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Note that the cost of equity for investment banking is significantly higher than the cost of equity for commercial banking, reflecting the higher risks.

For Aracruz, we will add the country risk premium estimated for Brazil of 7.67%, estimated earlier in the chapter, to the mature market premium, estimated from the U.S, of 4.82% to arrive at a total risk premium of 12.49%. The cost of equity in U.S. dollars for Aracruz as a company can then be computed using the bottom up beta estimated in illustration 4.7:

Cost of Equity = Riskfree Rate in US $ + Beta * Risk Premium

= 4% + 0.7040 (12.49%) = 12.79% As an emerging market company, Aracruz clearly faces a much higher cost of equity than its competitors in developed markets. We can also compute a cost of equity for Aracruz in real terms, by using a real riskfree rate in this calculation. Using the 10-year inflationindex U.S. treasury bond of 2% as the real riskfree rate, Aracruz's real cost of equity is:

Cost of Equity = 2% + 0.7040 (13.70%) = 10.79% If we want to compute the cost of equity in nominal BR terms, the adjustment is more complicated and requires estimates of expected inflation rates in Brazil and the United States. If we assume that the expected inflation in BR is 8% and in U.S. dollars is 2%, the cost of equity in BR terms is:

Cost of Equity in BR =(1+ Cost of Equity in $)(1 + Inflation RateBrazil) - 1

(1 + Inflation RateUS)

Note that these estimates of cost of equity are affected by the cash holdings of Aracruz. We can estimate the cost of equity for the paper and pulp business of Aracruz (independent of the cash holdings) by using the levered beta of 0.7576 for the business estimated in illustration 4.7:

Real Cost of Equity (paper business) = 2.00% + 0.7576 (12.49%) = 11.46%

US $ Cost of Equity (paper business) = 4.00% + 0.7576 (12.49%) = 13.46%

Finally, for Bookscape, we will use the beta of 0.82 estimated from illustration 4.6 in conjunction with the riskfree rate and risk premium for the US:

This cost of equity may seem incongruously low for a small, privately held business but it is legitimate if we assume that the only risk that matters is non-diversifiable risk.

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