## Info

The tax rates used were 32% for emerging market companies, 35% for U.S. companies and 33% for Global companies, based upon averaging the marginal tax rates in each group. The unlevered beta of emerging market companies is slightly higher than the U.S. and global groupings. While the average beta for U.S. companies is higher than the rest of the sample, the difference is entirely due to the higher debt to equity ratios of these companies. We will use an emerging market unlevered beta of 0.59 as the beta for the paper and pulp business that Aracruz is involved in.

We can estimate the unlevered beta for Aracruz in two steps. First, we consider the asset composition for Aracruz. In addition to being in the paper business, Aracruz has a cash balance of 1,018 million BR, which is roughly 7.07% of the firm value. Since this is much larger than the typical cash balances of the companies on our comparable firm list, and the beta of cash is zero, the unlevered beta for Aracruz can be estimated as follows:

Unlevered Beta for Aracruz = (0.9293) (0.585) + (0.0707) (0) = 0.5440 Aracruz had gross debt outstanding of 4.093 million BR at the end of 2003 and a market value of equity of 9,189 million BR leading to a debt/equity ratio of 44.59%. Allowing for a tax rate of 34% (the Brazilian marginal tax rate), the levered beta for Aracruz can then be estimated as follows:

Levered Beta for Aracruz = 0.5440 (1+ (1-.34) (.4459)) = 0.7040

If we wanted a levered beta for just the paper business of Aracruz, we would use the levered beta for the paper and pulp business and the gross debt to equity ratio for the firm:

Levered Beta for paper business = 0.585 (1+ (1-.34) (.4459))) = 0.7576

In Practice: Gross Debt or Net Debt

Many analysts in Europe and Latin America prefer to subtract the cash from the gross debt to arrive at a net debt figure. While there is no conceptual problem with this approach, they should remain consistent. Consider, the calculation of unlevered and levered betas in illustration 4.7. First, the computation of unlevered beta for the emerging market paper and pulp companies would have been based upon the net debt to equity ratio for firms in the sector rather than the debt to equity ratio: Net Debt/Equity = (Gross Debt - Cash)/ Equity = 29.22% Unlevered Beta = Levered Beta / (1 + (1- tax rate) (Net D/E))

= 0.6895/ (1 + (1-.32)(.2922)) = 0.5751 This unlevered beta is already corrected for cash and no further adjustments are needed. To make the levered beta calculation for Aracruz, we would use the net debt to equity ratio for the company. The net debt is computed by subtracting Aracruz's cash balance of 1,018 million BR from its gross debt of 4,093 million BR yielding a net debt to equity ratio of 33.47%.

Levered Beta for Aracruz = Unlevered Beta (1 + (1 - tax rate) (Net D./E))

= 0.5751 (1 + (1-.34)(.3347)) = 0.7022 Again, we can dispense with the adjustment for cash since the net debt to equity ratio captures the cash holdings.

Notice that the levered beta of 0.7040 computed for Aracruz in illustration 4.7 does not exactly match the computation using the net debt to equity ratio. The reason lies in an implicit assumption that we make when we net cash against debt. We assume that both debt and cash are riskless and that the tax benefit from debt is exactly offset by the tax paid on interest earned on cash. It is generally not a good idea to net debt if the debt is very risky or if the interest rate earned on cash is substantially lower than the interest rate paid on debt.

With a net debt to equity ratio, there is one more potential complication. Any firm that has a cash balance that exceeds its debt will have negative net debt and using this negative net D/E ratio will yield an unlevered beta that exceeds the levered beta. While this may trouble some, it makes sense because the unlevered beta reflects the beta of the business that the firm operates in. Firms that have vast cash balances that exceed their borrowing can have levered betas that are lower than the unlevered betas of the businesses they operate in.

Illustration 4.8: Bottom Up Beta for Deutsche Bank

There are a few banks in Germany that can be viewed as competitors to Deutsche Bank, though none of them are as large as it is, or have as large of a stake in investment banking. Since the rules and regulatory constraints governing banking in the United States are different from the rules governing banks in much of the Eurozone, we will look at the betas of European banks with market capitalizations exceeding \$ 5 billion to estimate the beta for the commercial banking arm of Deutsche Bank. To estimate the beta of Deutsche Bank's investment banking arm, which includes Morgan Grenfell and Banker's Trust, we use the betas of investment banking firms in the United States. The results are presented below:

Comparable Firms

Number of firms

Average Beta

Large commercial Banks in Europe

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