The abnormal performance measure in expression (4.6) is calculated using a time- varying cost o f equity capital based on a time-varying risk free rate plus a constant equity premium o f 5%, as follows:
rb+s = r fb+s + rP> (4.10)
where:
rfb+s = Country-specific risk-free rate at fiscal year b+s. This is computed as the 12-month moving average for the year ended at the balance sheet date o f the relevant annualised 3-month Treasury bill rate36;
rp = Equity risk premium, assumed to be 5%.
The cost o f equity for country j at time b+s is estimated to be the annualised 3-month Treasury Bill rate for country j for time b+s, plus an assumed risk premium o f 5%. The rates are adjusted for accounting periods that are o f other than 12-months duration, using the standard formula (l + r365 )p/365 _ i ? where r365 is the annual rate, on a 365-day basis, and p is the period, in days, for which the rate needs to be adjusted. For example, for an accounting period of eight months, which can occur if a company
36 In order to use comparable short-term risk free rates across the four countries I used the 3-month T reasury Bill rates reported by the International M onetary Fund available in Datastream.
changes its year-end, the cost o f equity capital is adjusted to an eight-month equivalent.
The method used to estimate the cost o f equity capital is similar to that employed in previous studies such as Frankel and Lee (1998). Other studies such as Francis, et al. (2000) and Penman and Sougiannis (1998) employ more sophisticated methodologies to estimate the cost o f equity. However, the evidence in these studies and in Sougiannis and Yaekura (2001) suggests that value estimates are relatively insensitive to the choice o f discount rate.
The choice o f 5% for the equity risk premium is based on recent evidence suggesting that the ex ante equity premium value lies somewhere in the region o f 4% to 6%. For example, Claus and Thomas (2001) find that the risk premium in US, U.K. Canada, France, Germany and Japan, during the period 1985 to 1998 lies between 2% and 4%. Similar results are reported by Easton, et al. (2002), who find an equity premium o f 5.3%. Lamdin (2002) estimates an average risk premium between 4.7% and 5.7%. Using a long-term and short-term risk free rate during the period 1981 to 2000 Copeland, Koller and Murrin (2000) suggest similar values: between 4.5% and 5%.
The procedure used to estimate the cost o f equity capital allows variability through time in line with interest rates but assumes that all companies have a beta equal to one and that the market risk premium is constant at 5%. I test the robustness o f the results to changes in the cost o f equity capital, namely by allowing for beta to vary across industry and country and by changing the equity risk premium (see section
7).
4.3.3 A lig n m en t o f year-end book value and m arket value
I compute the EVC values using market value as at three months after fiscal year-end This is achieved by adjusting the market value at the balance sheet date
( M Vb s) by tfre total return on the company's stock for the three months after the balance sheet date (R et3 ):37
l^ B S l = M^BS XRe t3 ’ (4-11)
where R e t3 is the three-month return given by the ratio o f the return index at three months after the balance sheet to the return index at the balance sheet data.38 This procedure ensures that the market value is likely to reflect information from the annual financial statements whilst remaining comparable with the balance sheet value o f shareholders’ funds. The analysis was repeated for market value at the fiscal year- end. Results are similar to those obtained for market value three months after year-end and therefore are not reported for reasons o f economy o f space.
Another necessary alignment between year-end book value and market value relates to the issue o f accounting for dividends. Because o f the accrual principle o f accounting, the dividend expense can be recognised in book value at the end o f the year whereas the payment may occur in the following year (this is the case in the U.K. and the U.S. but not in France and Germany, where the dividend is accounted for on a cash basis). This accrual accounting movement generates a dividend liability in the balance sheet, which is cancelled when payment occurs. Hence, at fiscal year-end, book value is an ex-dividend figure whereas market value is cum-dividend value. In these cases, and when necessary data is available, I overcome the discrepancy by
37 In a small number o f cases where the first year o f data coincides with the IPO o f the com pany, m arket value data were not available until shortly after the start o f the first accounting period. In these cases I used the first available data.
38 Return indexes are obtained from Datastream (code RI) and from CRSP for some U.S. com panies.
transforming book value into a cum-dividend figure. To achieve this, I add the creditor for ordinary dividend to reported book value. The creditor for ordinary dividend is estimated by multiplying the total dividend creditor by the ratio o f (1) ordinary dividend charged in the year to (2) total dividend charged in the year.39