How to Conceptualize and Value Earnings Growth

1. How to Conceptualize and Value Earnings Growth Jim Ohlson Stern School of Business New York University August 2008

2. Key Result A formula (“OJ”) that expresses value in terms of next year expected EPS and growth in EPS Model Variables: Value depends on • EPS1: Next-year expected EPS or “forward EPS”. • Year 2 vs. Year 1 growth (STG) in expected EPS • Some measure of long-term growth (LTG) in expected EPS • Discount factor which reflects risk (Cost of Equity Capital) P0 EPS1 EPS2 LTG

3. Compelling Empirical Realities • P0 / EPS1 correlates with short-term growth in EPS, but by no means perfectly • P0 / EPS1 rates often exceed any reasonable estimate of the inverse of the cost of capital • Short-term growth in EPS often substantially exceeds any reasonable estimate of cost of capital (e.g., Google’s growth in estimated 2008 EPS vs. 2008 EPS is 28%) • Analysts typically expect that superior EPS growth rates revert to “normal” rates over time

4. Implications of Empirical Realities • The Constant (Gordon) Growth Model works only if cost of capital exceeds the perpetual growth rate. • One must model a decaying growth rate in EPS when short-term growth is relatively large.

5. Approach to Assumptions • Short-term growth (EPS2 vs. EPS1 adjusted for DPS1) -- decays gradually to a steady state growth • also determines the rate of decay in EPS growth. • P0 equals the present value of expected DPS using the discount factor r (cost of equity capital). • Assumptions build in dividend policy irrelevancy.

6. A Hypothetical Example Model Dynamics: Assuming full payout: Numerical illustration: These assumptions imply the following growth pattern.

8. More generally, the model is determined by where r = cost of equity capital (8%, say) does NOT depend on the dividend policy!

9. r = cost of equity capital = long-term EPS growth given full payout = as arguably approximates steady state growth in GNP Basic Valuation Formula

10. Example: GE Adjustments for dividends; Ifand then

11. Example: GE Does estimated value exceed actual price because our specification of r is too low? Try is evidently sensitive to r

12. Reverse Engineering: Infer r • Familiar Problem: Estimates of intrinsic values are very sensitive to choice of discount factor • A More Sensible Approach: Solve for r given EPS1/P0, gs, and gL. Leads to square-root formula:

13. Reverse Engineering: Infer r • In the case of GE,

14. Comparative analysis r as P0 or EPS1 r as gs or gL If gL = 0 implies where PEG is “Price-to-Earnings divided by Growth”:

15. Very popular as a buy/sell signal, given risk is not a problem. • If two firms have the same and then the firm with the higher P0 / EPS1 ratio has lower risk.

16. What Factors Should Determine r? In theory: r equals expected return, which depends upon risk (e.g., CAPM b). In practice, r may be affected by the following: • Broader perceptions about equity risk • Market is expecting EPS1 (and/or EPS2) will soon be revised. • A high r implies an expected downward revision in EPS, and vice versa. • Mispricing

17. Can we say some about Why not assume Risk (premium) and growth are now two sides of the same coin

18. Empirical Evidence Do firm-specific measures of risk explain r using the square-root formula? Empirical question has been addressed for US data Assume all firms have the same (4%). r is regressed on the following variables: • Beta • Unsystematic risk • Debt/Equity • Earnings variability • Long term growth per analyst estimate • Book-to-Market • Industry mean risk premium

19. Pooled Cross-Sectional Regression UNSYST: Unsystematic risk as measured by the residual from the regression over prior year of a firm’s daily return on the daily market return ERNVAR: Earnings variance from a factor analysis of mean absolute error in analyst forecasts in the past five years, dispersion of analysts forecasts, and the coefficient of variation of earnings ln(D/M): Leverage as measured by the log of ratio of book value of long-term debt to the market value of equity ln(M): Size as measured by the log of the total market value of equity LTG: I/B/E/S estimate of long-term growth ln(B/M): Log of the ratio of the book value of equity to the market value of equity RPIND : Industry mean risk premium during the prior year for firms in the same industry as per the Fama-French (1992) classification

20. Means of Year-by-Year Cross-Sectional Regressions UNSYST: Unsystematic risk as measured by the residual from the regression over prior year of a firm’s daily return on the daily market return ERNVAR: Earnings variance from a factor analysis of mean absolute error in analyst forecasts in the past five years, dispersion of analysts forecasts, and the coefficient of variation of earnings ln(D/M): Leverage as measured by the log of ratio of book value of long-term debt to the market value of equity ln(M): Size as measured by the log of the total market value of equity LTG: I/B/E/S estimate of long-term growth ln(B/M): Log of the ratio of the book value of equity to the market value of equity RPIND : Industry mean risk premium during the prior year for firms in the same industry as per the Fama-French (1992) classification

21. Summary • Instead of using a constant growth assumption, we derive a simple formula expressing as a function of four variables: (i) next year estimated EPS (ii) short term EPS growth (iii) long term EPS growth (iv) cost of capital. • The valuation formula is easy to implement using analysts’ forecasts. • The “square-root” formula expresses the market’s assessment of a firm’s cost of capital; it depends only on (i) P0 / EPS1, and (ii), and (iii) • Inferred cost of capital (r) are explained by (i) risk (ii) misleading “consensus” estimates of EPS1 and , (iii) market inefficiencies.