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Current vs. Permanent Earnings for Estimating Alternative Dividend Payment Behavioral Model: Theory, Methods and Applications* Cheng-Few Lee Hong-Yi Chen Alice Lee Tzu Tai Rutgers University, USA lee@business.rutgers.edu National Central University, Taiwan State Street, USA Rutgers University, USA * Speech to be delivered to Stockholm University on April 29-30, 2013. Flow Chart of Dividend Policy and Dividend Behavior Dividend Policy Dividend Irrelevance Theory Dividend Relevance Theory without Tax Effect Empirical Work Theory Time-Series Dividend Relevance Theory with Tax Effect CAPM Approach Non-CAPM Approach Cross-Sectional 2 Flow Chart of Dividend Policy and Dividend Behavior Dividend Relevance Theory without Tax Effect Theory Empirical Work Time-Series Dividend Behavior Cross-Sectional Signaling Hypothesis Free Cash Flow Hypothesis Flexibility Hypothesis Life-Cycle Theory Price Multiplier Model Cov. btw ROE and g Partial Adjustment Process Information Content or Adaptive Expectations Myopic Dividend Policy Residual Dividend Policy 3 Empirical Analyses in Dividend Policy Research Descriptive Data Analysis Time Series Cross-Sectional Regression Analysis Time Series Probit / Logit Cross-Sectional Fama-MacBeth Procedure Panel Data Analysis Seemly Uncorrelated Regression (SUR) Fixed Effect Model 4 Outline 1. Introduction 2. Theoretical determination of firm’s permanent and transitory earnings and dividends 3. Alternative methods for decomposing current EPS into permanent- and transitory-EPS components 3.1 Darby’s (1974) method 3.2 Lee and Primeaux’s (1991) method 3.3 Garrett and Priestley’s (2000) Kalman filter method 3.4 Lambrecht and Myer’s (2012) method 4. Empirical results in estimating two alternative dividend behavior models 4.1 Darby’s method and Lee and Primeaux’s method 4.1.1 Results from 608 Individual Regressions 4.1.2 Results from Pooled Regression 4.2 Lambrecht and Myer’s method 4.3 Combined model 4.3.1 Results from 605 Individual Regressions 4.3.2 Results from Pooled Regression 5 Summary and Concluding Remarks 5 Introduction 1. Earnings of a firm are allocated to retained earnings or dividend payments by a financial decision. 2. The earnings of a firm can be classified into either permanent or transitory components; permanent earning power creates the permanent component, and the transitory component is composed of income of a temporary nature. 3. Forecasts of dividends are important to both security analysts and financial managers, and either conditional or unconditional methods are generally used to forecast dividend payments. 4. Lintner (1956) developed his well-known dividend payment behavior model to describe how managers determine their dividend payment. This model has been widely used in finance research (see Marsh and Merton, 1987; Lee and Primeaux,1991; Garrett and Priestley, 2000; Lambrecht and Myer, 2012). 5. However, using current EPS to estimate Lintner’s dividend behavior model might be also subject to measurement error problem (see Miller and Modigliani, 1966)) . 6 The main purposes of this paper are… 1. To theoretically explain why firms generally allocate permanent earnings and transitory earnings between dividends payments and retained earnings 2. To develop alternative methods for decomposing current earnings and dividends into permanent and transitory components 3. To empirically estimate alternative dividend payment behavior models by using two alternative permanent EPS estimates for both individual firms and pooled data 4. To test Lambrecht and Myer’s theoretically results related to alternative dividend payment behavior models. 7 Theoretical determination of firm’s permanent and transitory earnings and dividends • The permanent-income hypothesis explains that consumption is not a function of current income but a function of permanent income (Milton Friedman,1957).Current income is divided into two components: E = EP + ET (1) where E is the current income per share of the firm, EP is the permanent income per share of the firm, and ET is the transitory income per share of the firm. • Dividends can also be divided into two similar components: D = D P + DT (2) where D is the current dividends per share paid by the firm, DP is the permanent dividends per share paid by the firm, and DT is the transitory dividends per share paid by the firm. 8 Theoretical determination of firm’s permanent and transitory earnings and dividends • Permanent dividends are dividends that the business firm systematically pays based on its permanent earnings, dividends paid out of transitory earnings would constitute extra dividends. • All income is either paid out in dividends or retained by the business in the form of retained earnings: E =EP+ ET, E − (DP + DT) − R = 0 (3) where R is the retained earnings per share of the firm, the other terms are as defined in Equations (1) and (2), and ET and DT are ‘‘random” or “chance” variations in income and dividends per share. 9 Theoretical determination of firm’s permanent and transitory earnings and dividends • Different sources of dividend payment (i.e., permanent or current income) may have different implications in determining a firm’s dividend payment behavior. • This condition provides the motivation for examining both permanent and current earnings per share for describing a firm’s dividend payment behavior in the empirical section of this work. • In the next section, we will discuss alternative methods for decomposing current EPS into permanent and transitory EPS components. 10 Alternative methods for decomposing current EPS into permanent- and transitory-EPS components • Darby’s (1974) method • The relationship between current dividend and permanent earning can be defined as Di ,t EiP,t i ,t (4) where Di ,t and EiP,t are current DPS and permanent EPS for ith firm in period t respectively. • Since permanent earnings are not directly observable, we use Eq. (5) to estimate EiP,t as: EiP,t (1 i ) Ei ,t i (1 C) E Pi ,t 1, 0 i 1 (5) where λi represents the weight used to calculate the permanent earnings per share and C represents the trend rate of EPS growth. • Initial value of permanent EPS EPi,0 and trend rate C can be derived from Eqs. (6) and (7): Log Ei,t = a1 + a2t + ut (6) (7) 11 E Pi ,0 eaˆ1 , log(1 C) aˆ2 Alternative methods for decomposing current EPS into permanent- and transitory-EPS components • Lee and Primeaux’s (1991) method By using the adaptive-expectation model, the permanent EPS, EPi,t, can be determined as EiP,t (1 i ) Ei ,t i E Pi ,t 1 , 0 i 1 (9) By Koyck transformation, we can use Eq. (10) to obtain λi for firm i: Di ,t 0 0 Ei ,t Di ,t 1 (10) where 0 (1 i ), 0 (1 i ), and i • Then, by using estimated λi , current EPS, and initial permanent EPS which was described in Darby’s method, we can estimate permanent EPS in period t. 12 Alternative methods for decomposing current EPS into permanent- and transitory-EPS components • Garrett and Priestley’s (2000) Kalman filter method • Garrett and Priestley use Kalman filter to deal with measurement Eq. (11) and transition Eqs. (12) and (13) and to estimate unobservable permanent EPS: Ei ,t EiP,t ET i ,t (11) EiP,t EiP,t 1 t 1 t (12) t t 1 t (13) where Ei,t is current EPS, transitory EPS is ETi,t ,and the permanent EPS, EPi,t, evolve as a random walk with a changing trend, 𝛽𝑡 . 13 Alternative methods for decomposing current EPS into permanent- and transitory-EPS components • 3.4 Lambrecht and Myer’s (2012) method • Using the joint determination of manager’s rent and cash dividend payment to equity holders, Lambrecht and Myer (2012) derive a Lintner dividend payment behavior in terms of permanent income as: dt a0 a1dt 1 Yt et (14) where dt and dt 1 are total dividend payout at time t and t-1 respectively; Yt is the firm’s permanent income at time t. • If the profit margin t follows the autoregressive process t t 1 t , then permanent income Yt can be simplified as: i (15) Y ( K (1 )TD ) i ,t 1 i i i i ,t i i i ,t 1 where Kii,t is total operating income without corporate tax for ith firm in period t; TDi ,t 1 is the total debt for ith firm in period t-1; i is interest rate; and is the autoregression coefficient for operating income of the firm i. 14 Alternative methods for decomposing current EPS into permanent- and transitory-EPS components • 3.4 Lambrecht and Myer’s (2012) method • Lambrecht and Myer (2012) claim that Lintner model as traditionally estimated can be defined as: dt b0 bTE 1 t b2 dt 1 ut (16) • Their true model is: SOA 2 SOA (1 ) SOA dt TEt SOAdt 1 t TDt 1 et 1 1 1 (17) where dt dt dt 1 ; the current reported earnings is TEt pt t TDt 1; pt and t are permanent and transitory components respectively. TDt 1 is the component neither permanent nor transitory component of earnings. SOA is the speed of adjustment; is the constant term of dividend behavior model, it generally used to measure the degree of reluctance to cut dividend, defined as percentage of earnings paid as cash dividend, =1/(1+ ). 15 Alternative methods for decomposing current EPS into permanent- and transitory-EPS components • 3.4 Lambrecht and Myer’s (2012) method • If does not approach to 1, then equation (17) can be modified as P dt b0 bTE 1 t b2 dt 1 b3 TDt 1 ut (18) where TE Pt is the estimated permanent earnings. • Equation (18) is obtained by combining Lambrecht and Myer’s (2012) theory and estimating permanent earnings estimated by either Darby’s or Lee and Primeaux’s method. • This specification takes care both specification errors and the transitory components of earnings. This new specification is most important contribution of this research. 16 Empirical results in estimating three alternative dividend behavior models • Sample • EPS and DPS data of 608 firms from Compustat which has at least 30 years data ended in 2011 to perform the empirical studies (see Appendix C). • The methods used to do the empirical studies include (1) Darby’s method and Lee and Primeaux’s method (2) Lambrecht and Myer’s method (3) combined model as defined in Equation (18) 17 Darby’s and Lee and Primeaux’s methods • We use current and permanent EPS measures to estimate following two alternative dividend payment behavior models as: Di ,t c0 c1Ei ,t c2 Di ,t 1 ui ,t (19a) Di ,t c0 c1EiP,t c2 Di ,t 1 ui ,t (19b) Di ,t c '0 c '1 Ei ,t c '2 Di,t 1 c3 Di,t 2 ui,t (20a) Di ,t c '0 c '1 EiP,t c '2 Di,t 1 c3 Di ,t 2 ui,t (20b) • Following Lee and Chen (2013), we now analyze the biased associated with estimated c1 and c2 as follows: Case 1: when COV ( EiP,t , Di ,t 1 ) 0, 12 ( D D c2 D2 ) c1 12 (21a) ˆ plim cˆ1 c1 2 , plim c c 0 2 2 ( E 12 ) D2 ( E2 12 ) i ,t i ,t 1 P i ,t i ,t 1 i ,t 1 P i ,t Case 2: when COV ( EiP,t , Di ,t 1 ) 0, plim cˆ1 c1 E 2 P i ,t 2 c1 12 1 , plim cˆ2 c2 c1bD E P 2 i ,t 1 i ,t 1 E2 P (1 RE2P D ) bD E P 12 i ,t 1 i ,t i ,t i ,t i ,t 1 (21a) where 12 is the variance of EiT,t , bD E is the auxiliary regression coefficient of a regressing Di,t 1 on EiP,t , and RE2 D is the correlation coefficient between EiP,t and Di ,t 1 . P i ,t 1 i ,t P i ,t i ,t 1 18 Darby’s and Lee and Primeaux’s methods • Equations (21a) and (21b) imply that the estimated c1 and c2 are downward biased. Hence, the estimated intercept as defined in Equation (21c) is upward biased. (21c) cˆ0 Di ,t cˆ1Ei ,t cˆ2 Di ,t 1 • Therefore, we need to deal with this kind of errors-in-variable problem. • First, we use Darby’s and Lee and Primeaux’s methods to estimate permanent EPS. Then we will use DPS and both current EPS and permanent EPS to estimate equations (19a), (19b), (20a), and (20b) for individual firms and pooled data. 19 Darby’s and Lee and Primeaux’s methods Table 1 (A) Individual Regression Results for Equations (19a), (19b), (20a) and (20b) • Current EPS is used in Eqs. (19a) and (20a). • The permanent EPS calculated by Darby’s method, is used in Eqs. (19b) and (20b). • The permanent EPS calculated by Lee and Primeaux’s method, is used in Eqs. (19b)* and (20b)*. 20 Darby’s and Lee and Primeaux’s methods Table 1(B). Partial Adjustment Coefficient and Long-Term Payout Ratios • Current EPS is used in Eqs. (19a) and (20a). • The permanent EPS calculated by Darby’s method, is used in Eqs. (19b) and (20b). • The permanent EPS calculated by Lee and Primeaux’s method, is used in Eqs. (19b)* and (20b)*. 21 Darby’s and Lee and Primeaux’s methods • Table 2. Alternative EPS and Payout Ratios • According to the average estimated λi by using Darby’s and Lee and Primeaux’s methods, it implies that Lee and Primeaux’s method for estimating permanent earnings weights more heavily on current earnings than those from Darby’s method. 22 Darby’s and Lee and Primeaux’s methods Table 3 Pooled Regression Results for Equations (19a), (19b), (20a) and (20b) • Current EPS is used in Eqs. (19a) and (20a). • The permanent EPS calculated by Darby’s method, is used in Eqs. (19b) and (20b). • The permanent EPS calculated by Lee and Primeaux’s method, is used in Eqs. (19b)* and (20b)*. 23 Lambrecht and Myer’s method • Since i is not available for individual firm, therefore, we use limiting definition of Lambrecht and Myers’ (2012) method (see equation (15)) to estimate permanent income and apply permanent income to test dividend payment behavior models: di ,t a0 a1TEi ,t a2 d i ,t 1 ei ,t (22a) di ,t a0 a1Yi ,t a2 di ,t 1 ei ,t (22b) (23a) di ,t a0 a1TEi ,t a2 di ,t 1 a3di ,t 2 ei ,t (23b) di ,t a0 a1Yi ,t a2 di ,t 1 a3di ,t 2 ei ,t • In addition, Lambrecht and Myers (2012) show that the Lintner model may be subject to the model misspecification. We therefore test the model misspecification by using Equation (24): (24) di ,t a0 a1TEi ,t a2 di ,t 1 a3 iTDi ,t 1 ei ,t 24 Lambrecht and Myer’s method Table 4 Individual Regression Results for Equations (22a), (22b), (23a), (23b) and (24) • There are 25.45% of firms whose dividend payouts can be determined by their interest expenses. • It indicates that there exists specification error in Lintner’s model in terms of current earnings. 25 Combined model • We will modify Equation (18) in terms of EPS and DPS as follows: Di ,t b0 b1Ei ,t b2 Di ,t 1 b3 Ii ,t 1 ui ,t (25a) Di ,t b0 b1EiP,t b2 Di ,t 1 b3 Ii ,t 1 ui ,t (25b) where Di,t and Di,t-1 are dividend per share for firm i at time t and t-1, respectively; Ei,t and EPi,t are current and permanent EPS for firm i at time t ; Ii,t-1 is the interest expense per share firm i at time t-1. • Eqs. (25a) and (25b) can be used to test whether the companies’ annual EPS is following the random walk or not and also to test whether Lambrecht and Myers’s budget constraint in Eq. (26) is held for individual firm or not. dt rt t ( K ) TDt 1 (TDt TDt 1 ) (26) where dt is total dividend payout at time t , TDt and TDt 1 is the total debt in period t and t-1, respectively; is interest rate; rt is managerial rents at time t; t ( K ) is gross profit at time t. 26 Combined model Table 5 Individual Regression Results for Equations (25a) and (25b) • If the budget constraint does not hold, then the term associated with interest expense will not necessary exist. • There are only 22.64%, 21.16%, or 22.15% firms with budget constraints hold under Lambrecht and Myers theoretical model. 27 Combined model Table 6. Pooled Regression Results for Equations (25a) and (25b) • The insignificant coefficient of interest expense per share implies that the permanent EPS not only can remove random fluctuation of EPS but also can remove parts of misspecification error which is shown by Lambrecht and Myers. 28 Summary and Concluding Remarks • Based upon the theories and methods developed by Marsh and Merton (1987), Lee and Pri-meaux (1991), Garrett and Priestley (2000), and Lambrecht and Myers (2012), we perform both theoretically analyses and empirical studies in this paper. 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Weston, F.J., Brigham, E., and Besley,S., (2004) “Essentials of Managerial Finance,” Cengage South-Western 32 Optimal payout ratio under uncertainty and the flexibility hypothesis: Theory and empirical evidence The Model for Optimal Dividend Policy - 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 - The retained earnings of the firm, y t , can be expressed as y (t ) x(t ) m(t )d (t ) where m(t ) is the number of shares outstanding, and d (t ) is dividend per share at time t. 33 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. 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 - A differential equation can be formulated: p(t ) [ where m(t ) m(t ) k ] p(t ) G (t ) (a bI h) A(o)eth A(o)2 (t )2 (t )2 e2th G(t ) m(t ) m(t )2 • 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) [e( h k )(T t ) 1] (t ) 2 (t ) 2 = 1 h (a bI ) (h k ) (t ) 2 (t ) 2 34 Optimal Payout Ratio vs. Systematic Risk D(t ) / x (t ) (t ) 2 2 ( t ) h (1 a bI e( h k )(T t ) 1 ) h k High growth firms h a bI : negative relationship between optimal payout ratio and systematic risk. Low growth firms h a bI : positive relationship between optimal payout ratio and systematic risk 35 Multivariate Regression 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 Flexibility Hypothesis FCF Hypothesis 36 36 Sustainable Growth Rate, Optimal Growth Rate, and Optimal Payout Ratio: A Joint Optimization Approach Joint Optimization of Growth Rate and Payout Ratio • The new investment at time t is t dA t g s ds o A t g t A o e dt Y t D t n t p(t ) LA t Retained Earnings New Equity New Debt p t price per share at time t; degree of market perfections, 0 < l; L = the debt to total assets ratio n t P t the proceeds of new equity issued at time t; where D t the total dollar dividend at time t; 37 Joint Optimization of Growth Rate and Payout Ratio • 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 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. 38 Joint Optimization of Growth Rate and Payout Ratio p o dˆ t e kt dt T Discount cash flow 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 t t Risk Adj. Future Dividends maximize p(o) by jointly determine g(t) and n(t). Optimal Growth Rate g t * r go r rt 2 r rt 2 go r go e 1 1 e go Logistic Equation – Verhulst (1845) => a convergence process 39 Case I: Optimal Growth Rate v.s. Time Horizon r r t 2 e * 2 g t g* t 2 t r r t 2 1 1 e g o When g 0 r , g* t 0.When g 0 r , g* t 0.When g 0 r , g* t 0. r r 1 go 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 g o r g o e rt 2 2 g * t When initial growth rate is lower than the target rate (ROE), r is positive. => If the target rate (ROE) is higher, the adjustment process will be faster. 40 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 2 g u du ks 2 1 e 0 s r g * s ds * • Assuming 1 and g * t g * , ( g * k )(T t ) 2 e 1 D t g ( t ) * 1 1 g Y t r t (g* k ) (t ) 2 * - Wallingford (1972), Lee et al. (2010) 41 Stochastic Growth Rate and Specification Error dA t g s ds A t g t A o e Y t D t n t p (t ) LA t t o dt Retained Earnings New Equity New Debt When a stochastic growth rate is introduced, g t N g t , g2 t g s ds g s ds g s ds r t g t A o e 0 n t p t Cov r t , A o e 0 E t e 0 E d t n t n t t t t g s ds If Cov r t , A o e 0 is positive, d t in the previous analysis is overestimated. t 42 The higher of the Cov., the higher possibility to stop the cash dividends. 43 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 44 consideration of free cash flow problem. 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. 45