Select Page

# The Dividend Discount Model (DDM)

by | Oct 15, 2021 | Assignment

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&Ps 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 periods 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 YaleNobel Laureate in Economics in 2013used 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?

We help you get better grades, improve your productivity and get more fun out of college!!