Financial Analysis, Planning and
Forecasting
Theory and Application
Chapter 16
Dividend Policy and Empirical Evidence
By
Alice C. Lee
San Francisco State University
John C. Lee
J.P. Morgan Chase
Cheng F. Lee
Rutgers University
Outline
16.1 Introduction
 16.2 The value of dividend policy to the firm

 Methods of Determining the Relevance of Dividends

16.3 Issues marring the dividend problem
 The Classical CAPM
 Brennan’s CAPM with Taxes
 The Litzenberger and Ramaswamy CAPM with Taxes
 Empirical Evidence

16.4 Behavioral considerations of dividend policy
 Partial Adjustment and Information Content Models
 An Integration Models
16.5 Summary and conclusions
16.1 Introduction
Classical
CAPM
Neo-classical
Option pricing
(Further extension)
16.2 The value of dividend policy to the firm
 Methods
of determining the relevance of
dividends
a) The Discounted Cash-Flow Approach
b) The Investment Opportunities Approach
c) Stream-of-Dividends Approach
d) Stream-of-Earnings Approach
16.2 The value of dividend policy to the firm
D
1
,
P0 =
K-g
(16.1)
where
P0 = Today’s stock price,
K = Investor’s required rate-of-return, and
16.2 The value of dividend policy to the firm
P0 = f(D, g, K)
(1 - b)X
P0 =
K - br
d P0 X ( r - K )
=
db
( K - br ) 2
(16.2)
(16.3)
16.2 The value of dividend policy to the firm
Pjt 
rjt 
D jt  Pj ( t 1)
1  rjt
d jt  Pj ( t 1)  Pjt
Pjt
(16.4)
(16.5)
16.2 The value of dividend policy to the firm
16.2 The value of dividend policy to the firm
V jt 
D jt  V j ( t 1)
1  rjt
D jt + ( n jt )( P j(t+1) )
.
V jt =
1 + r jt
V jt  [ D jt  (n jt )( Pj (t 1)  m jt p j ( t 1) ) /1  rjt
N
(16.6a)
V j,N
X jt - I jt
+
V jt = 
t
N
(1
+
(1
+
r jt )
r jN )
t=1
(16.6b)
(16.7)
(16.8)
16.2 The value of dividend policy to the firm
The Discount Cash Flow Approach
N
N
CI jt
CO jt
V jN
+
V jt = 
t 
t
N
(1 + r jN )
t=1 (1 + r jt )
t=1 (1 + r jt )
The Investment Opportunity Approach
*
r jt - r jt
I jt [
].
r jt
(16.10)

*

X jt
I jt (r jt - r jt )

.
V jt  
t
t
t 1 (1  r jt )
t 1 r jt /[(1  r jt ) ]
(16.11)
(16.9)
16.2 The value of dividend policy to the firm
Stream of Dividends Approach
N
V jt  
t 1
D jt
.
t
(1  r jt )
N
X jt
I jt
.
V jt  
t 
t
t 1 (1  r jt )
t 1 (1  r jt )
(16.12)
N
(16.13)
Stream of Earnings Approach
N
N
t
X jt
r jt I j

.
V jt  
t
t
t 1 (1  r jt )
t 1  0 (1  r jt )
(16.14)
16.3 Issues marring the dividend problem




The classical CAPM
Brennan’s CAPM with taxes
The Litzenberger and Ramaswamy CAPM
with taxes
Empirical evidence
16.3 Issues marring the dividend problem
The classical CAPM
R jt  R f   j ( R mt - R f ),
where
Vi
Xji
z
Pj
tgi
dj
tdj
q
X0i
(16.15)
= Value of the ith person’s portfolio;
= Dollar amount of security j in the ith portfolio;
= Expected end-of-period price of security j;
= Initial equilibrium price of security j;
= Effective capital gains tax on ith investor;
= Dividend payment on security j;
= Effective marginal tax rate applicable to dividend receipt by the ith
investor;
= Expected return on the riskless asset;
= Dollar amount invested in the riskless asset at t = 0 by the ith investor.
16.3 Issues marring the dividend problem
Brennan’s CAPM with Taxes
N
V i   X ji[ z j  ( z j  P j )t gi
d
ji
(1  t di )]  X 0i[q  (q  1)t di],
(16.16)
j 1
N
N
     jk X ji (1- t gi ) X ki (1- t gi ),
2
i
(16.17)
j 1 k 1
where
σjk = Covariance between the returns on security j and
security k.
N
 P (X
j
ji
- X 0ji )  ( X 0i - X 00i )  0,
(16.18)
j 1
where
X 0ji and X 0i0 represent initial endowment of Xji and X0i,
respectively.
16.3 Issues marring the dividend problem
U i  U i ( i ,  )
2
i
N
L  U i (  i,  i2)  [ P j ( X
j 1
ji
(16.19)
 X )  (X  X
0
ji
0i
0
0i
)], (16.20)
( R j  r )   j [( Rm  r )  T (r  d m )]  T (d j  r )
(16.21)
16.3 Issues marring the dividend problem
The Litzenberger and Ramaswamy CAPM with taxes
N
k
L  f (  k ,  )   (1-  X i - X f )
k
k
2
k
k
1
i 1
N
  k2[ X ik d i  X kf r f - S 2k ]
i 1
where
(16.22)
N
  3k[(1-  )  X ik  X kf - S 3k ],
i 1
1k = Lagrange on the kth investor’s budget;
2k , S 2k = Lagrange on the kth investor’s income and the
associated slack variable;
 , S = Lagrange on the kth investor’s borrowing and the
associated slack variable;
di = Dividend yield on security i.
k
3
k
3
16.3 Issues marring the dividend problem
E ( R j ) - r f  A  B  j  C (d j - r f ).

k
k
k
C   m [T -  2 / f 1 ],
k 1 
N
(16.23)
k
(16.24)
 f (  k , 2k ) m
=
; =
 k
k
k
f1



k
C= m T - m
,
f
kn 
kb 
k
k
k
2
k
1

k .
k
(16.25)
16.3 Issues marring the dividend problem
E(Rj) - Tmdj = [rf(1 - Tm) + A](1 - βj) + [E(Rm) - Tmdm]βj,
(16.23a)
E(Rj) - Tmdj = [rf(1 - Tm)] + [E(Rm) - Tmdm - rf(1 - Tm)] βj.
(16.23b)
E(Rj) = (A + rf)(1 - βj) + E(Rm) βj.
E(Rj) = rf + [E(Rm) - rf)] βj.
(16.23c)
(16.23d)
16.3 Issues marring the dividend problem
Empirical Evidence
P = a0 + a1D + a2Y.
(16.26)
P = a0 + a1D + a2(Y - D).
(16.27)
16.3 Issues marring the dividend problem
P = B 0 + B 1d + B 2(d - d ) + B 3( g ) + E 4(g - g ),
where
P = Price per share/Book value;
d = 5-year average dividend/Book value;
d = Current year’s dividend/Book value;
g = 5-year average retained earnings/Book value;
g = Current year’s retained earnings/Book value.
P = a0 + a1D + a2R + F.
(16.29)
(16.28)
16.3 Issues marring the dividend problem
CAPM Approach Empirical Work
E( R j ) = T 2 R f +  j(E( R m ) - T 1d m - T 2 R f ) + T 1d j, (16.30)
where
dj = Dj/Vj,
dm = Dm/Vm,
T1 = (Td - Tg)/(1 - Tg),
T2 = (1 - Td)/(1 - Tg) = 1 - T1,
Td = Average tax rate applicable to dividends,
Tg = Average tax rate applicable to capital gains.
Rjt - Rft = A + Bβjt + C(djt - Rft)
Rit - Rm = a0 + a1 it,
(16.31)
(16.32)
16.4 Behavioral considerations of dividend
policy

Partial adjustment and information content
models

An integration model
16.4 Behavioral considerations of dividend policy
• Partial adjustment and information content models
D* = rEt,
(16.33)
and
Dt - Dt-1 = a + b(D* - Dt-1) + ut
(16.34)
where
D* = Firm’s desired dividend payment,
Ft = Net income of the firm during period t,
r = Target payout ratio,
a = A constant relating to dividend growth,
b = Adjustment factor relating the previous period’s
dividend and the new desired level of dividends,
where b is assumed to be less than one.
16.4 Behavioral considerations of dividend
policy
Dt - Dt-1 = a + b(rEt - Dt-1) + ut,
Dt = rE* + ut.
(16.36)
E  bEt  (1  b) E  1
*
t
(16.35)
*
t
(16.37)
Dt - Dt-1 = rbEt - bDt-1 + ut + ut-1(1 - b).
(16.38)
16.4 Behavioral considerations of dividend policy
• An Integration Model
D*  rEt*
Dt - Dt-1 = a + b1(D* - Dt-1) + ut,
Et*  Et*1  b2 ( Et  Et*1 )
(16.39)
(16.40)
(16.41)
Dt - Dt-1 = ab2 + (1 - b1 - b2)Dt-1
- (1 - b2)(1 - b1)Dt-2
+ rb1b2Et - (1 - b2)ut-1 + ut.
(16.42)
16.5 Summary and conclusions
In this chapter we examined many of the aspects of
dividend policy, primarily from the relevance-irrelevance
standpoint, and from multiple pricing-valuation frameworks.
From the Gordon growth model, or classical valuation view,
we found that dividend policy was not irrelevant, and that
increasing the dividend payout would increase the value of
the firm. Upon entering the world of Modigliani and Miller
where some ideal conditions are imposed, we found that
dividends were only one stream of benefits we could
examine in deriving a value estimate. However, even in
their own empirical work on those other benefit streams,
M&M were forced to include dividends, if only for their
information content.
16.5 Summary and conclusions
Building on the Sharpe, Lintner, and Mossin
CAPM derivations, Brennan showed that
dividends would actually be determinantal to a
firm’s cost of capital as they impose a tax penalty
on shareholders. While this new CAPM is useful,
however, Brennan considered only the effects
associated with the difference between the original
income tax and the capital-gains tax. Litzenberger
and Ramaswamy extended Brennan’s model by
introducing income, margin, and borrowing
constraints. Their empirical results are quite
robust, and show that higher and lower dividends
mean different things to different groups of
investors.
16.5 Summary and conclusions
Option-pricing theory was shown to make
dividends a valuable commodity to investors due
to the wealth-transfer issue. The theory (and the
method) of dividend behavior also showed
dividend forecasting to have positive value in
financial management. In sum, we conclude that
dividends policy does generally matter, and it
should be considered by financial managers in
doing financial analysis and planning. The
interactions between dividend policy, financing,
and investment policy will be explored in the next
chapter.