Question :
Consider the following data on the S&P 500 index on October 14, 1987, just before the crash of 1987:
| Index |
305.2 |
| P/E |
21.2 |
| Dividend yield |
2.90% |
| Payout |
61.40% |
| Beta |
1 |
| Equity Premium over long Treasury rate |
4.00% |
In addition, the long-term Treasury bond rate was 9%, and the consensus forecast of long-term inflation was 4.5% per annum.
a. What is the expected real growth rate of earnings implied by the S&P 500 P/E ratio according to Equation of the dividend growth model? Do you think the implied growth rate was sustainable in the long run?
b. Suppose that the consensus forecast of nominal earnings and dividend 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 American economy had been about 2%, allow dividend growth to drop to 2% after the fifth year and stay at that level in the future. How can you use these and the above data to estimate the prospective risk premium of equity over long-term Treasury bonds using Equation?