While the firms in this sample are very different in terms of market capitalization, the betas are consistent. To estimate the unlevered beta for the sector, we use the average beta across the firms in conjunction with the aggregate values of debt and market value of equity (with a marginal tax rate of 35%):

Debt to Equity Ratio for industry = 1314/6462 = 20.33%

Unlevered Beta = 0.7627/(1+(1-.35)(.2033)) = 0.6737

To correct for cash, we use the aggregate cash balance across the firms:

Unlevered Beta corrected for cash = 0.6737 (1 - 645/(1314+6462)) = 0.7346

Since Bookscape has a negligible cash balance, the unlevered beta for book retailing is also the unlevered beta for the firm.

Since the debt/equity ratios used are market debt equity ratios, and the only debt equity ratio we can compute for Bookscape is a book value debt equity ratio, we have assumed that Bookscape is_close to the industry average debt to equity ratio of 20.33%. Using a marginal tax rate of 40% (based upon personal income tax rates) for Bookscape, we get a levered beta of 0.82.

Levered beta for Bookscape = 0.7346 (1 +(1-.40) (.2033)) = 0.82

Illustration 4.7: Bottom up Beta for Aracruz

The bottom up beta for Aracruz is difficult to estimate if we remain within its home market, which is Brazil, for two reasons. First, there are only three publicly traded firms within the market that are in the same line of business as Aracruz (i.e. paper and pulp production). Second, the betas for all Brazilian firms are unreliable because the index used to estimate these betas, the Bovespa, is a narrow one, dominated by a few large companies.

There are three groups of comparable firms that we can use as comparable firms in the bottom-up beta estimate:

• Emerging Market Paper and Pulp companies: This is a much larger sample of firms. While the individual firm betas may skewed by the limitations of the local indices, the errors should average out over the sample.

• U.S Paper and Pulp companies: The advantage gained is not just in terms of the number of firms but also in terms of reliable betas. The peril in this approach is that the risk in U.S. companies can be different from the risk in Brazilian because of regulatory differences.40

• Global Paper and Pulp companies: This is the largest group and includes a diverse group of companies in both emerging and developed markets. Since betas are measures of relative risk, we would argue that barring significant differences in regulation and monopoly power across markets, it is reasonable to compare betas across markets.

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