Jim OhlsonStern School of Business

New York University

August 2008

How to Conceptualize and Value Earnings

Growth

2

Key ResultA 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.

LgLg

6

A Hypothetical Example

Model Dynamics:

Assuming full payout:

Numerical illustration:

These assumptions imply the following growth pattern.

1 (1 ) tLteps g eps

1

2

4%11.15

Lgepseps

7

0

3

6

9

12

15

18

2 12 22 32 42 52 62 72 82

Years

EPS Growth Rate (%)

4.18

8

More generally, the model is determined by

where

r = cost of equity capital (8%, say)

does NOT depend on the dividend policy!

1 (1 )t L treps g reps

1 1

1 1 1 2

t t t

t t t t

reps eps r bvps

bvps eps dps bvps

treps

1

1 /t t t t

t t

reps eps r x eps dps

eps dps r

9

Basic Valuation Formula

r = cost of equity capital

= long-term EPS growth given full payout

= as

arguably approximates steady state growth in GNP

10

s L

L

g gepsP PVED

r r g

2 1 1

1 1s

eps eps r dpsg

eps eps

1

1

t t

t

eps epseps

t

Lg

10

Example: GE

Adjustments for dividends;

If and then

2 $2.10EPS 2.10 1.98

6%1.98

1 $1.98EPS

1

1

0.08 1.205%

1.98r dpseps

6% 5% 11%sg

8%r 4%Lg

0

1.98 11 4ˆ $43.310.08 8 4

P $35.50actual

1 1.20DPS

11

Example: GE

Does estimated value exceed actual price because our specification of r is too low?

Try

is evidently sensitive to r

9%r

0

1.98 11 4ˆ $30.800.09 9 4

P

0̂P

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:

2

1

02 2L L

s L

g g epsr g g

P

13

Reverse Engineering: Infer r

In the case of GE,

8.56%r

20.04 0.04 1.98

0.11 0.042 2 35.5

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”:

1

rPEG

0 1

2 1

1 1

( / )P epsPEG

eps dpsr

eps eps

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.

sg Lg

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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

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Can we say some about

?Lg

Why not assume

?F Lr r g

Risk (premium) and growth are now two sides of the same coin

2 1

10 1

1

/

1 /

F

F

r eps eps epsr

dpsr P eps

eps

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Empirical EvidenceDo 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

Lg

19

Pooled Cross-Sectional Regression

UNSYST ERNVAR ln(D/M) ln(M) LTG ln(B/M) RPIND Adj-R2

+++ +++ +++ +++ --- 21.3%

+++ +++ +++ +++ --- +++ 22.6%

+++ +++ +++ +++ +++ +++ 25.4%

++ +++ +++ +++ +++ +++ +++ 28.6%

UNSYST: Unsystematic risk as measured by the residual from the regression over prior year of a firm’s daily return on the daily market returnERNVAR: 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 equityln(M): Size as measured by the log of the total market value of equityLTG: I/B/E/S estimate of long-term growthln(B/M): Log of the ratio of the book value of equity to the market value of equityRPIND : 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 ERNVAR ln(D/M) ln(M) LTG ln(B/M) RPIND Adj-R2

+++ + +++ +++ --- 23.6%

+++ +++ +++ --- +++ 25.4%

+++ ++ +++ +++ +++ +++ 28.5%

+ ++ +++ +++ +++ +++ +++ 30.8%

UNSYST: Unsystematic risk as measured by the residual from the regression over prior year of a firm’s daily return on the daily market returnERNVAR: 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 equityln(M): Size as measured by the log of the total market value of equityLTG: I/B/E/S estimate of long-term growthln(B/M): Log of the ratio of the book value of equity to the market value of equityRPIND : Industry mean risk premium during the prior year for firms in the same industry as per the Fama-

French (1992) classification

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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.

Lgsg

Sg