Dividend Policy and Dividend Payment Behavior:
Theory and Evidence*
Cheng-Few Lee
(lee@business.rutgers.edu)
Distinguished Professor of Finance, Rutgers University
Visiting Chair Professor, NCTU, Taiwan
Editor of RQFA and RPBFMP
*Keynote Speech delivered at International Academy of Information Technology and
Quantitative Management (IAITQM), Suzhou, China, May 16-May 18, 2013
Outline
I.
Flow Chart of Dividend Policy and Dividend Behavior
a)
b)
c)
d)
Theory
Dividend Behavior Models
Price-dividend Multiplier Model
Integration of Dividend Policy and CAPM
II. Optimal Payout Ratio Under Uncertainty and The Flexibility
Hypothesis: Theory and Empirical Evidence (Lee et al. 2011, JCF)
a)
b)
c)
d)
e)
f)
g)
I.
Introduction
Review of the literature
The model
Optimum dividend policy
Relationship between the optimal payout ratio and the growth rate
Relationship between optional payout ratio and risks
Empirical evidence
Sustainable growth rate, optimal growth rate, and optimal payout
ratio: A joint optimization approach (Chen et al. 2013, JBF)
a)
b)
c)
d)
Introduction
The model
Stochastic growth rate and specification error on expected dividend
Empirical evidence
2
Outline
IV. Current vs. Permanent Earnings for Estimating Alternative
Dividend Payment Behavioral Model: Theory, Methods and
Applications(Lee et al. 2013)
a)
b)
c)
Introduction
Theoretical determination of firm’s permanent and transitory earnings
and dividends
Alternative methods for decomposing current EPS into permanent- and
transitory-EPS components
1.
2.
3.
4.
d)
Empirical results in estimating two alternative dividend behavior models
1.
2.
3.
V.
Darby’s (1974) method
Lee and Primeaux’s (1991) method
Garrett and Priestley’s (2000) Kalman filter method
Lambrecht and Myer’s (2012) method
Darby’s method and Lee and Primeaux’s method
Lambrecht and Myer’s method
Combined model
Concluding Remarks and Future Research
a)
b)
c)
d)
Conclusion for paper 1
Conclusion for paper 2
Conclusion for paper 3
Dividend policy, dividend payment behavior, and price-dividend
multiplier are interrelated.
3
Dividend Policy and Dividend Payment Behavior
A-1. Flow Chart of Dividend Policy and Dividend Behavior
Dividend
Policy
Dividend
Irrelevance Theory
Dividend
Relevance Theory
without Tax Effect
Empirical Work
Theory
Time-Series
Dividend
Relevance Theory
with Tax Effect
CAPM
Approach
Non-CAPM
Approach
Cross-Sectional
4
Dividend Policy and Dividend Payment Behavior
A-1. Flow Chart of Dividend Policy and Dividend Behavior
Dividend
Relevance Theory
without Tax Effect
Theory
Empirical Work
Time-Series
Dividend
Behavior
Cross-Sectional
Signaling
Hypothesis
Free Cash Flow
Hypothesis
Flexibility
Hypothesis
Life-Cycle
Theory
Price Multiplier
Model
Cov. btw
ROE and g
Partial Adjustment
Process
Information
Content or
Adaptive
Expectations
Myopic Dividend
Policy
Residual Dividend
Policy
5
Dividend Policy and Dividend Payment Behavior
A-2. Empirical Analyses in Dividend Policy Research
Descriptive Data
Analysis
Time Series
Cross-Sectional
Regression
Analysis
Time Series
Probit / Logit
Cross-Sectional
Fama-MacBeth
Procedure
Panel Data
Analysis
Seemly
Uncorrelated
Regression
(SUR)
Fixed Effect
Model
6
Dividend Policy and Dividend Payment Behavior
B. Theory
(i) Dividend irrelevance (M&M, 1961) and corner solution (DeAngelo and
DeAngelo, 2006)
(ii) Dividend relevance (Gordon, 1962; and Lintner, 1964)
- A bird in hand theory (Bhatacharya, 1979)
- Signaling theory (John & Williams, 1985; Miller & Rock, 1985; and Lee et al.,
1993, RQFA)
- Free cash flow theory (Eastbrook,1984; Jensen, 1986; Lang and
Lizenberger,1989; and Lee et al., JCF, 2011)
- Financial flexibility theory (Jagannathan et al., 2000, DeAngelo and DeAngelo,
2006; Blau and Fuller, 2008; and Lee et al., JCF, 2011)
- Life-cycle theory (DeAngelo et al., 2006; Chen et al., JBF, 2013)
- Lambrecht and Myer (2012 JF, A Lintner Model of Payout and Managerial
Rents)
- Lee et al. (2013, Current vs. Permanent Earnings for Estimating Alternative
Dividend Payment Behavioral Model: Theory, Methods and Applications) 7
Dividend Policy and Dividend Payment Behavior
C. Dividend Behavior Models
(i) Partial Adjustment Model (Lintner, 1956 AER)
Dt  a0  a1 Dt 1  a2 Et  et
(1)
Current earnings  CEt 
Dt  a0  a1 Dt 1  a2CEt  et (1a)
=> Lintner’s model
Permanent earnings  PEt  Dt  a0  a1 Dt 1  a2 PEt  et (1b)
=> Lee and Primeaux (1991) and Lambrecht and Myers (2012)
(ii) Mixed Partial Adjustment and Adapted Expectation (Fama & Babiak, 1968
JASA)
(iii) Generalized Dividend Forecasting Model (Lee et al., 1987, Journal of
Econometrics)
Dt  a1  a2 Dt 1  a3 Dt  2  a4 Et  vt
(2)
where a1   , a2   2      , a3  1   1    , a4  r  , and vt  ut  1    ut 1.
8
Dividend Policy and Dividend Payment Behavior
D. Price-Dividend Multiplier Model
(i) Friend and Puckett (1964, AER) have proposed the relationship between
stock prices, dividends, and retained earnings as follows:
where
Pti  A  BDti  CRti
i  1,
,N
t  1,
,T 
(3)
Pti , Dti , and Rti represtne price per share, dividend per share and retained earnings
per share, respectively.
Based upon Eq. (1) and discount cash flow model in terms of optimal
forecasting, Granger (1975 JF) has shown that B and C can be written in
terms of discount rate, a1 , and a2 of Eq. (1). Therefore, it can be concluded
that Eq. (3) is a theoretical derived model instead of an ad-hoc model.
(ii) Lee (1976, JF), Chang and Lee (1977, JFQA), and Gilmore and Lee (1986,
RES) have done empirical studies on price multiplier model.
9
Dividend Policy and Dividend Payment Behavior
E. Integration of Dividend Policy and CAPM
(Litzenberger and Ramaswamy, 1982)
E ( R j ) - rf  A  B  j  C ( d j - r f )
A is the excess return on a zero-beta portfolio with a dividend yield equal to
the riskless rate of interest, relative to the market portfolio.
B is similar to the market-risk premium concept in the original CAPM.
C represents a balancing of risks.
The further discussion of Eq. (4) can be found in Litzenberger and
Ramaswamy (1982) or Lee et al. (2009).
10
Optimal Payout Ratio Under Uncertainty and The Flexibility
Hypothesis: Theory and Empirical Evidence
(Lee et al. 2011, JCF)
Introduction
Dividend Policy
Miller and Modigliani (1961)
- Firm Value is independent of dividend policy.
- Assumptions of M&M theory
1) no tax.
2) no capital market frictions (i.e., no transaction cost, asset trade restriction, or
bankruptcy cost)
3) firms and investors can borrow or lend at the same rate.
4) firm financial policy reveals no information.
5) only consider no payout and payout all free cash flow.
DeAngelo and DeAngelo (2006)
> M&M (1961) irrelevance result is “irrelevant” because it only considers payout
policies that pay out all free cash flow.
> Payout policy matters when partial payouts are allowed.
11
Introduction
•
•
•
Signaling Hypothesis
- The signaling hypothesis suggests managers with better information than
the market will signal this private information using dividends.
- A company announcements of an increase in dividend payouts act as an
indicator of the firm possessing strong future prospects.
[Bhatacharya (1979), John and Williams (1985), Miller and Rock (1985),
and Nissam and Ziv (2001)]
Free Cash Flow Hypothesis (Agency Cost)
- Dividend payment can reduce potential agency problem.
[Eastbrook (1984), Jensen (1986), Lang and Lizenberger(1989), Lie (2000),
and Grullon et al. (2002)]
Financial Flexibility
- Management trades off two aspects of Dividends. One is financial
flexibility by not paying dividends. Another is deterioration on stock price if
not paying dividends.
12
[Blau and Fuller (2008)]
Introduction
1. Based on the DeAngelo & DeAngelo (2006) static analysis, we derive a
theoratical dynamic model and show that there exists an optimal payout ratio
under perfect market.
2. We derive the relationship between firm’s optimal payout ratio and its risks.
3. We derive the relationship between firm’s optimal payout ratio and its growth.
4. We further develop a fully dynamic model for determining the time optimal
growth and dividend policy under the imperfect market, the uncertainty of
the investment, and the dynamic growth rate.
5. We study the effects of the time-varying horizons, the degree of market
perfection, and stochastic initial conditions in determining an optimal growth
and dividend policy for the firm.
6. When the stochastic growth rate is introduced, the expected return may suffer
a model specification.
7. Empirical evidence of the determination of the optimal payout policy.
13
The Model for Optimal Dividend Policy
- Let r (t ) represent the initial assets of the firm and h(t )
represent the growth rate. Then, the earnings of this firm are
given by Eq. (1), which is
x(t )  r (t ) A(o)eht
- The retained earnings of the firm, y  t  , can be expressed as
y (t )  x(t )  m(t )d (t )
where m(t ) is the number of shares outstanding, and
d (t ) is dividend per share at time t.
14
The Model for Optimal Dividend Policy
The new equity raised by the firm at time t can be defined as
e(t )   p (t )m(t )
where  = degree of market perfection, 0 <   1.
Therefore, the investment in period t can be written as:
hA(o)e ht  x(t )  m(t )d (t )   m(t ) p (t )
Rearranging the equation above, we can get


d (t )   r (t )  h  A(o)e ht   m(t ) p (t ) m(t )
15
The Model for Optimal Dividend Policy
- The stock price should equal the present value of this certainty
equivalent dividend stream discounted at the cost of capital (k)
of the firm.
p(o)   dˆ (t )e kt dt
T
0
( A  bI  h) A(o)eth   m(t ) p(t )   A(o) 2  (t ) 2  (t ) 2 e 2th  kt
 [

]e dt
2
0
m(t )
m(t )
T
- A differential equation can be formulated:
 m(t )
p(t )  [
 k ] p(t )  G (t )
m(t )
where
(a  bI  h) A(o)eth   A(o)2  (t )2  (t )2 e2th
G(t ) 

m(t )
m(t )2
16
Optimal Dividend Policy
Optimal Payout Ratio when 
 1:
D(t ) (a  bI  h)  (h  (t ) 2  (t ) 2   (t ) 2  (t ) 2   (t ) 2  (t ) 2 )[e( h  k )(T t )  1] 

1 

x (t )
(a  bI ) 
 (t ) 2  (t ) 2 (h  k )

(a  bI  h)  [e( h  k )(T t )  1] 
 (t ) 2  (t ) 2  
=

1 
h

2
(a  bI ) 
(h  k ) 
 (t )  (t ) 2  
17
Relationship between the Optimal Payout Ratio
and the Growth Rate
[ D(t ) / x (t )]
h
  k   h  h  k  (T  t )  e( h k )(T t )  k 
1
k  he( h  k )(T t )
h
 (
)[
]  (1 
)

2
a  bI
hk
a  bI 

h  k 

- The sign is not only affected by the growth rate (h), but is also
affected by the expected rate of return on assets (a  bI ), the duration
of future dividend payments (T-t), and the cost of capital (k).
- Sensitivity analysis shows that the relationship between the optimal
payout ratio and the growth rate is generally negative.
=>a firm with a higher rate of return on assets tends to payout less
when its growth opportunities increase.
18
19
Relationship between the Optimal Payout Ratio
and the Growth Rate
[ D(t ) / x (t )]  (a  bI )  h  (T  t )  h(T  t )  1 




h
a

bI


1
1 
When h  (a  bI ) 
, there is a negative

2
(T  t ) 
relationship between the optimal payout ratio and the growth rate.
=>when a firm with a high growth rate or a low rate of return on
assets faces a growth opportunity, it will decrease its dividend
payout to generate more cash to meet such a new investment.
20
Implications
Hypothesis 1: firms generally reduce their dividend payouts when
their growth rates increase.
The negative relationship between the payout ratio and the growth ratio
in our theoretical model implies that high growth firms need to
reduce the payout ratio and retain more earnings to build up
“precautionary reserves,” while low growth firms are likely to be
more mature and already build up their reserves for flexibility
concerns.
[Rozeff (1982), Fama and French (2001), Blau and Fuller (2008), etc.]
21
Optimal Payout Ratio vs. Total Risk
  D(t ) / x (t ) 
  (t ) 2 

2

(
t
)


h
 (1 
a  bI
 e( h k )(T t )  1 
)

h

k


 High growth firms  h  a  bI  :
negative relationship between optimal payout ratio and total
risk.
 Low growth firms  h  a  bI  :
positive relationship between optimal payout ratio and total risk
22
Optimal Payout Ratio vs. Systematic Risk
  D(t ) / x (t ) 
  (t ) 2 

2

(
t
)


h
 (1 
a  bI
 e( h k )(T t )  1 
)

h

k


 High growth firms  h  a  bI  :
negative relationship between optimal payout ratio and
systematic risk.
 Low growth firms  h  a  bI  :
positive relationship between optimal payout ratio and
systematic risk
23
Implications
• Hypothesis 2: the relationship between the firms’ dividend payouts
and their risks is negative when their growth rates are higher than
their rates of return on asset.
- Flexibility Hypothesis
High growth firms need to reduce the payout ratio and retain more
earnings to build up “precautionary reserves.” These reserves
become more important for a firm with volatile earnings over time.
=> For flexibility concerns, high growth firms tend to retain more
earnings when they face higher risk.
24
Implications
• Hypothesis 3: the relationship between the firms’ dividend payouts
and their risks is positive when their growth rates are lower than
their rates of return on asset.
- Free Cash Flow Hypothesis
1. Low growth firms are likely to be more mature and most likely
already built such reserves over time.
2. They probably do not need more earnings to maintain their low
growth perspective and can afford to increase the payout [see
Grullon et al. (2002)].
3. The higher risk may involve higher cost of capital and make free
cash flow problem worse for low growth firms.
=> For free cash flow concerns, low growth firms tend to pay more
dividends when they face higher risk
25
Optimal Payout Ratio vs. Total Risk and
Systematic Risk
 (t )2
 (t )2
d [ D(t ) / x (t )]   d (
)  d(
)
2
2
 (t )
 (t )
where
h
e ( hk )(T t )  1
  (1 
)[
]
a  bI
hk
• Relative effect on the optimal dividend payout ratio
 (t )2
 (t )2
d[
]  d [
]
2
2
 (t )
 (t )
(30)
26
Optimal Payout Ratio when No Change in Risk
h
k  he( hk )(T t )
[ D(t ) / x (t )]  (1 
)[
]
a  bI
hk
When there is no change in risk, the optimal payout ratio is identical to
the optimal payout ratio of Wallingford (1972).
27
Joint Optimization of Growth Rate and Payout Ratio
(Chen et al. 2013 JBF)
• The new investment at time t is
dA  t 
 A t 
dt
t
g  s  ds

o
 g t  A o  e
 Y  t   D t   n t  p(t )  LA t 
Retained Earnings New Equity
where
New Debt
D  t   the total dollar dividend at time t;
p  t   price per share at time t;
  degree of market perfections, 0 <   l;
n  t  P t   the proceeds of new equity issued at time t;
L = the debt to total assets ratio
28
Joint Optimization of Growth Rate and Payout Ratio
• The model defined in previous slide is for the convenience purpose. If we
want the company’s leverage ratio unchanged after the expansion of assets
then we need to modify the equation as
t
g  s ds

o
A t   g t  A  o  e
 Y  t   D t   n t  p(t )  1  D / E  Y t   D t   n t  p (t ) 
we can obtain the growth rate as
g (t ) 
Our Model
ROE 1  d 
1  ROE 1  d 

 n t  p t  / E
1  ROE 1  d  
Higgins’ sustainable g
which is the generalized version of Higgins’ (1977) sustainable growth rate
model. Our model shows that Higgins’ (1977) sustainable growth rate is
under-estimated due to the omission of the source of the growth related to
new equity issue which is the second term of our model.
29
Joint Optimization of Growth Rate and Payout Ratio
Discount cash flow
p  o    dˆ  t  e kt dt
T
0
The price per share can be expressed as PV of future dividends with a
risk adjustment.
p o 
1

n o

T
0
g  s  ds

 1
2
  2 2 0 g  s  ds   kt

2
0



r t   g t  A  o  e
 a A  o   t  n t  e
n t 
 e dt




Future Dividends
t
t
Risk Adj.
=> maximize p(o) by jointly determine g(t) and n(t).
30
Optimal Growth Rate
g t  
*

r

r   rt    2
1  1   e
 go 
go r
go   r  go  e
 rt    2 
Logistic Equation – Verhulst (1845) => a convergence process
31
Case I: Optimal Growth Rate v.s. Time Horizon
g* t  
g *  t 
t

  r   r t    2 
 e
 
     2 
2
 

r  r t    2
1  1   e

g
o 
 


r
r 1 
 go
When g0  r , g*  t   0.
When g0  r , g*  t   0.
When g0  r , g*  t   0.
32
Case I: Optimal Growth Rate v.s. Time Horizon
Convergence Process
- Firms with different initial growth rates all tend to converge to their target
rates (ROE).
33
Case II: Optimal Growth Rate v.s. Degree of Market
Perfection
g *  t 


 r
 r t    2 2rt
  1 e
2
g


2


 o 
 
r  r t    2  
1  1   e

g
o 
 

2
If the market is more perfect   is larger  , the speed of convergence is faster.
34
Case II: Optimal Growth Rate v.s. Degree of Market
Perfection
35
Case III: Optimal Growth Rate v.s. ROE
g *  t 
r



t
 rt    2  
 rt    2   

go  go 1  e
  g o  r 
re





2



 




 g o   r  g o  e rt    2 


2
When initial growth rate is lower than the target rate (ROE),
positive.
g *  t 
r
is
=> If the target rate (ROE) is higher, the adjustment process will be
faster.
36
Case IV: Optimal Growth Rate v.s. Initial
Growth Rate
2
g *  t 
g o
g *  t 
g o

 r   rt    2
  e
 go 
 
r   rt    2 
1  1   e

g
o 
 

2
is always positive.
=> The higher initial growth rate is, the higher optimal growth rate at
each time.
37
38
Optimal Dividend Payout Ratio
D t 
 g * t  
 1 

Y  t  
r  t  
2
*
*
2
*
t

 2
 
kt    g *  s  ds     t     t  g  t    r  g  t      t  g  t  

0
1  e
W


3



2
*
 


2



t
r

g




t 



T
where W  
t
s
2
g  u  du  ks 2
 1
e 0
  s   r  g *  s   ds

*
• Assuming   1 and g *  t   g * ,


( g *  k )(T t )

2 
e
1 
D t  

g 

(
t
)
*
 1 
1

g




Y  t   r  t   
(g*  k ) 
 (t ) 2  


*
- Wallingford (1972), Lee et al. (2010)
39
Optimal Dividend Payout Ratio v.s. Growth Rate
[ D(t ) / Y (t )]
g *


  k   g * g *  k (T  t )  e( g *  k )(T t )  k 
1 k  g e
g 


 (
)[
]

(1

)
2
*
*

r t 
g k
r t  
g

k


  r (t )  g *  (T  t )  g * (T  t )  1 



*


r (t )  g


* ( g *  k )(T t )
*


The relationship between optimal dividend payout and growth rate is
negative in general cases.
40
Stochastic Growth Rate and Specification Error
dA  t 
dt
t
g  s  ds

o
 A t   g t  A  o  e
 Y  t   D  t    n  t  p (t )  LA t 
Retained Earnings New Equity
New Debt
When a stochastic growth rate is introduced,
g  t   N  g  t  ,  g2  t  
41
Stochastic Growth Rate and Specification Error

0 g  s ds   n t p t  Cov  r t , A o e 0 g  s ds   E  t e 0 g  s ds 
   
    

 r  t   g  t   A  o  e
  







E  d  t   

n t 
n t 
t
t
t
g  s  ds 


0
If Cov  r  t  , A  o  e
 is positive, d  t  in the previous analysis


is overestimated.
t
42
Hypotheses Development
• Hypothesis 1: The firm’s growth rate follows a mean-reverting process.
H1a: There exists a target rate of the firm’s growth rate, and the target rate is
the firm’s return on equity.
H1b: The firm partially adjusts its growth rate to the target rate.
H1c: The partial adjustment is fast in the early stage of the mean-reverting
process.
• Hypothesis 2: The firm’s dividend payout is negatively associated with the
covariance between the firm’s rate of return on equity and the firm’s growth
rate.
H2a: The covariance between the firm’s rate of return on equity and the firm’s
growth rate is one of the key determinants of the dividend payout policy.
43
Hypotheses Development
• Hypothesis 3: The firm tends to pay a dividend if its covariance
between the firm’s rate of return on equity and the firm’s growth
rate is lower.
H3a: The firm tends to stop paying a dividend if its covariance between
the firm’s rate of return on equity and the firm’s growth rate is
higher.
H3b: The firm tends to start paying a dividend if its covariance
between the firm’s rate of return on equity and the firm’s growth
rate is lower.
44
Sample
• Stock price, stock returns, share codes, and exchange codes are CRPS.
Firm information, such as total asset, sales, net income, and dividends
payout , etc., is collected from COMPUSTAT.
• The sample period is from 1969 to 2008.
• Only common stocks (SHRCD = 10, 11) and firms listed in NYSE,
AMEX, or NASDAQ (EXCE = 1, 2, 3, 31, 32, 33) are included.
• Utility firms and financial institutions (SICCD = 4900-4999, 60006999) are excluded.
• For the purpose of estimating their betas to obtain systematic risks,
firm years in our sample should have at least 60 consecutively
previous monthly returns.
45
Summary Statistics of Sample Firm Characteristics
46
46
Summary Statistics of Sample Firm Characteristics
47
Multivariate Regression
 payout ratio
i ,t
ln 
 1  payout ratioi ,t




    1 Riski ,t   2 Di ,t  g  ROA  Riski ,t  3Growth _ Optioni,t   4 ln( Size)i,t  Fixed Effect Dummies  ei


Flexibility Hypothesis
FCF Hypothesis
48
48
Empirical Results – Mean Reverting Process of firms’
growth rates
49
Partial Adjustment Model for the Growth Rate
If t , j  1 => partial adjustment
50
Cov. is negatively related to the dividend payouts
51
The higher of the Cov., the higher possibility to stop the cash dividends.
52
Current vs. Permanent Earnings for Estimating
Alternative Dividend Payment Behavioral Model:
Theory, Methods and Applications (Lee et al. 2013)
The main purposes of this paper are…
1. To theoretically explain why firms generally allocate permanent
earnings and transitory earnings between dividends payments and
retained earnings
2. To develop alternative methods for decomposing current earnings
and dividends into permanent and transitory components
3. To empirically estimate alternative dividend payment behavior models
by using two alternative permanent EPS estimates for both individual
firms and pooled data
4. To test Lambrecht and Myer’s theoretically results related to
alternative dividend payment behavior models.
53
Introduction
1. Earnings of a firm are allocated to retained earnings or dividend payments by
a financial decision.
2. The earnings of a firm can be classified into either permanent or transitory
components; permanent earning power creates the permanent component, and
the transitory component is composed of income of a temporary nature.
3. Forecasts of dividends are important to both security analysts and financial
managers, and either conditional or unconditional methods are generally used
to forecast dividend payments.
4. Lintner (1956) developed his well-known dividend payment behavior model
to describe how managers determine their dividend payment. This model has
been widely used in finance research (see Marsh and Merton, 1987; Lee and
Primeaux,1991; Garrett and Priestley, 2000; Lambrecht and Myer, 2012).
5. However, using current EPS to estimate Lintner’s dividend behavior model
might be also subject to measurement error problem (see Miller and
Modigliani, 1966)) .
54
Theoretical determination of firm’s permanent
and transitory earnings and dividends
• The permanent-income hypothesis explains that consumption is not a
function of current income but a function of permanent income (Milton
Friedman,1957).Current income is divided into two components:
E = EP + ET
(1)
where E is the current income per share of the firm, EP is the permanent
income per share of the firm, and ET is the transitory income per share of
the firm.
• Dividends can also be divided into two similar components:
D = D P + DT
(2)
where D is the current dividends per share paid by the firm, DP is the
permanent dividends per share paid by the firm, and DT is the transitory
dividends per share paid by the firm.
55
Theoretical determination of firm’s permanent
and transitory earnings and dividends
• Permanent dividends are dividends that the business firm
systematically pays based on its permanent earnings, dividends
paid out of transitory earnings would constitute extra
dividends.
• All income is either paid out in dividends or retained by the
business in the form of retained earnings:
E =EP+ ET, E − (DP + DT) − R = 0
(3)
where R is the retained earnings per share of the firm, the other
terms are as defined in Equations (1) and (2), and ET and DT are
‘‘random” or “chance” variations in income and dividends per
share.
56
Theoretical determination of firm’s permanent
and transitory earnings and dividends
• Different sources of dividend payment (i.e., permanent or
current income) may have different implications in
determining a firm’s dividend payment behavior.
• This condition provides the motivation for examining both
permanent and current earnings per share for describing a
firm’s dividend payment behavior in the empirical section of
this work.
• In the next section, we will discuss alternative methods for
decomposing current EPS into permanent and transitory EPS
components.
57
Alternative methods for decomposing current EPS into
permanent- and transitory-EPS components
• Darby’s (1974) method
• The relationship between current dividend and permanent earning can be
defined as
Di ,t     EiP,t  i ,t
(4)
where Di ,t and EiP,t are current DPS and permanent EPS for ith firm in period t
respectively.
• Since permanent earnings are not directly observable, we use Eq. (5) to
estimate EiP,t as:
EiP,t  (1  i ) Ei ,t  i (1  C) E Pi ,t 1,
0  i  1
(5)
where λi represents the weight used to calculate the permanent earnings per share
and C represents the trend rate of EPS growth.
• Initial value of permanent EPS EPi,0 and trend rate C can be derived from Eqs.
(6) and (7):
Log Ei,t = a1 + a2t + ut
(6)
(7) 58
E Pi ,0  eaˆ1 ,
log(1  C)  aˆ2
Alternative methods for decomposing current EPS into
permanent- and transitory-EPS components
• Lee and Primeaux’s (1991) method
By using the adaptive-expectation model, the permanent EPS, EPi,t, can be
determined as
EiP,t  (1  i ) Ei ,t  i E Pi ,t 1 ,
0  i  1
(9)
By Koyck transformation, we can use Eq. (10) to obtain λi for firm i:
Di ,t  0  0 Ei ,t   Di ,t 1
(10)
where 0   (1  i ), 0   (1  i ), and   i
• Then, by using estimated λi , current EPS, and initial permanent EPS which
was described in Darby’s method, we can estimate permanent EPS in
period t.
59
Alternative methods for decomposing current EPS into
permanent- and transitory-EPS components
Ei ,t  EiP,t  ET i ,t
EiP,t  EiP,t 1  t 1  t
t  t 1  t
60
Alternative methods for decomposing current EPS into
permanent- and transitory-EPS components
• 3.4 Lambrecht and Myer’s (2012) method
• Using the joint determination of manager’s rent and cash dividend payment
to equity holders, Lambrecht and Myer (2012) derive a Lintner dividend
payment behavior in terms of permanent income as:
dt  a0  a1dt 1  Yt  et
(14)
where dt and dt 1 are total dividend payout at time t and t-1 respectively; Yt is
the firm’s permanent income at time t.
• If the profit margin  t follows the autoregressive process  t   t 1  t ,
then permanent income Yt can be simplified as:
i
(15)
Y 
( K    (1     )TD )
i ,t
1  i  i
i
i ,t
i
i
i ,t 1
where Kii,t is total operating income without corporate tax for ith firm in
period t; TDi ,t 1 is the total debt for ith firm in period t-1; i is interest rate; and
is the autoregression coefficient for operating income of the firm i.
61
Alternative methods for decomposing current EPS into
permanent- and transitory-EPS components
• 3.4 Lambrecht and Myer’s (2012) method
• Lambrecht and Myer (2012) claim that Lintner model as traditionally
estimated can be defined as:
dt  b0  bTE
1
t  b2 dt 1  ut
(16)
• Their true model is:
 SOA
 2  SOA
 (1   ) SOA
dt   
TEt  SOAdt 1 
t 
TDt 1  et
1  
1  
1  
(17)
where dt  dt  dt 1 ; the current reported earnings is TEt  pt   t  TDt 1; pt and  t
are permanent and transitory components respectively. TDt 1 is the component
neither permanent nor transitory component of earnings. SOA is the speed of
adjustment;  is the constant term of dividend behavior model, it generally
used to measure the degree of reluctance to cut dividend,  defined as
percentage of earnings paid as cash dividend,  =1/(1+  ).
62
Alternative methods for decomposing current EPS into
permanent- and transitory-EPS components
• 3.4 Lambrecht and Myer’s (2012) method
• If does not approach  to 1, then equation (17) can be modified as
P
dt  b0  bTE
1
t  b2 dt 1  b3 TDt 1  ut
(18)
where TE Pt is the estimated permanent earnings.
• Equation (18) is obtained by combining Lambrecht and Myer’s (2012)
theory and estimating permanent earnings estimated by either Darby’s or
Lee and Primeaux’s method.
• This specification takes care both specification errors and the transitory
components of earnings. This new specification is most important
contribution of this research.
63
Empirical results in estimating three alternative
dividend behavior models
• Sample
• EPS and DPS data of 608 firms from Compustat which has at least
30 years data ended in 2011 to perform the empirical studies (see
Appendix C).
• The methods used to do the empirical studies include
(1) Darby’s method and Lee and Primeaux’s method
(2) Lambrecht and Myer’s method
(3) combined model as defined in Equation (18)
64
Darby’s and Lee and Primeaux’s methods
• We use current and permanent EPS measures to estimate following two
alternative dividend payment behavior models as:
Di ,t  c0  c1Ei ,t  c2 Di ,t 1  ui ,t
(19a)
Di ,t  c0  c1EiP,t  c2 Di ,t 1  ui ,t
(19b)
Di ,t  c '0  c '1 Ei ,t  c '2 Di,t 1  c3 Di,t 2  ui,t
(20a)
Di ,t  c '0  c '1 EiP,t  c '2 Di,t 1  c3 Di,t 2  ui,t
(20b)
• Following Lee and Chen (2013), we now analyze the biased associated with
estimated c1 and c2 as follows:
Case 1: when COV (EiP,t , Di,t 1 )  0,
12 ( D D  c2 D2 )
c112
(21a)
ˆ
plim cˆ1  c1  2
,
plim
c

c


0
2
2
( E  12 )
 D2 ( E2  12 )
i ,t i ,t 1
P
i ,t
i ,t 1
i ,t 1
P
i ,t
Case 2: when COV (EiP,t , Di,t 1 )  0,
plim cˆ1  c1 
E
2
P
i ,t


c1 12
 12


, plim cˆ2  c2  c1bD E P
2
2
2
2
i ,t 1 i ,t
  1   E P (1  RE P D ) 
 bD E P   1
i ,t 1 i ,t
i ,t
i ,t i ,t 1


(21a)
where  12 is the variance of EiT,t , bD E is the auxiliary regression coefficient of a
regressing Di,t 1 on EiP,t , and RE2 D is the correlation coefficient between EiP,t and Di ,t 1 .
P
i ,t 1 i ,t
P
i ,t i ,t 1
65
Darby’s and Lee and Primeaux’s methods
• Equations (21a) and (21b) imply that the estimated c1 and c2
are downward biased. Hence, the estimated intercept as
defined in Equation (21c) is upward biased.
(21c)
cˆ0  Di ,t  cˆ1Ei ,t  cˆ2 Di ,t 1
• Therefore, we need to deal with this kind of errors-in-variable
problem.
• First, we use Darby’s and Lee and Primeaux’s methods to
estimate permanent EPS. Then we will use DPS and both
current EPS and permanent EPS to estimate equations (19a),
(19b), (20a), and (20b) for individual firms and pooled data.
66
Darby’s and Lee and
Primeaux’s methods
Table 1 (A)
Individual Regression Results
for Equations (19a), (19b),
(20a) and (20b)
• Current EPS is used in Eqs.
(19a) and (20a).
• The permanent EPS calculated
by Darby’s method, is used in
Eqs. (19b) and (20b).
• The permanent EPS calculated
by Lee and Primeaux’s
method, is used in Eqs. (19b)*
and (20b)*.
67
Darby’s and Lee and
Primeaux’s methods
Table 1(B).
Partial Adjustment Coefficient
and Long-Term Payout Ratios
• Current EPS is used in Eqs.
(19a) and (20a).
• The permanent EPS calculated
by Darby’s method, is used in
Eqs. (19b) and (20b).
• The permanent EPS calculated
by Lee and Primeaux’s
method, is used in Eqs. (19b)*
and (20b)*.
68
Darby’s and Lee and Primeaux’s methods
• Table 2. Alternative EPS and Payout Ratios
• According to the average estimated λi by using Darby’s and Lee and
Primeaux’s methods, it implies that Lee and Primeaux’s method for
estimating permanent earnings weights more heavily on current
earnings than those from Darby’s method.
69
Darby’s and Lee and
Primeaux’s methods
Table 3
Pooled Regression Results
for Equations (19a), (19b),
(20a) and (20b)
• Current EPS is used in Eqs.
(19a) and (20a).
• The permanent EPS calculated
by Darby’s method, is used in
Eqs. (19b) and (20b).
• The permanent EPS calculated
by Lee and Primeaux’s
method, is used in Eqs. (19b)*
and (20b)*.
70
Lambrecht and Myer’s method
• Since i is not available for individual firm, therefore, we use limiting
definition of Lambrecht and Myers’ (2012) method (see equation (15)) to
estimate permanent income and apply permanent income to test dividend
payment behavior models:
di ,t  a0  a1TEi ,t  a2 d i ,t 1  ei ,t
(22a)
di ,t  a0  a1Yi ,t  a2 di ,t 1  ei ,t
(22b)
(23a)
di ,t  a0  a1TEi ,t  a2 di ,t 1  a3di ,t  2  ei ,t
(23b)
di ,t  a0  a1Yi ,t  a2 di ,t 1  a3di ,t 2  ei ,t
• In addition, Lambrecht and Myers (2012) show that the Lintner model may
be subject to the model misspecification. We therefore test the model
misspecification by using Equation (24):
(24)
di ,t  a0  a1TEi ,t  a2 di ,t 1  a3 iTDi ,t 1  ei ,t
71
Lambrecht and Myer’s method
Table 4
Individual Regression
Results for Equations (22a),
(22b), (23a), (23b) and (24)
• There are 25.45% of firms
whose dividend payouts
can be determined by their
interest expenses.
• It indicates that there exists
specification error in
Lintner’s model in terms of
current earnings.
72
Combined model
• We will modify Equation (18) in terms of EPS and DPS as follows:
Di ,t  b0  b1Ei ,t  b2 Di ,t 1  b3 Ii ,t 1  ui ,t
(25a)
Di ,t  b0  b1EiP,t  b2 Di ,t 1  b3 Ii ,t 1  ui ,t
(25b)
where Di,t and Di,t-1 are dividend per share for firm i at time t and t-1,
respectively; Ei,t and EPi,t are current and permanent EPS for firm i at time t ;
Ii,t-1 is the interest expense per share firm i at time t-1.
• Eqs. (25a) and (25b) can be used to test whether the companies’ annual
EPS is following the random walk or not and also to test whether
Lambrecht and Myers’s budget constraint in Eq. (26) is held for individual
firm or not.
dt  rt   t ( K )  TDt 1  (TDt  TDt 1 )
(26)
where dt is total dividend payout at time t , TDt and TDt 1 is the total debt in
period t and t-1, respectively;  is interest rate; rt is managerial rents at time
t;  t ( K ) is gross profit at time t.
73
Combined model
Table 5
Individual Regression Results
for Equations (25a) and (25b)
• If the budget constraint does
not hold, then the term
associated with interest
expense will not necessary
exist.
• There are only 22.64%,
21.16%, or 22.15% firms
with budget constraints hold
under Lambrecht and Myers
theoretical model.
74
Combined model
Table 6.
Pooled Regression Results for
Equations (25a) and (25b)
• The insignificant coefficient
of interest expense per share
implies that the permanent
EPS not only can remove
random fluctuation of EPS
but also can remove parts of
misspecification error which
is shown by Lambrecht and
Myers.
75
Conclusion - 1
• We derive an optimal payout ratio using an exponential utility
function to derive the stochastic dynamic dividend policy
model.
- Different from M&M model, our model considers 1) partial
payout; 2)uncertainty (risks); 3) stochastic earnings.
• A negative relationship between the optimal dividend payout
ratio and the growth rate.
• The relationship between firm’s optimal payout ratio and its
risks depends on its growth rate relative to its ROA.
- high growth firms pay dividends due to the consideration of
flexibility and low growth firms pay dividends due to the
76
consideration of free cash flow problem.
Conclusion - 2
• We derive a dynamic model of optimal growth rate and payout
ratio which allows a firm to finance its new assets by retained
earnings, new debt, and new equity.
• The optimal growth rate follows a convergence processes, and
the target rate is firm’s expected ROE.
• The firm’s dividend payout is negatively associated with the
covariance between the firm’s rate of return on equity and the
firm’s growth rate.
• The firm tends to pay a dividend if its covariance between the
firm’s rate of return on equity and the firm’s growth rate is
lower.
77
Potential Future Research
1. Time-series v.s. cross-sectional research
2. Relationship among discount cash flow, dividend partial
adjustment model, and price multiplier model
3. Tax effect on dividend policy in terms of CAPM with
dividend Effect
4. Limitations of cross-sectional approach to investigate
dividend policy
5. We need to use dividend behavior model to supplement crosssectional approach to obtain more meaningful conclusion for
decision making.
6. The impacts of Integrated Tax System can be further explored.
78
Conclusion - 3
• Based upon the theories and methods developed by Marsh and Merton
(1987), Lee and Pri-meaux (1991), Garrett and Priestley (2000), and
Lambrecht and Myers (2012), we perform both theoretically analyses and
empirical studies in this paper.
The major findings are:
• The average long-term payout ratio is downward biased and the average
estimated intercept is upward biased when current instead of permanent
EPS are used in dividend behavioral model.
• We also empirically investigate Lambrecht and Myers’ misspecification
issue and find that interest expense per share might be important for
estimating dividend behavior model for some firms
Future research:
• Revise Lambrecht and Myers’ permanent earnings measurement
• Extend aggregate dividend behavior model to individual dividend behavior
model to test either signaling theory hypothesis or free cash flow
79
hypothesis for individual firms.
Reference
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Ang, J. S. (1975). “Dividend Policy: Informational Content or Partial Adjustment?” Review of Economics and
Statistics 57: 65-70.
Ando, A., and Modigliani. F. (l963). “The ‘Life Cycle’ Hypothesis of Saving.” American Economic Review 53: 55-84.
Almeida, H., M. Campello, and A. F. Galvao Jr. (2010). Measurement errors in investment equations, Review of
Financial Studies, 23, 3279-3328.
Bhattacharya, S., 1979. Imperfect information, dividend policy, and “the bird in the hand” fallacy. Bell J. Econ. 10,
259–270.
Black, F. (1976). “The Dividend Puzzle.” Journal of Portfolio Management II (Winter): 5-8.
Blau, B. M., and K. P. Fuller, 2008, Flexibility and dividends, Journal of Corporate Finance 14, 133-152.
Cochran, W. G. (1970). “Some Effects of Errors of Measurement on Multiple Correlation.” Journal of American
Statistical Association 65: 22-34.
Chang H.S. and Lee, c. F. (1977) “Using Pooled Time-Series and Cross Section Data to Test the Firm and Time
Effects in Financial Analysis,” Journal of Financial and Quantitative Analysis
Chen, H. Y., Gupta, M. C., Lee, A. C., and Lee, C. F. (2013). “Sustainable Growth Rate, Optimal Growth Rate,
and Optimal Payout Ratio: A Joint Optimization Approach.” Journal of Banking & Finance 37, 1205-1222.
Darby, M. R. (1972). “The Allocation of Transitory Income Among Consumers’ Assets.” American Economic
Review (September): 928-41.
Darby, M. R. (1974), “The Permanent Income Theory of Consumption—A Restatement.” Quarterly Journal of
Economic, (May): 228-50.
DeAngelo, H., and L. DeAngelo, 2006, The irrelevance of the MM dividend irrelevance theorem, Journal of
Financial Economics 79, 293-315.
Dichev, I. D., and Tang, V. W. (2009) “Earnings volatility and earnings predictability.” Journal of Accounting and
Economics 47, 160–181.
Duesenberry, J. S. (1949). Income, Savings, and the Theory of Consumption Behavior. Cambridge MA: Harvard
University Press.
Easterbrook, F.H., 1984. Two agency-cost explanations of dividends. Am. Econ. Rev. 74, 650–659
80
Eisner, R. (1967). “A Permanent Income Theory of Investment.” American Economic Review 57: 363-90. .
Reference
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Eisner, R. (1978). Factors in Business Investment. General Series No. 102. Washington. D.C.: National Bureau of
Economic Research
Fama, E. F., and Babiak, H. (1968). “Dividend Policy: An Empirical Analysis.” Journal of American Statistical
Association 63: 1132-61.
Fama, E. F., and K. R. French, 2001, Disappearing dividends: Changing firm characteristics or lower propensity to
pay? Journal of Financial Economics 60, 3-43.
Frankel, R., and Litov, L. (2009) “Earnings persistence.” Journal of Accounting and
Economics 47, 182–190.
Friedman, M. (1957). A Theory of the Consumption Function. Princeton. NJ: Princeton University Press.
Friend, I. and Puckett, M. (1964) “Dividend and Stock Prices” American Economic Review, 54, 656-682.
Garrett, I. and Priestley, R. (2000). “Dividend Behavior and Dividend Signaling.” The Journal of Financial and
Quantitative Analysis (June) 35: 173-189.
Gilmore R.H. and Lee, C. F. (1986) “Empirical Tests of Granger Proposition on Dividend Controversy,” Review of
Economics and Statistics
Gordon, M. J., 1962, The savings investment and valuation of a corporation, Review of Economics and Statistics
44, 37-51.
Granger, C. W. J. (1975) “Some Consequences of The Valuation Model When Expectations Are Taken to Be
Optimum Forecasts”. Journal of Finance, 30, 135-145.
Grullon, G., R. Michaely, and B. Swaminathan, 2002, Are dividend changes a sign of firm maturity? Journal of
Business 75, 387-424.
Higgins, R. (1977). “How Much Growth Can a Firm Afford?” Financial Management 6, 7-16.
Higgins R. C. (1981) “Sustainable growth under Inflation.” Financial Management 10, 36-40.
Higgins R. C. (2008) Analysis for financial management, 9th ed. (McGraw-Hill, Inc, New York, NY).
Jagannathan, M., Stephens, C.P., Weisbach, M.S., 2000. Financial flexibility and the choice between dividends
and stock repurchases. J. Financ. Econ. 57, 355–384.
Jensen, M.C., 1986. Agency costs of free cash flow, corporate finance, and takeovers. Am. Econ. Rev. 76, 323–81
329.
Reference
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
John, K., Williams, J., 1985. Dividends, dilution, and taxes: a signaling equilibrium. J. Finance 40, 1053–1070.
Johnston. J. (1972). Econometric Methods, 2nd ed. New York; McGraw-Hill.
Kmenta, J. (1986). Elements of Econometrics, second edition. New York: Macmillan.
Lambrecht, B. M. and Myers, S. C. (2012). “A Lintner Model of Payout and Managerial Rents.” Journal of Finance
(October) 67: 1761-1810
Lang, L.H.P., Litzenberger, R.H., 1989. Dividend announcements: cash flow signaling vs. free cash flow
hypothesis? J. Financ. Econ. 24, 181–191
Latane, H. A., and Jones, C. P. (1979). “Standardized Unexpected Earnings-1971-77.” Journal of Finance 34: 71724,
Lee, A. C., J. C. Lee and Lee, C. F. (2009) Financial Analysis, Planning, and Forecasting: Theory and Application,
2ed. World Scientific Publishing Co..
Lee, C. F., and Chen, H.Y. (2013). “Alternative Errors-in-Variables Models and Their Applications in Finance
Research,” working paper.
Lee, C. F., M. C. Gupta, H. Y. Chen, and Lee, A. C. (2011) “Optimal payout ratio under uncertainty and the
flexibility hypothesis: Theory and empirical evidence.” Journal of Corporate Finance, 17: 483-501.
Lee, Cheng F., Shi, J., 2010. Application of alternative ODE in finance and econometric research. In: Lee, Cheng
F., Lee, Alice C., John, Lee (Eds.), Handbook of Quantitative Finance and Risk Management. Springer, pp. 1293–
1300.
Lee, C. F. and Han, Dong. (1993). “Dividend Policy under Conditions of Capital Markets and Signaling
Equilibrium,” Review of Quantitative Finance and Accounting.
Lee, C. F., and Primeaux, W.J.(1991). “ Current- Versus Permanent- Dividend Payments Behavioral Model:
Methods and Applications,” Advances in Quantitative Analysis of Finance and Accounting. Vol 1 (Part A) 109- 130.
Lee, C. F., M. Djarraya, and C. Wu. (1987) “A further empirical investigation of the dividend adjustment process.”
Journal of Econometrics,267-285.
Lee, C. F. (1976) “Functional Form and the Dividend Effect of the Electric Utility Industry,” Journal of Finance
Leibenstein, H. (1950). “Bandwagon, Snob, and Veblen Effects in the Theory of Consumers’ Demand,” Quarterly
82
Journal of Economics (May): 183-207.
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Lie, E., 2000. Excess funds and agency problems: an empirical study of incremental cash disbursements. Rev.
Financ. Stud. 13, 219–248.
Lintner, J. (1956). “Distribution of Income of Corporations Among Dividends, Retained Earnings, and Taxes.”
American Economic Review (May): 97-113.
Lintner, J., 1964, Optimal dividends and corporate growth under uncertainty, Quarterly Journal of Economics 78,
49-95.
Litzenberger,R.H, and Ramaswamy, K., 1982. The Effects of Dividends on Common Stock Prices Tax Effects of
Information Effects? J. Finance 37, 429-443.
Marsh, T.A. and Merton, R.C. (1987). “Dividend Behavior for the Aggregate Stock Market.” The Journal of
Business (Jan) 60: 1-40.
Miller, M. H., and Modigliani, F. (1961). “Dividend Policy, Growth and Valuation of Shares.” Journal of Business 34
(October): 411-33.
Miller, M. H., and Modigliani, F. (1966). “Some Estimates of the Coast of Capital to the Electric Utility Industry.”
American Economic Review 56: 334-91.
Miller, M.H., Rock, K., 1985. Dividend policy under asymmetric information. J. Finance 40, 1031–1051.
Miller, M. H., and Scholes, M. S. (1982). “Dividends and Taxes: Some Empirical Evidence.” Journal of Political
Economy.
Modigliani, F., and Miller, M. H. (1958). “The Cost of Capital, Corporation Finance and The Theory of Investment.”
American Economic Review 4B: 261-97.
Modigliani, F., and Miller, M. H. (1963). “Corporate Income Tax and the Cost of Capital: A Correction.” American
Economic Review 53: 433-43.
Nissim, D., Ziv, A., 2001. Dividend changes and future profitability. J. Finance 56, 2111–2133.
Peterson, W. C. (1978). Income. Employment and Growth. 4th ed. New York: W. W. Norton.
Rozeff, M. S., 1982, Growth, beta and agency costs as determinants of dividend payout ratios, Journal of Financial
Research 5, 249-259.
Wallingford, II, B. A., 1972a, An inter-temporal approach to the optimization of dividend policy with predetermined
investments, Journal of Finance 27, 627-635.
Wang, N., (2003). “Caballero Meets Bewley: The Permanent-Income Hypothesis in General Equilibrium.”
83
American Economic Review 93, 927-936.
Weston, F.J., Brigham, E., and Besley,S., (2004) “Essentials of Managerial Finance,” Cengage South-Western