Consider the following data on the S&P 500 on 1987, just before the crash: The l

Question

Consider the following data on the S&P 500 on 1987, just before the crash:

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

Explanation / Answer

Dividend Payout Ratio = 0.029/(1/21.2) =0.6148

Cost of Equity = 9% + 1 * 4% = 13%

Solving for the Implied Growth Rate

g = (21.2 * 0.13 - 0.6148)/(21.2 + 0.6748) = 2.1412/21.8748

=9.79%

1+g = (1+ Expected Inflation Rate) (1+ Real Growth Rate)

1.0979 = (1.045) (1+Real Growth Rate)

Real Growth Rate= (1.0979/1.045)-1

=5.062%

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