riskless debt How to estimate the risk premium - E(km – krf) --1 Look up a value in Dimson, Marsh & Staunton (2003) --2 Arithmetic or geometric average? --3 Estimate it - using same choices as when estimating b Weighted Average Cost of Capital --Calculating cost of equity in practice II
EXHIBIT 11.5 Arithmetic Versus Geometric Returns:A Sample Calculation Year 1 2 3 4 5 Mean Share price 10 12 10 12 14 Arithmetic change +20.00% -16.67% +20.00% +16.67% +10.00% Geometric change +8.78% +8.78% +8.78% +8.78% +8.78% Arithmetic change is calculated year-by-year as P/P-1].The simple average of the series is the mean.The geometric change is calculated usingony the beginning and ending values.10and 14.and the geometric roo of (14/1-1]is found (four periods of change).The geometric change assumes reinvested compounding,whereas the arithmetic mean only assumes point-to-point investment
EXHIBIT 11.4 Equity Risk Premiums Around the World,1900-2002 Relative to Bills Relative to Bonds Geometric Arithmetic Geometric Arithmetic Mean Mean SD Mean Mean SD Australia 6.8 8.3 17.2 6.0 7.6 19.0 Belgium 2.2 4.4 23.1 2.1 3.9 20.2 Canada 4.2 5.5 16.8 4.0 5.5 18.2 Denmark 2.2 3.8 19.6 1.5 2.7 16.0 France 6.4 8.9 24.0 3.6 5.8 22.1 Germany 3.9 9.4 35.5 5.7 9.0 28.8 Ireland 3.6 5.5 20.4 3.2 4.8 18.5 Italy 6.3 10.3 32.5 4.1 7.6 30.2 Japan 6.1 9.3 28.0 5.4 9.5 33.3 The Netherlands 4.3 6.4 22.6 3.8 5.9 21.9 South Africa 5.9 7.9 22.2 5.2 6.8 19.4 Spain 2.8 4.9 21.5 1.9 3.8 20.3 Sweden 5.2 7.5 22.2 4.8 7.2 2.5 Switzerland 3.2 4.8 18.8 1.4 2.9 17.5 United Kingdom 4.2 5.9 20.1 3.8 5.1 17.0 United States 5.3 7.2 19.8 4.4 6.4 20.3 Average 4.5 6.9 22.8 3.8 5.9 21.6 World 4.4 5.7 16.5 3.8 4.9 15.0 Source:Elroy Dimson,Paul Marsh,and Mike Staunton,"Global Evidence on the Equity Risk Premium,"Journal of Applied Corporate Finance,2003,Vol.15,No.4,p.31.The equity risk premium is measured as 1 +equity rate of return divided by 1 risk-free return, minus 1.The statistics reported in this table are based on 103 annual observations for each country,except Germany,which excludes 1922-1923,when bill and bondholders experienced returns of-100%due to hyperinflation.The row labeled"Average"is a simple, unweighted average of the statistics for the 16 individual countries.The row marked "World"is for the world index.SD is standard deviation
EXHIBIT 11.6 Alternative Estimates of Cost of Equity for a Hypothetical U.S.Firm Assuming B=1 and k=4% Equity Risk Cost of Source Premium Equity Differential Ibbotson 8.800% 12.800% 3.800% Finance textbooks 8.500% 12.500% 3.500% Investor surveys 7.100% 11.100% 2.100% Dimson,et al. 5.000% 9.000% Baseline Source:Equity risk premium quotes from"Stockmarket Valuations:Great Expectations,"The Economist,January 31,2002