The P/E Ratio and the S&P 500The Dividend Discount Model (DDM) can be used to think about an entire market index such asthe S&P 500 in the same way it is used to think about an individual firm. In this problem we usethe DDM with a constant dividend growth rate and constant discount rates to think about thevaluation of the U.S. stock market overall during a particularly interesting period. As of August1999, the value-weighted average P/E (price-earnings) ratio for the U.S. stock market (or, moreprecisely, for the S&P 500 Index) was at a historical high of 36. In contrast, over the period from1/1968 to 12/2000, the S&Ps average P/E ratio was 16.For the following problems, assume the dividend payout ratio on the S&P 500 Index is 50%(which is its historical average from 1/1968 to 12/2000) and that it does not change in any of thescenarios considered.Hint: Use the perpetuity-version of the DDM to express the price as a function of the nextdividend (DIV1), the cost of capital (r), and the growth rate (g) of expected earnings (and hencedividends given the constant payout ratio). Then realize that next periods earnings per share(EPS1) can be rewritten as EPS0(1+g). Then divide the price by EPS0 to obtain the P/E ratio.2Now you have an expression linking the P/E ratio to r, g, and the dividend payout ratio(DIV/EPS). From this expression, you can answer the following.Note: Robert J. Shiller of YaleNobel Laureate in Economics in 2013used similarcalculations in his best-selling book Irrational Exuberance, published in 2000, right before theburst of the Dot-com bubble.Backing out expected returns. First, suppose that, over the entire period, the expectedgrowth rate of earnings was a constant 7.2%. (Note that, if the expected growth rate and thepayout ratio are constant, variation over time in the P/E ratio must reflect variation in theexpected return.)5) What was the average expected return on the market (i.e. r) over this period, based on thehistorical average P/E ratio of 16?6) What was the expected return on the market (i.e. r as of 8/1999, when the S&P’s P/E ratiowas 36?Backing out expected growth rates. Next suppose instead that, over the entire period, theexpected return on the market was a constant 10.55%. (Note that, if the expected return and thepayout ratio are constant, variation over time in the P/E ratio must reflect variation in theexpected earnings growth rate.)7) What was the average expected growth rate of earnings over this period, based on thehistorical average P/E ratio of 16?

# The Dividend Discount Model (DDM)

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