Dividend Policy and Dividend Payment Behavior: Theory and Evidence

Cheng-Few Lee Rutgers University

Flow Chart of Dividend Policy and Dividend Behavior

Dividend Policy

Dividend Irrelevance Theory

Dividend Relevance Theory without Tax Effect

Time-Series Cross-Sectional

Dividend Relevance Theory

with Tax Effect

CAPM Approach

Non-CAPM Approach

2

Empirical WorkTheory

Flow Chart of Dividend Policy and Dividend Behavior

3

Signaling Hypothesis

Free Cash Flow Hypothesis

Flexibility Hypothesis

Dividend Behavior

Partial Adjustment Process

Information Content or Adaptive

Expectations

Myopic Dividend Policy

Residual Dividend Policy

Time-Series Cross-Sectional

Life-Cycle Theory

Empirical Work

Dividend Relevance Theory without Tax Effect

Theory

Cov. btw ROE and g

Price Multiplier Model

Empirical Analyses in Dividend Policy Research

Descriptive Data Analysis

Regression Analysis

Time Series Cross-Sectional Time Series Cross-Sectional Panel Data Analysis

Fixed Effect Model

Fama-MacBeth Procedure

Seemly Uncorrelated Regression

(SUR)

Probit / Logit

4

Dividend Policy and Dividend Payment Behavior

A. 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)

- Life-cycle theory (DeAngelo et al., 2006)

5

Dividend Policy and Dividend Payment BehaviorB. Dividend Behavior Models

(i) Partial Adjustment Model (Lintner, 1956 AER)

Current earnings

=> Lintner’s model

Permanent earnings

=> 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)

1 2 1 3 2 4

1 2 3 4 1

(2)

where , 2 , 1 1 , , and 1 .

t t t t t

t t t

D a a D a D a E v

a a a a r v u u

0 1 1 2 (1)t t t tD a a D a E e

6

0 1 1 2 (1a)t t t tD a a D a CE e

0 1 1 2 (1b)t t t tD a a D a PE e

tCE

tPE

Dividend Policy and Dividend Payment Behavior

C. Price Multiplier Model

(i) Friend and Puckett (1964, AER) have proposed the relationship between stock prices, dividends, and retained earnings as follows:

where

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, , and 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 (1977, JFQA), and Gilmore and Lee (RES) have done empirical studies on price multiplier model.

1, , 1, , (3)ti ti tiP A BD CR i N t T

, , represtne price per share, dividend per share and retained earnings

per share, respectively.ti ti tiP D and R

1a 2a

7

Dividend Policy and Dividend Payment Behavior

D. Integration of Dividend Policy and CAPM

(Litzenberger and Ramaswamy, 1982)

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).

8

( ) - ( - )j jf fjE r A B C r dR

Outline1. Introduction2. The Model for Optimal Dividend Policy3. Comparative Static Analysis of Dividend Payout Policy

3.1 Case I: Total Risk3.2 Case II: Systematic Risk3.3 Total Risk and Systematic Risk3.4 No Change in Risk3.5 Relationship between the Optimal Payout Ratio and the Growth Rate

4. Joint Optimization of Growth Rate and Payout Ratio

4.1 Optimal Growth Rate v.s. Time Horizon

4.2 Optimal Growth Rate v.s. Degree of Market Perfection

4.3 Optimal Growth Rate v.s. ROE

4.4 Optimal Growth Rate v.s. Initial Growth Rate

4.5 Optimal Dividend Policy v.s. Optimal Growth Rate

9

Outline

5. Dividend Behavior Model5.1 Partial Adjustment Model (Lintner, 1956 AER) 5.2 Mixed Partial Adjustment and Adapted Expectation (Fama & Babiak,

1968 JASA)5.3 Generalized Dividend Forecasting Model (Lee et al., 1987, Journal of

Econometrics)6. Empirical Evidence

6.1 Sample Description6.2 Multivariate Analysis6.3 Fama-MacBeth Analysis6.4 Fixed Effect Analysis

7. Summary and Concluding Remarks7.1 Limitations of cross-sectional approach to investigate dividend policy7.2 We need to use dividend behavior model to supplement cross-sectional approach to obtain more meaningful conclusion for decision making.

10

IntroductionDividend PolicyMiller 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.

[Blau and Fuller (2008)] 12

Introduction1. 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 represent the initial assets of the firm and represent the growth rate. Then, the earnings of this firm are given by Eq. (1), which is

- The retained earnings of the firm, , can be expressed as

where is the number of shares outstanding, and is dividend per share at time t.

( )d t( )m t

( ) ( ) ( ) ( )y t x t m t d t

( ) ( ) ( ) htx t r t A o e

( )r t ( )h t

y t

14

The Model for Optimal Dividend Policy

The new equity raised by the firm at time t can be defined as

where = degree of market perfection, 0 < 1.

Therefore, the investment in period t can be written as:

Rearranging the equation above, we can get

( ) ( ) ( ) ( ) ( ) ( )htd t r t h A o e m t p t m t �

( ) ( ) ( ) ( ) ( ) ( )hthA o e x t m t d t m t p t �

( ) ( ) ( )e 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.

- A differential equation can be formulated:

where2 2 2 2

2

( ) ( ) ( ) ( ) ( )( )

( ) ( )

th tha bI h A o e A o t t eG t

m t m t

0

2 2 2 2

20

ˆ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ]

( ) ( )

T kt

th thT kt

p o d t e dt

A bI h A o e m t p t A o t t ee dt

m t m t

�

( )( ) [ ] ( ) ( )

( )

m tp t k p t G t

m t

��

16

Optimal Dividend Policy

Optimal Payout Ratio when :

2 2 2 2 2 2 ( )( )

2 2

( )( ) 2 2

2 2

( ) ( ) ( ( ) ( ) ( ) ( ) ( ) ( ) )[ 1]1

( ) ( ) ( ) ( ) ( )

( ) [ 1] ( ) ( ) = 1

( ) ( ) ( ) ( )

h k T t

h k T t

D t a bI h h t t t t t t e

x t a bI t t h k

a bI h e t th

a bI h k t t

��

��

1

17

Relationship between the Optimal Payout Ratio and the Growth Rate

- The sign is not only affected by the growth rate (h), but is also affected by the expected rate of return on assets ( ), 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.

( )( )( )( )

2

[ ( ) / ( )]

( )1( )[ ] (1 )

h k T th k T t

D t x t

h

k h h k T t e kk he h

a bI h k a bI h k

a bI

18

19

Relationship between the Optimal Payout Ratio and the Growth Rate

When , there is a negative

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.

( ) ( ) ( ) 1[ ( ) / ( )] a bI h T t h T tD t x t

h a bI

1 1( )

2 ( )h a bI

T t

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

High growth firms :

negative relationship between optimal payout ratio and total risk.

Low growth firms :

positive relationship between optimal payout ratio and total risk

( )( )

2

2

( ) / ( ) 1(1 )

( )( )

h k T tD t x t h e

a bI h ktt

�

h a bI

h a bI

22

Optimal Payout Ratio vs. Systematic Risk

High growth firms :

negative relationship between optimal payout ratio and systematic risk.

Low growth firms :

positive relationship between optimal payout ratio and systematic risk

h a bI

h a bI

( )( )

2

2

( ) / ( ) 1(1 )

( )( )

h k T tD t x t h e

a bI h ktt

�

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

where

• Relative effect on the optimal dividend payout ratio

]1

)[1())((

kh

e

bIa

h tTkh

2 2

2 2

( ) ( )[ ] [ ] (30)

( ) ( )

t td d

t t

��

2 2

2 2

( ) ( )[ ( ) / ( )] ( ) ( )

( ) ( )

t td D t x t d d

t t

��

26

Optimal Payout Ratio when No Change in Risk

When there is no change in risk, the optimal payout ratio is identical to the optimal payout ratio of Wallingford (1972).

( )( )

[ ( ) / ( )] (1 )[ ]h k T th k he

D t x ta bI h k

27

Joint Optimization of Growth Rate and Payout Ratio• The new investment at time t is

where

t

og s ds

g t A o e

dA tA t

dt �

( )Y t D t n t p t LA t � �

the total dollar dividend at time ;D t t

price per share at time ;p t t

degree of market perfections, 0 < l;

n the proceeds of new equity issued at time ;t P t t �

= the debt to total assets ratioL

Retained Earnings New Equity New Debt

28

• 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

we can obtain the growth rate as

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.

( ) 1 / ( )t

og s ds

A t g t A o e Y t D t n t p t D E Y t D t n t p t � ��

1 /( )

1 1 1 1

ROE d n t p t Eg t

ROE d ROE d

�

Our Model

Higgins’ sustainable g

Joint Optimization of Growth Rate and Payout Ratio

29

Discount cash flow

The price per share can be expressed as PV of future dividends with a risk adjustment.

=> maximize p(o) by jointly determine g(t) and n(t).

0

ˆT ktp o d t e dt

0 0

21 2 22

0

1t t

T g s ds g s ds ktp o n t r t g t A o e a A o t n t e e dtn o

Future Dividends Risk Adj.

Joint Optimization of Growth Rate and Payout Ratio

30

Optimal Growth Rate

Logistic Equation – Verhulst (1845) => a convergence process

*

2

2

1 1

rt

o

ort

o o

rg t

re

g

g r

g r g e

31

Case I: Optimal Growth Rate v.s. Time Horizon

2

**

2

2

12

1 1

r t

o

r t

o

r rr e

gg tg t

t re

g

�

*0

*0

*0

When , g 0.

When , g 0.

When , g 0.

g r t

g r t

g r t

�

�

�

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

2

2*

2

2

21

2

1 1

r t

o

r t

o

r rte

gg t

re

g

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

When initial growth rate is lower than the target rate (ROE), is positive.

=> If the target rate (ROE) is higher, the adjustment process will be faster.

2 2

*

22

12

rt rto o o

rto o

tg g e g r re

g t

r g r g e

*g t

r

36

Case IV: Optimal Growth Rate v.s. Initial Growth Rate

is always positive.

=> The higher initial growth rate is, the higher optimal growth rate at each time.

2

2

*

2

21 1

rt

o

o rt

o

re

g t g

g re

g

*

o

g t

g

37

38

Optimal Dividend Payout Ratio

where

• Assuming ,

- Wallingford (1972), Lee et al. (2010)

*

0

*

2 2 * * 2 *

32 *

1

1 2

tkt g s ds

D t g t

Y t r t

t t g t r g t t g te W

t r g t

��

*

0212 *

sT g u du ks

tW e s r g s ds

* *1 and g t g

*( )( )* 2

** 2

1 ( )1 1

( ) ( )

g k T teD t g tg

Y t r t g k t

�

39

Optimal Dividend Payout Ratio v.s. Growth Rate

**

*

* * ( )( )* ( )( ) *

2* *

* *

*

[ ( ) / ( )]

( )1( )[ ] (1 )

( ) ( ) ( ) 1

( )

g k T tg k T t

D t Y t

g

k g g k T t e kk g e g

r t g k r t g k

r t g T t g T t

r t g

The relationship between optimal dividend payout and growth rate is negative in general cases.

40

Stochastic Growth Rate and Specification Error

When a stochastic growth rate is introduced,

( )t

og s dsdA t

A t g t A o e Y t D t n t p t LA tdt

�� �

2, gg t N g t t

Retained Earnings New Equity New Debt

41

Stochastic Growth Rate and Specification Error

0 0 0,t t tg s ds g s ds g s ds

r t g t A o e n t p t Cov r t A o e E t e

E d tn t n t

�

0If , is positive, in the previous analysis

is overestimated.

tg s ds

Cov r t A o e d 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, 6000-6999) 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

4646

47

Summary Statistics of Sample Firm Characteristics

48

Multivariate Regression

48

,1 , 2 , , 3 , 4 ,

,

ln _ ln( )

1

i ti t i t i t i t i t i

i t

payout ratioRisk D g ROA Risk Growth Option Size Fixed Effect Dummies e

payout ratio

48

Flexibility Hypothesis

FCF Hypothesis

Empirical Results – Mean Reverting Process of firms’ growth rates

49

Partial Adjustment Model for the Growth Rate

50

If => partial adjustment, 1t j

51

Cov. is negatively related to the dividend payouts

52

The higher of the Cov., the higher possibility to stop the cash dividends.

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 consideration of free cash flow problem. 53

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.

54

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 cross-sectional approach to obtain more meaningful conclusion for decision making.

6. The impacts of Integrated Tax System can be further explored.

55

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