# What is the expected real growth rate of earnings implied by S&P 500 P/E according to the dividend growth model?

Consider the following data on the S&P 500 on 1987 just before the crash: Index 305.2 P/E 21.2 Show more Consider the following data on the S&P 500 on 1987 just before the crash: Index 305.2 P/E 21.2 Div Yield 2.9% Payout 61.4% Beta 1.0 Equity premium 4.0% The long-term T bond rate was 9% the consensus forecast of long-term inflation was 4.5% per annum. a/ What is the expected real growth rate of earnings implied by S&P 500 P/E according to the dividend growth model? b/ Suppose the consensus forecast of nominal earnings and div growth of the S&P 500 for the next 5 years was 16% or 11% in real terms. Furthermore since the long-term real growth of earnings and dividends in the U.S economy had been about 2% allow div growth to 2% after the 5 year and stay at that level in the future. How can you use these and above data to estimate the prospective risk premium of equity over long-term T-bonds using this equation? P0/E1=p1(1+k) -1 +p2(1+g2)(1+k) -2 where: P0/E1: forward P/E k: cost of equity pt : payout ratio at time t Show less

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