Dividend Policy:
Theory and Empirical Evidence
Cheng-Few Lee
Rutgers University
3
4
Announcement for
Handbook of Financial Econometrics and Statistics
• The purpose of this handbook is to publish original papers that apply
either econometrics or statistics methods in important topics of
empirical finance research. Chapters that update or expand upon
well-known empirical papers are also acceptable. In this handbook,
each paper should have appendices of 5 to 15 pages to demonstrate
how empirical research has been executed. The tentative outline of
this handbook is as follows:
• Part I. Introduction
In this introduction, we will discuss overall application of
econometrics and statistics in finance accounting research.
5
• Part II. Overview of Financial Econometrics and Statistics
A. Financial Econometrics
B. Financial Statistics
• Part III. Financial Econometrics
A. Asset Pricing Research
B. Corporate Finance Research
C. Financial Institution Research
D. Investment and Portfolio Research
E. Option Pricing Research
F. Future and Hedging Research
G. New Financial Products Research
H. Mutual Fund Research
I. Financial Accounting Research
6
• Part IV. Financial Statistics
A. Asset Pricing Research
B. Investment and Portfolio Research
C. Credit Risk Management Research
D. Market Risk Research
E. Operation Risk Research
F. Option Pricing Research
G. Mutual Fund Research
H. Value at Risk Research
• We expect to include approximately 100 chapters in this handbook,
which will published online and in three print volumes by Springer
in 2012. Anybody who wishes to contribute a chapter to this
handbook please send a proposal to Professor Cheng-Few Lee at the
email:
lee@business.rutgers.edu
7
Policy Framework of Finance Research
• Investment Policy
• Financing Policy
• Production Policy
• Dividend Policy
(a) Forecasting Model
(i) Partial Adjustment Model (Lintner, 1956 AER)
(ii) Mixed Partial Adjustment and Adapted Expectation (Fama & Babiak, 1968
JASA)
(iii) Generalized Dividend Forecasting Model (Lee et al., 1987, Journal of
econometrics)
D*  rEt*


Dt  Dt 1  a  b1 D*  Dt 1  ut

Et*  Et*1  b2 E *  Et 1
then

Dt  Dt 1  ab2  1  b1  b2  Dt 1  1  b2 1  b1  Dt 2  rb1b2 Et  1  b2  ut 1  ut
8
Policy Framework of Finance Research
(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)
- Free cash flow theory (Eastbrook,1984; Jensen, 1986; and Lang and
Lizenberger,1989)
- Financial flexibility theory (Jagannathan et al. 2000, DeAngelo and
DeAngelo, 2006; Blau and Fuller, 2008)
9
Abstract
We develop a theoretical model of the optimal payout ratio under
perfect markets and uncertainty. First, we theoretically derive the
proposition of DeAngelo and DeAngelo's (2006) optimal payout policy
when a partial payout is allowed. Second, we theoretically derive the
impact of total risk, systematic risk, and growth rate on the optimal payout
ratio.
Taking the time varying growth rate, the imperfect market, and debt
issuing into account, we further derive a dynamic model which jointly
optimizes growth rate and payout ratio. We also derive a logistic equation
which was first introduced by Pierre Verhulst (1845 and 1847) to obtain
the optimal growth rate.
Using the U.S. data during 1969 to 2008 to investigate the impact of
total risk, systematic risk, and growth rate on the optimal payout ratio. We
find that the relationship between the payout ratio and risk is negative (or
positive) when the growth rate is higher (or lower) than the rate of return 10
on assets. In addition, we also find that a company will generally reduce its
Outline of Paper I
1. Introduction
Policy Framework of Finance Research
2. The Model
3. Optimal Dividend Policy
4. Implications
4.1 Case I: Total Risk
4.2 Case II: Systematic Risk
4.3 Total Risk and Systematic Risk
4.4 No Change in Risk
5. Relationship between the Optimal Payout Ratio and the Growth Rate
6. Empirical Evidence
6.1 Sample Description
6.2 Multivariate Analysis
6.3 Fama-MacBeth Analysis
6.4 Fixed Effect Analysis
7. Summary and Concluding Remarks
11
Introduction & Motivation of Paper I
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 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.
12
Introduction & Motivation of Paper I
•
•
•
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.
13
[Blau and Fuller (2008)]
Introduction & Motivation of Paper I
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.
14
Introduction & Motivation of Paper I
• Paper I:
1. 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.
(depends on its growth rate relative to its ROA)
3. We derive the relationship between firm’s optimal payout ratio and
its growth.
(Negative)
4. Empirical evidence on the optimal payout ratio.
(support our theoretical results)
Paper I
- 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
(1)
- The retained earnings of the firm, y  t  , can be expressed as
y(t )  x(t )  m(t )d (t )
(2)
where m(t ) is the number of shares outstanding, and
d (t ) is dividend per share at time t.
Paper I
The new equity raised by the firm at time t can be defined as
e(t )   p(t )m(t )
(3)
where  = degree of market perfection, 0 <   1.
Therefore, the investment in period t can be written as:
hA(o)eht  x(t )  m(t )d (t )   m(t ) p(t )
(4)
Rearranging Eq.(4), we can get


d (t )   r (t )  h  A(o)e ht   m(t ) p(t ) m(t )
(5)
Paper I
Because r (t ) (,  (t )2 ) ,


E[d (t )]     h A(o)eht   m(t ) p(t ) / m(t )
(6)
Var[d (t )]  A(o)2  (t ) 2 e2th / m2 (t )
Postulate a exponential utility function, U[d (t )]  e d (t )
We can get a certainly equivalent dividend stream
(  h) A(o)eth   m(t ) p(t )   A(o)2  (t ) 2 e2th
d (t ) 

m(t )
m(t )2
(9)
Paper I
Under CAPM, r (t )  a  bI (t )   (t )
I is the market index, and
(10) .
 (t ) is the correlation coefficient between r (t ) and I .
 (t )2  (t )2 : nondiversifiable risk;
(1   (t )2 ) (t )2 : diversifiable risk.
The unsystematic risk usually can be diversified away by the
investors. Therefore, Eq.(9) can be revised as
th
2
2
2 2th

(
a

bI

h
)
A
(
o
)
e


m
(
t
)
p
(
t
)

A
(
o
)

(
t
)

(
t
)
e
ˆ

d (t ) 

m(t )
m(t )2
(12)
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
(14)
- Eq.(14) can be formulated a differential Equation:
 m(t )
p(t )  [
 k ] p(t )  G (t )
(17)
m(t )
(a  bI  h) A(o)eth   A(o)2  (t ) 2  (t ) 2 e2th
where G(t ) 

m(t )
m(t )2
(18)
Optimal Dividend Policy
- Solve the differential equation
1
p (o ) 
m(o)
 (a  bI  h) A(o)e
T
0
th

m(t ) 1    A(o) 2  (t ) 2  (t ) 2 e2th m(t ) 2 e  kt dt
(20)
- Optimization=>max p(0)
(2   )  A(o)eth  (t )2  (t ) 2
=> m(t ) 
(1   )(a  bI  h)
(22)
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) 
 (t )2  (t ) 2  
 [e( h k )(T t )  1] 
=

1 
h
2
2 
(a  bI ) 
(
h

k
)

(
t
)

(
t
)




If
  1 , the optimal payout ratio still exists.
(26)
Implications:
Optimal Payout Ratio vs. Total Risk
  D(t ) / x (t ) 
  (t ) 

2

(
t
)


2
h
 (1 
a  bI
 e( h  k )(T t )  1 
)

h

k


(27)
- 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.
23
Implications:
Optimal Payout Ratio vs. Systematic Risk
  D(t ) / x (t ) 
  (t ) 

2

(
t
)


2
h
 (1 
a  bI
 e( h  k )(T t )  1 
)

h

k


(28)
- 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.
- Financial Flexibility:
Firm’s risks are related to its financial risk from financial leverage.
When a firm faces higher financial risk, it will decrease its payout ratio
to obtain more cash for the preparation for the interest payment in the
future. [Jagannathan et al. (2000), DeAngelo and DeAngelo (2006), and
Blau and Fuller (2008)]
24
Implications:
Optimal Payout Ratio vs. Total Risk and Systematic Risk
 (t )2
 (t )2
d[ D(t ) / x (t )]   d (
)   d(
)
2
2
 (t )
 (t )
(29)
h
e ( hk )(T t )  1
)[
]
where   (1 
a  bI
hk
- Relative effect on the optimal dividend payout ratio
 (t )2
 (t )2
d[
]  d [
]
2
2
 (t )
 (t )
(30)
25
Implications:
Optimal Payout Ratio When No Change in Risk
h
k  he( hk )(T t )
[ D(t ) / x (t )]  (1 
)[
]
a  bI
hk
(30)
When there is no change in risk, the optimal payout ratio is
identical to the optimal payout ratio of Wallingford (1972).
26
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 

(32)
- 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.
27
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


(34)
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.
28
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.
29
Summary Statistics of Sample Firm Characteristics
30
Summary Statistics of Sample Firm Characteristics
31
Multivariate Regression – Fama MacBeth Model
 payout ratioi 
ln 
   1BetaRiski  2Growth _ Optioni  3 ln( Sizei )  ei
 1   payout ratio  
i 

32
Multivariate Regression (with Growth Dummy)
 payout ratioi 
ln 
   1BetaRiski  2 D  g  ROA  Riski  3Growth _ Optioni  4 ln(Sizei )  ei
 1   payout ratio  
i 

33
Multivariate Regression – Fixed Effect Model
 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


34
Outline of Paper II
• Introduction and Motivation
• Model
• Optimal Growth Rate
- Optimal Growth Rate v.s. Time Horizon
- Optimal Growth Rate v.s. Degree of market Perfection
- Optimal Growth Rate v.s. ROE
- Optimal Growth Rate v.s. Initial Growth Rate
• Optimal Dividend Policy
- Optimal Dvidend Policy v.s. Optimal Growth Rate
• Stochastic Growth Rate
• Conclusion
35
Introduction & Motivation of Paper II
Dividend Policy and Growth Rate
•
Gordon (1962), Lintner (1964), Lerner and Carleton (1966),
Modigliani and Miller (1961), Miller and Modigliani (1966)
- Relationships between optimal dividend policy and rate of return under no
growth and under both internally and externally, financed growth assumptions.
•
Higgins (1977, 1981, and 2008)
- Sustainable growth rate: assuming that a firm can use retained earnings and
issue new debt to finance the growth opportunity of the firm.
•
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.
36
Introduction & Motivation of Paper II
• Rozeff (1982)
- The optimal dividend payout is related to the fraction of insider holdings, the
growth of the firm, and the firm’s beta coefficient.
• DeAngelo et al. (1996 and 2006) Grullon et al. (2002)
-
Increases in dividends convey information about changes in a firm’s life cycle from
a higher growth phase to a lower growth phase.
Is there an optimal dividend policy for a firm under the
imperfect market, the uncertainty of the investment, and the
dynamic growth rate?
37
Introduction & Motivation of Paper II
Paper II
• We develop a fully dynamic model for determining the time optimal
growth and dividend policy under stochastic conditions.
- Given the uncertainty of ROE, the theoretical model shows the existence
of an optimal payout ratio and an optimal growth rate by maximizing firm
value.
2. 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.
- A convergence process in the optimal growth rate.
- A negative relationship between optimal dividend payout and optimal
growth rate.
3. When the stochastic growth rate is introduced, the expected return
may suffer a model specification.
38
Paper II
The total asset of a firm at time t
t
A t   A  o  eo
where
g  s ds
(1)
A o  initial total asset
At   total assets at time t
g t   time variant growth rate
s  the proxy of time in the integration.
39
Paper II
• The earnings at time t is a stochastic variable.
t
g  s  ds

o
Y  t   ROA  t  A  o  e

ROA  t 
1 L
t
g  s  ds
A  o 1  L  e o
(2)
t
g  s  ds
 r  t  A  o  e o
where Y t   earnings of the leveraged firm at time t,
ROA  t   the rate of return on total asset for a leverage firm at time t ,
ROA  t 
r t  
= the rate of return on total equity at time t ,
1 L
normally distributed with mean r  t  and variance  2  t  ,
A  o  1  L A o  the total equity at time 0,
L = the debt to total assets ratio.
40
Paper II
• The new investment at time t is
dA  t 
 A t 
dt
t
 g  t  A  o  eo
g  s ds
(3)
 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
41
Paper II
• The model defined in the equation (3) is for the convenience purpose. If
we want the company’s leverage ratio unchanged after the expansion of
assets then we need to modify equation (3) 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’ (1997) 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.
42
Paper II
The dividend per share is
d t  
D t 
n t 
t

r  t   g  t  A  o  eo
n t 
g  s  ds
 n t  p t 
(4)
Concerning the risk of ROE,
U  d  t   e
 ad  t 
,
 0
(6)

o g  s ds   n t p t 
t



r
t

g
t
A
o
e
2










2


o g  s ds
2



a
A
o

t
e





dˆ  t   
2
n t 
n t 
t
(7)
Risk Adj.
43
Paper II
Discount cash flow
p  o    dˆ  t  e kt dt
T
(8)
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).
44
Optimal Growth Rate
g t  
*

r

r   rt    2
1  1   e
 go 
go r
go   r  go  e
(19)
 rt    2 
Logistic Equation – Verhulst (1845) => a convergence process
45
Case I: Optimal Growth Rate v.s. Time Horizon
g* t  
g *  t 
t


r   r   r t    2
r 1   
 e
 go      2  
 
r  r t    2  
1  1   e

g
o 
 

2
(20)
When g0  r , g*  t   0.
When g0  r , g*  t   0.
When g0  r , g*  t   0.
46
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).
47
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
(21)
If the market is more perfect   is larger  , the speed of convergence is faster.
48
Case II: Optimal Growth Rate v.s. Degree of Market
Perfection
49
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










 go   r  go  e

 rt    2 


2
(22)
When initial growth rate is lower than the target rate (ROE), eq. (22) is
positive.
=> If the target rate (ROE) is higher, the adjustment process will be
faster.
50
Case IV: Optimal Growth Rate v.s. Initial
Growth Rate
2
g *  t 
go

 r   rt   2
  e
 go 
 
r   rt   2 
1  1   e

g
o 
 

2
(23)
Eq. (23) is always positive.
=> The higher initial growth rate is, the higher optimal growth rate at
each time.
51
52
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
g
e 0

*
 u  du  ks
 2 s
 1
 r  g *  s 
2
(29)
ds
• Assuming   1 and g* t   g* ,


( g *  k )(T t )


e
1 
D t  
g 
 (t )2  
*
 1 
 1 
g 

*
Y  t   r  t  
(g  k) 
 (t )2  


*
- Wallingford (1972), Lee et al. (2010)
53
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 )
*


(31)
(33)
The relationship between optimal dividend payout and growth rate is
negative in general cases.
54
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
(3)
New Debt
When a stochastic growth rate is introduced,
g  t   N  g  t  ,  g2  t  
55
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
(32a)
g  s  ds 

If Cov  r  t  , A  o  e 0
 is positive, d  t  in the previous analysis


is overestimated.
t
56
Conclusion
Paper I
• We derive a stochastic dynamic dividend policy model under
perfect market and uncertainty.
• Different from M&M model, our model considers 1) partial
payout; 2)uncertainty (risks); 3) stochastic earnings.
• The theoretical model shows that the relationship between
firm's optimal payout ratio and its risks depends on its growth
rate relative to its ROA.
• The theoretical model shows that the relationship between
firm's optimal payout ratio and its risks is generally negative.
• The empirical results are consistent to the implications of our
model.
Conclusion
Paper II
• Based upon Model (I), 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 theoretical model shows the existence of an optimal
payout ratio jointly determined by the number of shares
outstanding and the growth rate.
• The optimal growth rate follows a convergence processes, and
the target rate is firm’s expected ROE.
• The relationship between the optimal dividend payout and the
optimal growth rate is negative in general.
58
References
(1) Bhattacharya, S. Imperfect information, dividend policy, and “the bird in the hand”
fallacy. Bell Journal of Economics, 10, 259-270, 1979.
(2) Blau, B.M., and K.P. Fuller. Flexibility and Dividends. Journal of Corporate
Finance, 14, 133-152, 2008.
(3) DeAngelo, H., L. DeAngelo, and D. J. Skinner. “Reversal of fortune: dividend
signaling and the disappearance of sustained earnings growth.” Journal of
Financial Economics, 40, 341–371, 1996.
(4) DeAngelo, H., and L. DeAngelo. “The irrelevance of the MM dividend irrelevance
theorem.” Journal of Financial Economics, 79, 293–315, 2006.
(5) DeAngelo, H., L. DeAngelo, and R. Stulz. “Dividend policy and the
earned/contributed capital mix: a test of the life-cycle theory.” Journal of
Financial Economics, 81, 227-254, 2006.
(6) Easterbrook, F. H. Two agency-cost explanations of dividends. American
Economic Review, 74, 650-659, 1984.
(7) Fama, E. and H. Babiak. Dividend policy: an empirical analysis. Journal of
American Statistical Association, 63, 1132-1161.
References
(1) Gordon, M. J. “The savings and valuation of a corporation.” Review of Economics
and Statistics, 1962.
(2) Grullon G., R. Michaely, and B. Swaminathan. “Are dividend changes a sign of
firm maturity?” Journal of Business, 75, 387-424, 2002.
(3) Higgins R. C. “How much growth can a firm afford?” Financial Management, 6,
7-16, Fall 1977.
(4) Higgins R. C. “Sustainable growth under inflation.” Financial Management, 10,
36-40, Autumn 1981.
(5) Higgins R. C. Analysis for financial management, 9th ed. McGraw-Hill, Inc, NY,
2008.
(6) Jagannathan, M., C. P. Stepens, and M. S. Weisbach 2000, Financial Flexibility
and the Choice Between Dividends and Stock Repurchases, Journal of Financial
Economics, 57, 355-384.
(7) Jensen, M. Agency costs of free cash flow, corporate finance, and takeovers.
American Economic Review, 76, 323–329, 1986.
(8) John, K. and J. Williams. Dilution, and taxes: a signaling equilibrium. Journal of
Finance, 40 (4), 1053-1070, 1085.
References
(16) Lang, L. H.P. and R. H. Lizenberger. Dividend announcements: cash flow
signaling vs. free cash flow hypothesis? Journal of Financial Economics, 24, 181191, 1989.
(17) Lee, C. F., C. C. Wu, and D. Hang. Dividend policy under conditions of capital
market and signaling equilibria. Review of Quantitative Finance and Accounting, 3
(1), 47-59, 1993.
(18) Lee, C. F., M. C. Gupta, H. Y. Chen, and A. C. Lee. “Dynamic model of optimal
growth rate and payout ratio: theory and implications.” Working Paper, 2010a.
(19) Lee, C. F., M. C. Gupta, H. Y. Chen, and A. C. Lee. “Optimal payout ratio under
perfect market and uncertainty: theory and empirical evidence.” Working Paper,
2010b.
(20) Lerner, E. M., and W. T. Carleton. “Financing decisions of the firm.” Journal of
Finance, 1966.
(21) Lie, E. Excess funds and agency problems: an empirical study of incremental cash
disbursements. Review of Financial Studies, 13, 219–248, 2000.
(22) Linter, J. Distribution of incomes of corporations among dividends, retained
earnings and taxes. The American Economic Review, 46 (2), 97-113.
(23) Lintner, J. “Optimal dividends and corporate growth under uncertainty.” Quarterly
Journal of Economics, February 1964.
References
(24) Miller, M., and K. Rock. Dividend policy under asymmetric information. Journal of
Finance, 40, 1031–1051, 1985.
(25) Miller, M. H., and F. Modigliani (1966). “Some estimates of the cost of capital to the
utility industry, 1954-1957.” American Economic Review, 56, 333-391.
(26) Modigliani, F. and M. H. Miller. “Dividend policy, growth, and the valuation of
shares.” Journal of Business, October 1961.
(27) Nissim, D., and A. Ziv. Dividend changes and future profitability. Journal of
Finance, 56, 2111–2133, 2001.
(28) Rozeff. Growth, beta, and agency costs as determinants of payout ratios. Journal of
Financial Research, 5, 249–259, 1982.
(29) Verhulst, P.-F. “Recherches mathématiques sur la loi d'accroissement de la
population.” Nouv. mém. de l'Academie Royale des Sci. et Belles-Lettres de Bruxelles
18, 1-41, 1845.
(30) Verhulst, P.-F. “Deuxième mémoire sur la loi d'accroissement de la population.”
Mém. de l'Academie Royale des Sci., des Lettres et des Beaux-Arts de Belgique 20, 132, 1847.
(31) Wallingford, B. A. III. “An inter-temporal approach to the optimization of dividend
policy with predetermined investments.” Journal of Finance, 27, June 1972.