aCash flow in the first year = 2.81% of 1111.91 (1.095) If we assume that these are reasonable estimates of the cash flows and that the index is correctly priced, then

T , , , _____ 34.26 37.52 41.08 44.98 49.26 49.26(1.0425)

(1 + r) (1 + r)2 (1 + r)3 (1 + r)4 (1 + r)5 (r - .0425)(1 + r)5 Note that the last term of the equation is the terminal value of the index, based upon the stable growth rate of 4.25%, discounted back to the present. Solving for r in this equation yields us the required return on equity of 7.94%. Subtracting out the treasury bond rate of 4.25% yields an implied equity premium of 3.69%.

The advantage of this approach is that it is market-driven and current and it does not require any historical data. Thus, it can be used to estimate implied equity premiums

17 Stock buybacks during the year were added to the dividends to obtain a consolidated yield.

18 We used the average of the analyst estimates for individual firms (bottom-up). Alternatively, we could have used the top-down estimate for the S&P 500 earnings.

in any market. It is, however, bounded by whether the model used for the valuation is the right one and the availability and reliability of the inputs to that model. For instance, the equity risk premium for the Brazilian market in January 2004 was estimated from the following inputs. The index (Bovespa) was at 21050 and the current dividend yield on the index was 4%. Earnings in companies in the index are expected to grow 14% (in US dollar terms) over the next 5 years and 4.5% thereafter. These inputs yield a required return on equity of 10.70%, which when compared to the treasury bond rate of 4% on that day results in an implied equity premium of 6.70%. For simplicity, we have used nominal dollar expected growth rates20 and treasury bond rates, but this analysis could have been done entirely in the local currency.

The implied equity premiums change over time much more than historical risk premiums. In fact, the contrast between these premiums and the historical premiums is best illustrated by graphing out the implied premiums in the S&P 500 going back to 1960 in Figure 4.2.

19 The treasury bond rate is the sum of expected inflation and the expected real rate. If we assume that real growth is equal to the real rate, the long term stable growth rate should be equal to the treasury bond rate.

20 The input that is most difficult to estimate for emerging markets is a long term expected growth rate. For Brazilian stocks, I used the average consensus estimate of growth in earnings for the largest Brazilian companies which have listed ADRs . This estimate may be biased, as a consequence.

Figure 4.2: Implied Premium for US Equity Market

Figure 4.2: Implied Premium for US Equity Market

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