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    EFFECTIVENESS OF DIVIDEND POLICY UNDER THE CAPITAL ASSET

    PRICING MODEL: A DYNAMIC ANALYSIS

    Manak C. Gupta

    Professor of Finance

    Temple University

    205B Speakman Hall

    Fox School of Business

    Philadelphia, PA 19122

    E-mail: [email protected]

    Phone 215-204-8143

    Fax 215-204-1976

    Alice C. Lee

    Assistant Professor of Finance

    San Francisco State University

    1600 Holloway Avenue

    San Francisco, CA 94025

    E-mail: [email protected]

    Phone 415-338-1701

    Fax 415-338-0997

    Cheng-Few Lee

    Distinguished Professor of Finance

    Rutgers University

    Janice H. Levin Building

    Piscataway, N.J. 08854-8054

    Email: [email protected]

    Phone 732-445-3907

    Fax 732-445-5927

    April, 2008

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    EFFECTIVENESS OF DIVIDEND POLICY UNDER THE CAPITAL ASSET

    PRICING MODEL: A DYNAMIC ANALYSIS

    ABSTRACT

    Most contemporary dividend policy models, including that of M&M, tend to be

    basically static while our analysis shows that dividend policy is dynamic in nature.

    This is clearly seen when the stochasticity and nonstationarity of the firms profit

    rates is analytically treated and formally introduced into the model. In contrast to the

    static models, this model permits an analysis of the dynamic process of the firm

    moving from one equilibrium state to another. Furthermore, the dynamic dividend

    payout model presented here integrates the advances in the theory of capital asset

    pricing with the managerial decision making on dividend policy. The separate effects

    of the relative changes in the total risk, and its diversifiable and nondiversifiablecomponents, on the optimal corporate dividend policy are identified. Without such

    decompositions of risk, it would be difficult, for example, to identify the effects on

    corporate dividend policy of a shift in the systematic risk within a stationary total risk

    of the firm. Using assumptions similar to those of DeAngelo and DeAngelo (2006),

    we show the existence of an optimal payout ratio under a frictionless market. We

    also explicitly derive the theoretical relationship between the optimal payout ratio

    and important financial variables. Additionally, we perform a comparative analysis

    between payout ratio and the following: (i) change in total risk; (ii) change in

    systematic risk; (iii) change in total risk and systematic risk, simultaneously; (iv) no

    change in risk.

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    EFFECTIVENESS OF DIVIDEND POLICY UNDER THE CAPITAL ASSET

    PRICING MODEL: A DYNAMIC ANALYSIS

    I. INTRODUCTION

    Corporate dividend policy has long engaged the attention of financial

    economists, dating back to the irrelevance theorem of Miller and Modigliani (1961;

    M&M) where they state that there are no illusions in a rational and a perfect

    economic environment. Since then, their rather controversial findings have been

    challenged and tested by weakening the assumptions and/or introducing

    imperfections into the analysis. The signaling models developed by Bhatacharya

    (1979) and Miller and Rock (1985) have yielded mixed results. Studies by Nissim

    and Ziv (2001), Charlton and Hendershot (1998), Bernheim and Wantz (1995), Kao

    and Wu (1994), and Healy and Palapu (1988) support the signaling (asymmetric

    information) hypothesis by finding a positive association between dividend increases

    and future profitability. Kalay and Lowenstein (1986) and Asquith and Mullins

    (1983) find that dividend changes are positively associated with stock returns in the

    days surrounding the dividend announcement dates and Sasson and Kalody (1976)

    conclude that there is a positive association between the payout ratio and average

    rates of return. On the other hand, studies of Benartzi, Michaely, and Thaler (1997)

    and DeAngelo, DeAngelo, and Skinner (1996) find no support for the hypothesized

    relationship between dividend changes and future profitability.

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    Another important factor affecting dividend policy, it is argued, is agency costs

    (Eastbrook, 1984; Jensen, 1986). Again the results of empirical studies have been

    mixed at best. Several researchers, among them, Agarwal and Jayaraman (1994),

    Jensen, Solberg, and Zorn (1992), and Lang and Litzenberger (1989) find positive

    support for the agency cost hypothesis, while others find no support for this

    hypothesis (e.g., Lie, 2000; Yoon and Starks, 1995; and Denis, Denis, and Sarin,

    1994).

    Economists have also addressed other possible imperfections as well, such as

    taxes and tax-induced clientele effects. Kalay and Michaely (l993), Litzenberger and

    Ramaswamy (l979), for example, find positive support while Black and Scholes

    (l974) find no such support for a tax-effect hypothesis. Other explanations for

    market imperfections range from transactions cost and flotation costs to irrational

    behavior. Behavioral theories have recently found increasing attention, among them

    avoiding the regret, habit, and bounded rationality explanations for the so-

    called dividend puzzle. Lee, Djarraya, and Wu (1987) have developed a dynamic

    dividend adjustment model. Besides, there have been several industry specific

    studies, for example, Akhibe, Borde, and Madura (1993), Baker and Powell (1999)

    and Gupta and Walker (l975).

    DeAngelo and DeAngelo (2006) have reexamined the irrelevance of the M&M

    dividend irrelevance theorem by allowing not to pay out all free cash flow. They

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    argue that the original Miller and Modigliani (1961) irrelevance result is irrelevant

    because it only considers payout policies that pay out all free cash flow. Payout

    policy matters a great deal if the payout policies under consideration are those in

    which all free cash is paid out as to compared to those in which free cash flow is not.

    The main purpose of this paper is to extend the DeAngelo and DeAngelo (2006)

    static analysis into a dynamic framework. When dynamics are added, there can be

    some value to cash balances. In other words, a dynamic model makes holding some

    amount of cash into a positive NPV project. Using assumptions similar to that of

    DeAngelo and DeAngelo (2006), we have shown the existence of an optimal payout

    ratio under a frictionless market. We also explicitly derive the theoretical

    relationship between the optimal payout ratio and important financial variables.

    Additionally, we perform comparative analysis between payout ratio and the

    following: (i) change in total risk; (ii) change in systematic risk; (iii) changes in total

    risk and systematic risk, simultaneously; (iv) no change in risk.

    Furthermore, the implication of Miller and Modiglianis (1961) analysis of

    corporate dividend policy under uncertainty is also explored in accordance with the

    model derived in this paper. Uncertainty is directly built into the synthesis model and

    the dynamic nature of the synthesis model permits an analysis of the process of

    moving from one equilibrium state to another. The importance of the stochasticity

    and nonstationarity of the firms profit rates in analyzing the effectiveness of

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    dividend policy is explored in some detail. Then, the separate effects of relative

    changes in the total risk, and its diversifiable and nondiversifiable components, on

    the optimal corporate dividend policy are also identified.

    In section II, we lay out the basic elements of the stochastic control theory

    model that we use in the subsequent sections to examine the existence, or

    nonexistence, of an optimal dividend policy. The model assumes a stochastic rate of

    return and is not restricted to firms growing entirely through retained earnings. The

    model is developed in the most general form assuming a nonstationary profit rate of

    the firm and using the systematic risk concept of risk.

    In section III, we carry out the optimization procedure and derive the final

    expression for the optimal dividend policy of the firm. In section IV, the implications

    of the results are explained. In particular, the separate, and then the combined effects

    of market dependent and market independent components of risk on the optimal

    dividend policy are identified. Also, we examine in detail the effects of variations in

    the profit rate, its distribution parameters, and their dynamic behavior on the optimal

    dividend policy of the firm. Finally, Section V presents the conclusion.

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    II. THE MODEL

    We develop the dividend policy model under the assumptions that the capital

    markets represent the closest approximation to the economists ideal of a perfect

    market zero transaction costs, rational behavior on the part of investors, and the

    absence of tax differentials between dividends and capital gains. It is assumed that

    the firm is not restricted to financing its growth only by retained earnings, and that its

    rate of return, )(~ tr , is a nonstationary random variable, normally distributed with

    mean and variance2( )t .

    Let )(oA represent the initial assets of the firm and h the growth rate. Then, the

    earnings of this firm are given by (1), which is

    hteoAtrtx )()(~)(~ = , (1)

    where )(~ tx represents the earnings of the firm, and the tilde (~) denotes its

    random character.

    Now the retained earnings of the firm, )(ty , can be expressed as follows,

    )(~

    )()(~)( tdtmtxty = ,

    (2)

    where )(~ td is the dividend per share and m(t) is the total number of shares

    outstanding at time t.

    Equation (2) further indicates that the focus of the firms decision making is on

    retained earnings, which implies that dividend )(td also becomes a random variable.

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    The growth of a firm can be financed by retained earnings or also by issuing new

    equity.

    The new equity raised by the firm in time tcan be defined as follows:

    )()()( tmtpte = , (3)

    where )(tp = price per share;

    dttdmtm /)()( = ;

    = degree of market perfection, 0

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    Also, let us postulate a utility function of the following form:1

    ( )[ ( )] d tU d t e=

    %% >0. (7)

    Following the moment generating function, we have

    )](~

    [2

    )](~

    [)(

    ~2

    tdVartdEtd ee

    +

    = , (8)

    where )(~

    td is the certainty equivalent value of )(td .2

    From (6) and (8), the certainty equivalent dividend stream can be written as

    2

    222

    )(

    )()(

    )(

    )()()()()(

    ~

    tm

    etoA

    tm

    tptmeoAhtd

    thth

    +=

    , (9)

    where 2/ = . Also, )(~

    td reduces to the certainty case, where2)(t = 0.

    In accordance with the capital asset pricing theory as developed by Sharpe

    (1964), Lintner (1963), and Mossin (1966), the total risk can be decomposed into

    systematic risk and unsystematic risk. That is, )(~ tr can be defined as:

    )()(~

    )(~ ttIbatr ++= ,

    (10)

    1For a detailed analysis of the various utility functions see, Pratt (1964). Exponential, hyperbolic, and quadratic forms

    have been variously used in the literature but the first two seem to have preference over the quadratic form since the

    latter has the undesirable property that it ultimately turns downwards.

    2 From moment generating function discussed in Hogg and Craig (1994), we know that

    )(2

    1)( 2

    )(yVartytE

    ty eeE+

    = . Letting t=- , then right hand side of (8) is easily obtained.

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    where )(~

    tI is the market index; )(t ~N(0,2

    ); a and b are regression parameters;

    and Var( )(~

    tIb ) and Var( )(t ) represent the systematic and unsystematic risk,

    respectively.

    Following (10), (6) can be rewritten as:

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

    E d t a bI h A o e m t p t m t = + +% & , (11)

    2 2 2 2[ ( )] ( ) [ ( ( )) ( ( ))] / ( )

    thVar d t A o b Var I t Var t e m t = +% % ,

    2222222)(/])())(1()()([)( tmettttoA

    th += ,

    where )(t = the correlation coefficient between )(~ tr and )(

    ~tI ;

    a= market independent component of the firms rate of return;

    Ib =market dependent component of the firms rate of return;

    22 )()( tt = nondiversifiable risk;

    22)())(1( tt =diversifiable risk.

    The unsystematic risk can usually be diversified away by the investors.3

    Therefore, the certainty equivalent value in (9) should be revised as:

    2

    2222

    )(

    )()()(

    )(

    )()()()()(

    tm

    ettoA

    tm

    tptmeoAhIbatd

    thth

    ++=

    . (12)

    Following Lintner (1962), we observe that the stock price should equal the

    present value of this certainty equivalent dividend stream discounted at a riskless rate

    of return. Therefore,

    3 See Lintner (1965), Mossin (1966), Sharpe (1964).

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    dtetdop ktT

    = )()( 0 , (13)

    where )(op = the stock price at t(o);

    k= the risk free rate of return;

    T= the planning horizon, T .

    We use this model in the subsequent sections to find the functional form ofm(t)

    and optimize the payout ratio. The formulation of our model is different from that of

    M&M (1961), Gordon (1962), Lerner (1966), and Lintner (1964). M&M, for

    example, in contrast to our model, did not consider the nonstationarity of the firms

    rate of return, nor explicitly incorporated uncertainty in their valuation model. Also,

    their models are essentially static and would not permit an extensive analysis of the

    dynamic process of moving from one equilibrium state to another. Furthermore, the

    formulation of our model is different from those that propose to capitalize the market

    dependent and independent components of the uncertain stream of earnings at the

    risky and the riskless rates, respectively.4 Rather, following the lead by Lintner

    (1964), we view the market values as riskless rate present values of certainty

    equivalents of random future receipts. In the next section, we carry out the

    optimization of (13) and derive the final expression for the optimal payout ratio.

    5

    4 See Brennan (1973).

    5 For further explanation of the optimization of the deterministic and stochastic control models and their applications to

    economic problems, see Aoki (1967), Astrom (1970), Bellman (1957), Bellman (1961), and Intriligator (1971).

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    III. OPTIMUM DIVIDEND POLICY

    Substituting equation (12) into (13), we obtain

    dtetm

    ettoA

    tm

    tptmeoAhIbAop

    ktthth

    T

    ++

    = ])()()()(

    )(

    )()()()([)( 2

    2222

    0

    . (14)

    To maximize (14), we observe that

    ==

    T

    t

    kskttskT

    tdsesdedsesdtp )()()( )( , (15)

    wheres = the proxy of time in the integration.

    From (15) we can formulate a differential equation as:

    ( ) ( ) ( ) ( )

    ( )

    dp t p t kp t d t

    d t= = & . (16)

    Substituting (12) into (16), we obtain the differential equation

    )()(])(

    )([)( tGtpk

    tm

    tmtp =+

    , (17)

    where

    2

    2222

    )(

    )()()(

    )(

    )()()(

    tm

    ettoA

    tm

    eoAhIbatG

    thth

    +

    = . (18)

    Solving the differential equation (17), we have

    ( ) ( ) ( )( )

    ktT

    ks

    te p t G s m s e ds

    m t

    = . (19)

    Equation (18) and (19) imply

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    { } +=

    Tktthth

    kt

    dtetmettoAtmeoAhIbaom

    eop

    0

    222221)()()()()()()(

    )()(

    .

    (20)

    The Euler-Lagrange condition for the optimization ofp(o) is given by (21),

    0)2()()()()()()())(1( 322222 =+ tmettoAtmeoAhIba thth , (21)

    i.e.,

    ))(1(

    )()()()2()(

    22

    hIba

    tteoAtm

    th

    +

    =

    . (22)

    From (18), (19), and (22), we can obtain

    2 2 2

    2 2 2

    ( ) (1 ) ( ( ) ( ))( )

    (2 ) ( ) ( )

    Tkt th hs ks

    ta bI h e e s s ds

    p tt t

    + =

    .

    (23)

    From (22), we also obtain

    { }2 2 2 2 2 2(2 ) ( ) ( ) ( ) (2 ) ( ) [ ( ) ( ) ( ) ( )( )

    (1 )( )

    th thh A o e t t A o e t t t t

    m ta bI h

    + +=

    +

    &&& . (24)

    From (23) and (24), we have

    ( 1) 2 2 2 2 2 2 ( ) 2 2

    2 2

    ( ) ( )

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

    (2 ) ( ) ( )

    Tkt th s h k

    t

    m t p t

    a bI h e A o h t t t t t t e s s ds

    t t

    =

    + + +

    &

    &&

    (25)

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    From (5) and (25), we can obtain )()()( tdtmtD = . From (1) and (10), we can

    obtainhteAIbatx )0()()( += . When approaches unity, we can derive the

    optimized payout ratio as:

    +++

    +

    +=

    )()()(

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

    )(

    )(

    )(

    )(22

    ))((222222

    khtt

    etttttth

    Iba

    hIba

    tx

    tD tTkh

    . (26)

    The equation (26) implies that there exists an optimal payout ratio when we use

    an exponential utility function to derive the stochastic dynamic dividend policy

    model. This result does not necessarily imply that the dividend policy results derived

    by Modigliani and Miller (1961) are false. This is because we allowed some free

    cash flow to be paid out, as assumed by DeAngelo and DeAngelo (2006), instead of

    paying out all free cash flows as assumed by Modigliani and Miller (1961).

    In the following section, we use equation (26) to explore the implications of the

    stochasticity, the stationarity (in the strict sense), and the nonstationarity of the firms

    rate of return for its dividend policy.6 Also, we investigate in detail the differential

    effects of variations in the systematic and unsystematic risk components of the firms

    stream of earnings on the dynamics of its dividend policy.

    IV. IMPLICATIONS

    Equation (26) implies that the optimal payout ratio is a function of expected

    profit rate ( Iba+ ), growth rate (h ), risk free rate of return ( k ), age (T-t), total risk

    6 See Hamilton (1994), pp. 45-46.

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    ( 2)(t ), correlation coefficient between profit and market rate return ( 2)(t ). In

    addition, equation (26) is also a function of two dynamic variables -- the relative time

    rate of change in the total risk of the firm, ])(/)([ 22 tt , and the relative time rate of

    change in the covariability of the firm's earnings with the market, ])(/)([ 22 tt . This

    theoretical dynamic relationship between the optimal payout ratio and other

    determinants can be used to do empirical studies for dividend policy determination.

    The dynamic effects of variations in ])(/)([ 22 tt and ])(/)([ 22 tt on the time path

    of optimal payout ratio can be investigated under the following four different cases:

    1) changes in total risk; 2) changes in correlation between profit and the market rate

    of return (i.e., systematic risk); 3) changes in total risk and systematic risk; 4) no

    changes in risk.

    A. Case I: Total Risk

    First we examine the effect of ])(/)([ 22 tt on the optimal payout ratio. By

    differentiating (26) with respect to ])(/)([ 22 tt , we obtain

    ]1

    )[1(])(/)([

    )](/)([ ))((

    22 kh

    e

    Iba

    h

    tt

    txtDtTkh

    +=

    . (27)

    In equation (27) the risk free rate, k, can be either larger or smaller than the

    growth rate h. It can be shown thatkh

    etTkh

    1))((

    is always larger than 0, regardless or

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    whetherkis larger or smaller than h.7 Thus, the sign of equation (27) depends on the

    sign of )1(Iba

    h

    + , which depends on the growth rate h relative to ).( Iba+

    If the growth rate h is equal to )( Iba+ , then )1(Iba

    h

    + is equal to zero.

    Equation (27) is thus zero, and the change of total risk will not affect the payout

    ratio, as the first derivative of the optimized payout ratio, equation (26), with respect

    to ])(/)([ 22 tt is always zero.

    If growth rate h is larger than )( Iba+ , then the entire first derivative of

    equation (26) with respect to ])(/)([ 22 tt is negative (i.e., equation (27) is negative).

    This implies that a relative increase in the total risk of the firm would decrease its

    optimal payout ratio. Furthermore, h > )( Iba+ implies that the growth rate of a

    firm is larger than its expected profit rate. This situation can occur when a company

    is in a very high growth stage, (e.g., Google). To support this high

    growth opportunity, a company should use both internal and external funds.

    Under this situation, a company will decrease its payout ratio.

    7 Ifh > k, then 1))(( > tTkhe , and both the numerator and denominator are greater than zero, resulting in a positive

    value; ifh < k, then 1))((

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    An alternative case is h < )( Iba+ , which implies that the growth rate of a firm

    is smaller than expected profit rate. This situation can occur when a company is

    either in a low growth, no growth, or negative growth stage. Under this situation, a

    company will increase its payout ratio as can be seen in equation (27). If h )( Iba+ ). The possible explanation is that in the case of high

    growth firms, a firm needs to reduce the payout ratio and retain more earnings to

    build up precautionary reserves. These reserves become all the more important for

    a firm with volatile earnings over time. In addition, the age of the firm (T-t), which is

    one of the variables in equation (26), becomes an important factor because the very

    high growth firms are also the newer firms with very little build-up precautionary

    reserves. Furthermore, these high growth firms need more retained earnings to meet

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    their future growth opportunities since the growth rate is the main determinant of

    value in the case of such companies.

    In case of established low growth firms (h < )( Iba+ ), such firms are

    likely to be older firms and most likely already built such reserves over time. In

    addition, they probably do not need more earnings to maintain their low growth

    perspective and can afford to increase the payout.

    Thus we provide, under more dynamic conditions, further evidence on the

    validity of Lintners (1965) observations that, ceteris paribus, optimal dividend

    payout ratios vary directly with the variance of the firm's profit rates. The rationale

    for such relationships, even when the systematic risk concept is incorporated into the

    analysis, is obvious. That is, holding 2)(t constant and letting the 2)(t increase

    implies that the covariance of the firm's earnings with the market does not change

    though its relative proportion to the total risk increases.

    A. Case II: Systematic Risk

    To examine the effect of a relative change in ])(/)([ 22 tt (i.e., systematic risk)

    on the dynamic behavior of the optimal payout ratio, we differentiate equation (26) to

    obtain

    ]1

    )[1(])(/)([

    )](/)([))((

    22 kh

    e

    Iba

    h

    tt

    txtD tTkh

    +=

    . (28)

    The sign of equation (28) can be analyzed as with equation (27). Therefore, the

    conclusions of equation (28) are similar to those of equation (27). A relative change

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    in 2)(t can either decrease or increase the optimal payout ratio, ceteris paribus. The

    effect of nonstationarity in the firm's nondiversifiable risk would tend to be

    obliterated should both the systematic and the unsystematic components of total risk

    not be clearly identified in the expression for optimal payout ratio. Thus, it is

    conceivable that while the total risk of the firm is stationary (i.e., ])(/)([ 22 tt is

    equal to zero) there still could be a change in the total risk complexion of the firm

    because of an increase or decrease in the covariability of its earnings with the market.

    Equations (26) and (28) clearly identify the effect of such a change in the risk

    complexion of the firm on its optimal payout ratio.

    Furthermore, an examination of equation (26) indicates that only when the

    firms earnings are perfectly correlated with the market (i.e., 2 = 1), it does not

    matter whether the management arrives at its optimal payout ratio using the total

    variance concept of risk or the market concept of risk. For every other case, the

    optimal payout ratio followed by management using the total variance concept of risk

    would be an over-estimate of the true optimal payout ratio for the firm based on the

    market concept of risk underlying the capital asset pricing theory.

    Also, the management may decide not to use the truly dynamic model and

    instead substitute an average of the long run systematic risk of the firm. However, for

    )(2 t > 0, it is evident that since the average initially is higher than the true )(

    2t , the

    management would be paying out less or more in the form of dividend than is

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    implies that the total risk of the firm increases and, in addition, its relative

    decomposition into systematic and unsystematic components also changes, making

    the firm's earnings still more correlated with the market. Under this circumstance, the

    decrease or increase in the optimal payout would now represent the compounded

    effect of both these changes. However, it is conceivable that while 2)(t is positive

    2)(t is negative, which then would tend to offset the decrease or increase in the

    optimal payout ratio resulting from the former. Alternatively,2)(t could be

    negative indicating a reduction in the total risk of the firm and may offset the

    increase in the optimal payout ratio resulting from a positive2)(t .

    To what extent the inverse variations in the total risk and the risk complexion of

    the firm would offset each other's effects on the optimal payout ratio for the firm

    would, of course, be dependent upon the relative magnitudes of 2)(t and 2)(t . To

    see the precise trade off between the two dynamic effects of ])(/)([ 22 tt and

    ])(/)([22

    tt on the optimal payout ratio, let the total differential of (26), given in

    equation (29), be set equal to zero, yielding:

    d ])(/)([ 22 tt =d ])(/)([ 22 tt . (30)

    Equation (30) implies that the relative increase (or decrease) in 2)(t has a one

    to one correspondence with the relative decrease (or increase) in 2)(t . Thus, in (30)

    conditions are established for relative changes in 2)(t and 2)(t , which lead to a

    null effect on the optimal dividend payout ratio.

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    D. Case IV: No Change in Risk

    Now we consider the least dynamic situation where there are no changes in total

    risk or systematic risk, assuming 2)(t =0 and 2)(t =0. Under this circumstance,

    equation (26) reduces to

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

    kh

    hek

    Iba

    htxtD

    tTkh

    +

    +=

    . (31)

    Thus, when the firm's total risk and also the covariability of its earnings with the

    market are assumed stationary, equation (31) indicates that a firm's optimal payout

    ratio is independent of its risk. Notice that neither 2)(t nor 2)(t now appear in the

    expression for the optimal payout ratio given in equation (31). These conclusions,

    like those of Wallingford (1972) for example, run counter to the intuitively appealing

    and well accepted theory of finance emphasizing the relevance of risk for financial

    decision making.8 Our model clearly shows that the explanation for such

    unacceptable implications of the firms total risk and its market dependent and

    market independent components for the firms optimal payout policy lies, of course,

    in the totally unrealistic stationarity assumptions underlying the derivation of such

    results as illustrated in equation (31).

    V. CONCLUSION

    8 For example, see Lintner (1963).

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    Most contemporary dividend policy models, including that of M&M, tend to be

    basically static while our analysis shows that dividend policy is dynamic in nature.

    This is clearly seen when the stochasticity and nonstationarity of the firms profit

    rates are analytically treated and formally introduced into the model. In contrast to

    the static models, this permits an analysis of the dynamic process of the firm moving

    from one equilibrium state to another. Furthermore, the dynamic dividend payout

    model presented here integrates the recent advances in the theory of capital asset

    pricing with the managerial decision making on dividend policy. The separate effects

    of the relative changes in the total risk, and its diversifiable and nondiversifiable

    components, on the optimal corporate dividend policy are identified.

    Without such decompositions of risk, it would be difficult, for example, to

    identify the effects on corporate dividend policy of a shift in the systematic risk

    within a stationary total risk of the firm. Also, in the absence of the dynamic

    structure of our model, some very troublesome results are obtained. For example,

    when 2)(t and 2)(t are both assumed stationary (as in our case IV), neither the

    total risk of the firm nor its relative decomposition into market dependent and

    independent components seems to affect the corporate dividend policy. This rather

    curious result is shown to follow from the assumption that 2)(t = 2)(t =0.

    When the nonstationarity in 2)(t and 2)(t is recognized, several important

    policy implications follow. The most interesting case is shown to occur when 2)(t

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    and 2)(t are both nonstationary (our case III). For example, when the total risk of

    the firm varies and 2)(t also varies, it results in a compounded effect on the firms

    optimal payout policy. The magnitude of the effect of variations in 2)(t and 2)(t

    on the corporate dividend policy depends, of course, upon whether these variations

    reinforce each other or are mutually offsetting. The exact trade-off conditions for

    variations in 2)(t and 2)(t that would leave the corporate dividend policy

    unaffected have also been identified.

    This paper derives an optimal payout ratio using an exponential utility function

    to derive the stochastic dynamic dividend policy model. The results vary from those

    of the M&M model since their model is stationary and does not allow for

    uncertainty. Also, our dynamic model presented in this paper allows holding some

    amount of cash account into a positive NPV project. Therefore, our assumptions are

    similar to those of DeAngelo and DeAngelo (2006) instead of those of Modigliani

    and Miller (1961). Extending the DeAngelo and DeAngelo analysis into a dynamic

    analytical model, and we also provide some comparative analysis between the payout

    ratio and the following: (i) change in total risk; (ii) change in systematic risk; (iii)

    change in total risk and systematic risk, simulataneously; (iv) no change in risk.

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