financial analysis, planning and forecasting theory and application

Financial Analysis, Planning and Forecasting

Theory and Application

ByAlice C. Lee

San Francisco State UniversityJohn C. Lee

J.P. Morgan ChaseCheng F. Lee

Rutgers University

Chapter 16 Dividend Policy and Empirical Evidence

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

CAPM

Neo-classical

Option pricing(Further extension)

Classical

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


(16.1)

where

P0 = Today’s stock price,

K = Investor’s required rate-of-return, and

,g - K

D = P 10


P0 = f(D, g, K)

(16.2)

(16.3)

br - Kb)X - (1 = P0

20

)()(

br - KK -r X =

dbPd


(16.4)

(16.5)

( 1)

1jt j t

jtjt

D PP

r

( 1)jt j t jtjt

jt

d P Pr

P


(16.6a)

(16.6b)

(16.7)

(16.8)

( 1)

1jt j t

jtjt

D VV

r

.r + 1

)P)(n( + D = Vjt

1)+j(tjtjtjt

( 1) ( 1)[ ( )( ) /1jt jt jt j t jt j t jtV D n P m p r

Njt jt j,N

jt t Nt=1 jt jN

- VX I = + V(1 + (1 + ) )r r


(16.9)N N

jt jt jNjt t t N

t=1 t=1jt jt jN

CI CO V = - + V(1 + (1 + (1 + ) ) )r r r

* -[ ]. (16.10)jt jt

jtjt

r rIr

The Discount Cash Flow Approach

The Investment Opportunity Approach

*

1 1

( - ). (16.11)

(1 /[(1 ]) )jt jt jt jt

jt t tt tjt jt jt

X I r r V r r r


1

. (16.12)(1 )

Njt

jt tt jt

D V r

1 1

- . (16.13)(1 (1) )

N Njt jt

jt t tt tjt jt

X I V r r

1 1 0

. (16.14)(1 (1) )

N N tjt jt j

jt t tt tjt jt

X r I V r r

Stream of Dividends Approach

Stream of Earnings Approach

16.3 Issues marring the dividend problem

The classical CAPM Brennan’s CAPM with taxes The Litzenberger and Ramaswamy CAPM

with taxes Empirical evidence


where Vi = Value of the ith person’s portfolio; Xji = Dollar amount of security j in the ith portfolio; z = Expected end-of-period price of security j; Pj = Initial equilibrium price of security j; tgi = Effective capital gains tax on ith investor; dj = Dividend payment on security j; tdj = Effective marginal tax rate applicable to dividend receipt by the ith investor; q = Expected return on the riskless asset; X0i = Dollar amount invested in the riskless asset at t = 0 by the ith invest

or.

( - ), (16.15)f fjt mtj R RR R

The classical CAPM


where σjk = Covariance between the returns on security j and security k.

where

and represent initial endowment of Xji and X0i, respectively.

2

1 1

(1- ) (1- ), (16.17)N N

ji kii jk gi gij k

t tX X

000 0

1

( - ) ( - ) 0, (16.18)N

j ji ji i ij

X P X X X

0jiX 0

0iX

01

[ ( ) (1 )] [ ( 1) ], (16.16)N

ji j j j igi ji di diij

q qV t d t tX z z P X

Brennan’s CAPM with Taxes


(16.19)

(16.20)

(16.21)

2( , )i i i iU U

02 00 0

1

( , ) [ )],( ) (N

j ji ji ii i iij

L XU P X X X

( ) [( ) ( )] ( )j j m m jR r R r T r d T d r

The Litzenberger and Ramaswamy CAPM with taxes

where = Lagrange on the kth investor’s budget; = Lagrange on the kth investor’s income and the associated slack variable; = Lagrange on the kth investor’s borrowing and the associated slack variable; di = Dividend yield on security i.

21

1

2 21

3 31

( , ) (1- - )

[ - ] (16.22)

[(1- ) - ],

Nk kk k

i fkki

Nk kk k

i f fii

Nk kk k

i fi

fL X X

d SX X r

SX X

1k

2 2, k kS

3 3, k kS


( ) - ( - ). (16.23)j f fjjE A B C dR r r

2 11

[ - / ], (16.24)N k

kkkm

k

C fT

1k

kk k

2

k

m

k

kf = f ( , )

; = .

, (16.25)k k k

2kkm m

k n k b 1

C = - Tf



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. (16.23c)

E(Rj) = rf + [E(Rm) - rf)] βj. (16.23d)

P = a0 + a1D + a2Y. (16.26)

P = a0 + a1D + a2(Y - D). (16.27)


Empirical Evidence


where

P = Price per share/Book value; = 5-year average dividend/Book value; d = Current year’s dividend/Book value; = 5-year average retained earnings/Book value; g = Current year’s retained earnings/Book value.

, (16.28)0 1 2 3 4P = + d + (d - d ) + ( g ) + (g - g )B B B B E

d

g

P = a0 + a1D + a2R + F. (16.29)


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.

, (16.30)2 f 1 2 f 1m jj mjE( ) = + (E( ) - - ) + d dT R T T R TR R

CAPM Approach Empirical Work

Rjt - Rft = A + Bβjt + C(djt - Rft) (16.31)

, (16.32)m 0 1it it - = + a aRR

16.4 Behavioral considerations of dividend

policy

Partial adjustment and information content models

An integration model

16.4 Behavioral considerations of dividend policy

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.

• Partial adjustment and information content models

16.4 Behavioral considerations of dividend

policy Dt - Dt-1 = a + b(rEt - Dt-1) + ut, (16.35)

Dt = rE* + ut. (16.36)

(16.37)

Dt - Dt-1 = rbEt - bDt-1 + ut + ut-1(1 - b). (16.38)

* * (1 ) 1t t tE bE b E

16.4 Behavioral considerations of dividend policy

(16.39)

Dt - Dt-1 = a + b1(D* - Dt-1) + ut, (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)

** tD rE

* * *1 2 1( )t t t tE E b E E

• An Integration Model

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 CAP

M 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.

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