Estimating the Cost of Capital  513 there is a single, real-terms risk-free rate, and the market risk premium and beta are measured against a global market portfolio: E r r E r r j f j G G f ( ) [ ( ) ] , = + − β where    rj = return for asset j rf = risk-free rate βj,G = beta of asset j versus global market portfolio G rG = return for global market portfolio G Effectively, this means applying the approach described in Chapter 15. The cost of capital for domestic and foreign assets is determined in exactly the same way. What matters is their beta, relative to the global market portfolio, and the market risk premium of that same portfolio, relative to the risk-free rate. We recommend this approach because capital markets are global. A con- siderable share of all equity trades is international, and traders, primarily large institutional investors, draw their capital and invest it globally. For ex- ample, consider the consumer goods companies Procter & Gamble and Uni- lever. Both sell their household products around the world and have roughly the same geographic spread. The shares of both are traded in the United States and Europe. The primary difference is that Procter & Gamble is domiciled in the United States, and Unilever is domiciled in the United Kingdom and the Netherlands. With such similar business profiles and investor bases, it would be odd if the two companies had different costs of capital. In general, we find that the domicile of otherwise-comparable companies does not influence their valuation levels. For example, the valuation multiples of U.S. and European pharmaceutical companies are all in a very narrow range around 10 times enterprise value to EBIT, regardless of the company domicile. As explained in Appendix G, the global CAPM technically holds only if purchasing power parity (PPP) holds, which is the case in the long run.3 Al- though evidence on PPP has been mixed, academic research has converged around the conclusion that on average, deviations from PPP between curren- cies are reduced to half their value within three to five years. In other words, exchange rates ultimately adjust for differences in inflation between countries, although not immediately and perfectly. Estimating Market Risk Premium in Global CAPM  In the absence of capital controls for investors, the global market risk premium should be based on a global index that includes most of the world’s investment assets. As explained in Chapter 15, the market risk premium for an index can be estimated from its 3 For an overview, see A. M. Taylor and M. P. Taylor, “The Purchasing Power Parity Debate,” Journal of Economic Perspectives 18, no. 4 (Fall 2004): 135–158. 514  Cross-Border Valuation historical returns or from forward-looking models, which by and large lead to similar results. Global indexes rarely go far back in time, so long-term esti- mates of historical market risk premiums are not readily available. Therefore, we generally resort to specially compiled estimates for the global market or the well-diversified U.S. market as a basis for a global market risk premium. Correlation between the S&P 500 and global market indexes (such as the MSCI World Index) has, so far, been very high, making the S&P 500 a good proxy. Estimates from both sources are typically not far apart, falling in the range of 4.5 to 5.5 percent (also see Chapter 15). Estimating Beta across Currencies in Global CAPM  Since we are using a global market risk premium, a global beta also should be used. Follow the guidelines from Chapter 15 on how to estimate beta. There is one special issue to consider when estimating betas for stocks in international markets: the currency in which returns are measured. For example, should a Swiss investor estimate the beta of IBM based on returns in U.S. dollars or Swiss francs? If you use total returns to estimate beta, the results will be differ- ent when returns are expressed in U.S. dollars or Swiss francs, because the dollar-to-franc exchange rate fluctuates over time. But a stock’s beta should be the same in all currencies, as any difference would imply differences in the real-terms cost of capital across currencies. The solution is to use excess returns over the risk-free rate, rather than total returns.4 Beta estimates are consistent across currencies when the stock’s excess returns are regressed against the excess return of a global market portfolio, as follows for any pe- riod ending at time t: r r r r j t A f t A j M t A f t A , , , , − ( ) = − ( ) β where    rj t A , = realized return for stock j in currency A rf t A , = risk-free rate in currency A rM t A , = realized return for global market portfolio in currency A If the international Fisher effect and purchasing power parity would hold, differences in international interest rates would reflect differences in inflation across countries, and differences in inflation across countries would also be reflected in changes in exchange rates. In that case, the risk-free rate for each 4 Most practitioners use the so-called market model, estimating beta from absolute returns instead of excess returns. This is an approximation that produces good results if the risk-free rate is relatively stable. When translating returns from another currency, the approximation no longer holds, as the nominal risk-free rate will fluctuate with exchange rates.