price level of the S&P 500 of 1,685.73. The consensus analyst view was that earnings on the S&P 500 would grow from a trailing amount of $91.53 to $109.09 over the next year, a 19.1 percent growth rate. However, reported earnings have grown at approximately a 7 percent rate over the last four decades.27We will use the 7 percent long-term average growth rate as the long-term earnings growth forecast. Dividend (6)25Fama and French (2001) found that prior to 1950, the historical and Gordon growth model estimates for the US equity risk premium agree, but from 1950–99, the Gordon growth model estimate averages less than half the historical estimate. They attribute the difference to the effect of positive earnings surprises relative to expectations on realized returns.26Recent examples of the application of this model (to US markets) are Jagannathan, McGrattan, and Scherbina (2000) and Fama and French (2001). The GGM estimate has also been used in institutional research for international markets (Stux 1994). Most analysts forecast the earnings growth rate rather than the dividend growth rate, which is technically specified in theory, so we use the earnings growth rate in the expression. Given a constant dividend payout ratio, a reasonable approximation for broad equity indexes, the two growth rates should be equal.27.
The Equity Risk Premium ■Member Use Only19C F A I N S T I T U T E M E M B E R U S E O N LYgrowth should track earnings growth over the long term. The 20-year US government bond yield was 3.0 percent. Therefore, according to Equation 6, the Gordon growth model estimate of the US equity risk premium was 2.1% + 7.0% – 3.0% or 6.1%. Like historical estimates, Gordon growth model estimates generally change through time. For example, the risk premium estimate of 6.1 percent just given compares with a GGM estimate of 2.4 percent (computed as 1.2% + 7% – 5.8%) made in the first edi-tion of this reading, as of the end of 2001. In the second edition of this reading, the GGM estimate was 3.9 percent (computed as 1.9% + 7.0% – 5%), as of the end of 2009.Equation 6 is based on an assumption of earnings growth at a stable rate. An assumption of multiple earnings growth stages is more appropriate for very rapidly growing economies. Taking an equity index in such an economy, the analyst may fore-cast a fast growth stage for the aggregate of companies included in the index, followed by a transition stage in which growth rates decline and a mature growth stage char-acterized by growth at a moderate, sustainable rate. The discount rate rthat equates the sum of the present values of the expected cash flows of the three stages to the current market price of the equity index defines an IRR. Letting PVFastGrowthStage(r) stand for the present value of the cash flows of the fast earnings growth stage with the present value shown as a function of the discount rate r, and using a self-explanatory notation for the present values of the other phases, the equation for IRR is as follows:Equity index pricePVFastGrowthStagePVTransitionPV=( )+( )+rrMatureGrowthStager( )The IRR is computable using a spreadsheet’s IRR function. Using the IRR as an esti-