AN INVESTIGATION OF GORDON'S COMMON STOCK VALUATION MODEL by PATRICK JOHN SMITH B.A., U n i v e r s i t y of B r i t i s h Columbia, 1958 A t h e s i s submitted i n p a r t i a l f u l f i l l m e n t o the requirements f o r the Degree of Master o f B u s i n e s s A d m i n i s t r a t i o n i n t h e Department of Commerce and B u s i n e s s A d m i n i s t r a t i o n We a c c e p t t h i s t h e s i s as conforming required standard THE UNIVERSITY OF BRITISH September, 1968 to the COLUMBIA In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. thesis I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of this f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s representatives. It is understood that copying o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f COMMERCE The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada SEPTEMBER 13, 1968 ABSTRACT The purpose of t h i s study was t o determine whether a model based upon the d i v i d e n d formulation o f Myron J . Gordon provides an adequate e x p l a n a t i o n o f t h e v a r i a t i o n i n common s t o c k p r i c e s . In p a r t i c u l a r , the hypothesis tested i s that i n v e s t o r s mainly consider dividends, t h e r a t e of growth i n d i v i d e n d s c h a r a c t e r i s t i c s o f the f i r m s The and t h e r i s k i n v a l u i n g shares o f common model was t e s t e d by u s i n g m u l t i p l e r e g r e s s i o n on a c r o s s - s e c t i o n o f U.S. companies i n . t h e machinery stock. analysis industry i n each o f the y e a r s 1956 t o 1965. A l t e r n a t i v e measures o r proxies f o r "normalized" earnings, growth, b u s i n e s s r i s k and f i n a n c i a l r i s k were used i n t e s t i n g t h e model. E m p i r i c a l r e s u l t s s u p p o r t e d the p r o p o s i t i o n t h a t Gordon's model p r o v i d e s prices. an adequate e x p l a n a t i o n o f the v a r i a t i o n i n s t o c k On average, between 76% and 81% o f the t o t a l v a r i a t i o n was explained by the model over the t e n - y e a r p e r i o d . each y e a r ranged between .68 and .90. dividend, The R^ v a l u e s f o r The c o e f f i c i e n t s o f the growth and s i z e v a r i a b l e s were s i g n i f i c a n t a t the 5% l e v e l o r b e t t e r i n almost a l l t h e y e a r s t e s t e d and except f o r growth in two y e a r s , these c o e f f i c i e n t s had the s i g n i n d i c a t e d by the theory. B u s i n e s s r i s k and f i n a n c i a l r i s k performed p o o r l y as explanatory variables. The c o e f f i c i e n t s f o r both v a r i a b l e s were n o t s t a t i s t i c a l l y significant a t the 5% l e v e l i n most y e a r s and the b u s i n e s s coefficient f r e q u e n t l y d i d n o t have t h e expected ii sign. risk TABLE OF CONTENTS PAGE ABSTRACT i i LIST OF TABLES v i CHAPTER I. INTRODUCTION TO THEORETICAL COMMON STOCK VALUATION MODELS 1 A. Purpose o f the Study 1 B. Importance of the Study 2 C. Methodology 2 D. O u t l i n e of P r e s e n t a t i o n 2 E. P r e s e n t V a l u e Approach t o V a l u a t i o n 3 F. Growth Models of V a l u a t i o n 4 1. "No Growth" 4 2. Simple Growth 4 3. Constant Growth 6 G. H. II. A l t e r n a t i v e F o r m u l a t i o n s o f Constant Growth. 9 1. D i v i d e n d Approach 9 2. Investment O p p o r t u n i t i e s Approach 10 3. Stream of E a r n i n g s Approach 12 4. D i s c o u n t e d cash f l o w approach 13 Reasons f o r A d o p t i n g Gordon's Model 14 GORDON'S STOCK VALUATION MODEL 16 A. 16 Assumptions iii CHAPTER PAGE B. III. Interpretation C. Assumptions under which k is an Increasing function of br 23 REVIEW OF GORDON'S EMPIRICAL INVESTIGATIONS ... 25 A. 25 Linear Models B. Refinement 32 C. Nonlinear Model 34 D. Nolev Model 37 E. Sim lev Model 43 F. Adlev Model 48 G. Eko Model 48 H. Conclusions IV. 18 from Empirical Findings ....... 54 FORMULATION AND TESTING OF THE MODEL 55 A. Selection of Variables 55 1. Basic Model 55 2. Risk Variables 55 a. Business Risk 56 b. Financial Risk 56 c. Size 56 3. Complete Model 57 B. Data ... C. Measurement of the Variables 57 58 1. Dependent Variable - Price (P) ........ 58 2. Independent Variables 59 iv CHAPTER PAGE D. V. a. Dividends (D) b. Growth Rate ( b r ) 59 c. B u s i n e s s R i s k (u) 63 d. F i n a n c i a l R i s k (h) 65 e. Size 65 (S) 59 66 Methodology RESULTS AND CONCLUSIONS 67 A. Regression Results 68 B. Conclusions 79 82 BIBLIOGRAPHY v LIST OF TABLES TABLE 1-1 PAGE Investment O p p o r t u n i t i e s Approach t o Constant Growth 11 3-1 R e g r e s s i o n of P r i c e on D i v i d e n d and Income .. 3-2 R e g r e s s i o n of P r i c e on D i v i d e n d and Earnings Retained 3-3 3-4 3-5 26 30 R e g r e s s i o n of P r i c e on D i v i d e n d , R e t a i n e d E a r n i n g s , Change i n D i v i d e n d , Change i n R e t a i n e d E a r n i n g s , A l l D e f l a t e d by Book Value 33 R e g r e s s i o n of P r i c e on D i v i d e n d , Growth Rate, and U n c e r t a i n t y V a r i a b l e s . 36 R e g r e s s i o n of P r i c e on E x p o n e n t i a l l y Averaged D i v i d e n d and Growth Rate and on R i s k V a r i a b l e s * 40 3-6 Regression S t a t i s t i c s f o r the Simlev Model .. 45 3-7 Regression S t a t i s t i c s f o r the Adlev Model ... 49 3-8 Regression S t a t i s t i c s f o r the Eko Model 52 5-1 R e g r e s s i o n S t a t i s t i c s f o r Ln P = lncc + In D + a In (1 + b r ) + 0 3 l n (1 + u) + 0:4 l n (1+h) + InS Q 0:5 2 5-2 R e g r e s s i o n S t a t i s t i c s f o r Ln P = l n a + cq. l n D + a In (1+br) + a l n (1+u) + 0:4 l n (1+h) + 0:5 InS A f t e r Change i n Growth V a r i a b l e from G 2 "i b 5-3 r 3 . Y_ -. D . _Y .- D , 71 7 t o R e g r e s s i o n S t a t i s t i c s f o r Ln P = l n a + ct]_ In D + a In (1+br) + a l n (1+u) + 0 4 In (1+h) + 0:5 InS A f t e r Change i n B u s i n e s s R i s k V a r i a b l e °Y °Y from u = .-*» to ~ Q 2 5-4 69 3 -7 0 /-> R e g r e s s i o n S t a t i s t i c s f o r Ln P = l n a + a]_ In D + a In (1+br) + a In (1+u) + 0:4 In (1+h) + a5 InS A f t e r Change t o O p e r a t i n g Income w i t h D 2 u = 22 W 3 and br = 75 A vi PAGE TABLE 5-5 R e g r e s s i o n S t a t i s t i c s f o r Ln P = I n a + a-^ I n D + a i n (1+br) + 0:3 i n (1+u) + a4 I n (1+h) + 0:5 InS A f t e r Change t o O p e r a t i n g Income w i t h Q 2 0 5-6 Y 77 R e g r e s s i o n S t a t i s t i c s f o r Ln P = l n a + a-^ I11 D + a I n (1+br) + 0:3 In (1+u) + 0:4 I n (1+h) + InS A f t e r Change to O p e r a t i n g Income w i t h D 2 °Y u = — W -,. U+P.S.+C.L. and h = — E vii CHAPTER I INTRODUCTION TO THEORETICAL COMMON STOCK VALUATION MODELS A. The Purpose o f t h e Study purpose o f t h i s study i s to determine whether a model based upon t h e d i v i d e n d f o r m u l a t i o n o f Myron J . Gordon p r o v i d e s an adequate e x p l a n a t i o n The f o r t h e v a r i a t i o n i n common s t o c k p r i c e s . Gordon model, which i s commonly l a b e l e d t h e "Gordon and S h a p i r o model,"1 equates t h e v a l u e o f a share value of a l l i t s future o f common s t o c k t o t h e p r e s e n t dividends. I t w i l l be shown t h a t under c e r t a i n assumptions the p r i c e o f a share equals the c u r r e n t d i v i d e n d d i v i d e d by t h e d i f f e r e n c e between t h e r a t e o f r e t u r n r e q u i r e d by i n v e s t o r s and t h e r a t e o f growth i n t h e d i v i d e n d . The i n v e s t o r s ' r e q u i r e d r a t e o f r e t u r n a l s o i s the r a t e a t which the d i v i d e n d e x p e c t a t i o n i s discounted. T h i s r a t e o f p r o f i t depends upon t h e growth r a t e o f t h e d i v i d e n d and the r i s k c h a r a c t e r i s t i c s of t h e f i r m . then, The h y p o t h e s i s t o be t e s t e d , i s t h a t i n v e s t o r s , i n v a l u i n g a share o f common s t o c k , m a i n l y consider the d i v i d e n d , the growth r a t e o f the d i v i d e n d and t h e r i s k c h a r a c t e r i s t i c s of t h e company. ^The i n i t i a l a r t i c l e on t h i s model appeared i n Myron J . Gordon and E l i S h a p i r o , " C a p i t a l Equipment A n a l y s i s : The Required Rate of P r o f i t , " Management S c i e n c e , I I I (October, 1956), 102-110. 1 2 2. By Importance of the Study t e s t i n g a s t o c k v a l u a t i o n model i n c o r p o r a t i n g a about i n v e s t o r b e h a v i o r we determinants of share these determinants by hope to g a i n i n f o r m a t i o n on p r i c e s and the the r e l a t i v e weights a t t a c h e d the s t o c k market. u s e f u l not o n l y to i n v e s t o r s s e e k i n g a l s o to c o r p o r a t e managers s e e k i n g of hypothesis to T h i s i n f o r m a t i o n would to maximize t h e i r wealth to maximize the market be but price the company's s t o c k . C. The model was Methodology t e s t e d by u s i n g m u l t i p l e r e g r e s s i o n a n a l y s i s on a c r o s s - s e c t i o n of f i r m s i n the machinery i n d u s t r y i n the U n i t e d S t a t e s i n each of the y e a r s 1956 l e a s t - s q u a r e s was the parameters of the r e g r e s s i o n equations. used to e s t i m a t e H i s t o r i c a l d a t a was to 1965. The method of p r o v i d e d by Standard and Poor's Compustat s e r v i c e . D. The concept O u t l i u e of P r e s e n t a t i o n r e s t of t h i s chapter w i l l i n t r o d u c e the p r e s e n t of v a l u a t i o n , d i s c u s s s e v e r a l growth models of value stock v a l u a t i o n , d e s c r i b e the a l t e r n a t i v e f o r m u l a t i o n s of c o n s t a n t and conclude for t e s t i n g purposes. of by s t a t i n g the reasons f o r adopting Gordon's model Chapter I I d e s c r i b e s the t h e o r e t i c a l b a s i s the Gordon model, i n c l u d i n g i t s assumptions, components interpretation. growth Chapter I I I reviews Gordon's i n v e s t i g a t i o n s . the s t a t i s t i c a l and r e s u l t s of Chapter IV d e s c r i b e s the f o r m u l a t i o n t e s t i n g of the model used i n t h i s study, and i n c l u d i n g the measurement 3 problems encountered. c o n c l u s i o n s of the E. Although Chapter V p r e s e n t s the r e s u l t s and study. P r e s e n t Value Approach to V a l u a t i o n t h e r e i s evidence t h a t p r e s e n t v a l u e approaches t o s t o c k v a l u a t i o n date back at l e a s t to 1869, 2 J.B. W i l l i a m s i s g e n e r a l l y c r e d i t e d as the o r i g i n a t o r of s t o c k v a l u a t i o n models. In a book p u b l i s h e d i n 1938, W i l l i a m s d e f i n e d the investment a s t o c k as the p r e s e n t v a l u e of i t s f u t u r e i n f i n i t e stream t Vo = t I = iTj-vt 3 + TT-JV Tr v 2 2 + H3V 3 + ... (1-1) value at s t a r t = d i v i d e n d i n year t 1 -, by 1 + i i of d i v i d e n d s : = o o where Vo = investment ir v a l u e of definition = i n t e r e s t r a t e sought by the investor. By r e p l a c i n g Vo w i t h Po, v w i t h — i — E q u a t i o n (1) can be w r i t t e n 1 + i i n a more f a m i l i a r form as Po = E t = 1 D t E (1 + i ) t I f the d i v i d e n d stream = Di _ 1 + i + D? — (1 + i ) 2 + D3 (1 + i ) 3 + ... (1-2) remains c o n s t a n t , as i s the case w i t h p r e f e r r e d s t o c k , the e q u a t i o n reduces to Po = (1-3) S e e Robert M. S o l d o f s k y , "A Note on the H i s t o r y of Bond T a b l e s and Stock V a l u a t i o n Models," J o u r n a l of F i n a n c e , XXI (March, 1966), 103-111. 2 J o h n Burr W i l l i a m s , The Theory of Investment Value N o r t h - H o l l a n d P u b l i s h i n g Company, 1938), p. 56. 3 (Amsterdam: 4 F. Growth Models of Valuation An investor who purchases a share of common stock for the future dividends r e a l i s t i c a l l y w i l l expect a growing stream of dividends. Although the growth rate w i l l vary over time, shareholders can be considered as forming a subjective probability distribution of future growth rates at any particular period of time. The mean of this distribution can be considered as the constant normal growth rate. This section describes and illustrates various types of growth encountered in stock valuation models. 1. "No Growth" ^ A static company can be defined as one which expects to receive a constant annual net income, Y , from its existing assets and has t no future investment opportunities that w i l l provide a rate of return greater than the return expected by shareholders. Hence, there is no growth possible for earnings or dividends and the price of the company's share is the sum of an annuity discounted at the shareholder's required rate of return, k, P = I t=l and . (1 + k)t = Y k k = -XP (1-5) being the reciprocal of the price-earnings ratio. 2. Simple Growth To illustrate simple growth i t is useful to adopt the model of Ezra Solomon, which is based upon the investment opportunities approach A to v a l u a t i o n . of The p r i c e o f a common share i s equated t o t h e sum t h e p r e s e n t worth o f t h e c o n s t a n t annual n e t e a r n i n g s e x i s t i n g a s s e t s and t h e premium r e s u l t i n g from ability from the c o r p o r a t i o n ' s to i n v e s t a c o n s t a n t amount a t r a t e s o f r e t u r n g r e a t e r than the s h a r e h o l d e r s r e q u i r e d r a t e o f r e t u r n . Let P = market p r i c e o f a l l - e q u i t y company Y = c o n s t a n t annual n e t e a r n i n g s from existing assets b = f r a c t i o n of earnings r e t a i n e d f o r investment r = c o n s t a n t r a t e o f r e t u r n on f u t u r e investment opportunities k = shareholder's required rate of r e t u r n r > k Then an investment o f bY i n each y e a r s t a r t i n g i n p e r i o d 0 ( t h e present) w i l l generate a d d i t i o n a l p e r p e t u a l income streams of ( b Y ) r , each w i t h a p r e s e n t v a l u e a t t h e time t h e investment i s made equal to t T =l (bY)r (1 + k ) t bYr ~k~ which i s t h e v a l u e of the f i r s t payment. of t h i s stream (1-6) The p r e s e n t worth today of a d d i t i o n a l payments bYr/k i s ~ ^ bYr/k (1 + k ) t _ bYr k^ To produce t h i s a d d i t i o n a l income, i t was n e c e s s a r y each year to i n v e s t bY which has a p r e s e n t v a l u e o f bY/k. The n e t p r e s e n t E z r a Solomon, The Theory o f F i n a n c i a l Management (New York: Columbia U n i v e r s i t y P r e s s , 1963), pp. 59-62. 6 v a l u e of the a d d i t i o n a l income from investment opportunities, therefore, i s bYr bY — k k l , (1-8) which s i m p l i f i e s t o M . k x (1-9) k 1 Then the p r i c e of a common share i s The second term i s the investment o p p o r t u n i t i e s growth I t i n c r e a s e s p r o p o r t i o n a t e l y w i t h the p r o f i t a b i l i t y being r-k. factor. o f investment, I f r=k, the growth f a c t o r e q u a l s z e r o , w h i l e i f r<k, t h e p r i c e i s decreased. 3. Constant Growth While t h e s i m p l e growth model assumed a c o n s t a n t amount of investment each y e a r , t h e dynamic growth model assumes i n c r e a s i n g investment at a constant r a t e . Myron J . Gordon has developed f r e q u e n t l y used i s based (a) 5 a d i v i d e n d model which i s f> f o r growth models o f s t o c k v a l u a t i o n . upon the f o l l o w i n g The model assumptions: t h e c o r p o r a t i o n engages i n no o u t s i d e e q u i t y financing; (b) i t does n o t use debt financing; (c) i t w i l l e a r n a r e t u r n , r , on investment i n every f u t u r e p e r i o d ; "*For example, see Solomon, Theory o f F i n a n c i a l Management, pp. 62-67. % y r o n J . Gordon, The Investment, F i n a n c i n g and V a l u a t i o n of the C o r p o r a t i o n , Homewood, 111., R i c h a r d D. I r w i n , I n c . , 1962, c h s . A and 5. 7 (d) i t w i l l retain the fraction, b, of its income in every future period. Since there is no outside financing, the expected dividend is a function of the corporation's current income, the investment or retention rate (which are the same) and its rate of return on investment. The dividend in any future period is certain D t = (1 - b) Y (1-11) t If the net income when t = o was Yo then Y 1 = Yo + rbYo = Yo (1 + rb) (1-12) since during period t = o, retained earnings of bYo have been invested at rate r . Yo and rbYo. Income in t=l therefore equals the sum of Equation (1 - 12) is a compound interest expression which, i f Y grows continuously at the rate g = br, can be written. t Y = Yo (1 + rb) t t = Yo erbt (1-13) The product rb is also necessarily the rate at which earnings and reinvestment as well as dividends w i l l grow. If k is the stockholder's required return on the dividend D , t -*» ' the share value at the end of t = o is t Po = / * D e-ktdt (1-14) t which can be rewritten using equations (1-11) and (1-13) as Po = Io (1 - b) Y erbt -ktdt (1-15) Po = (1-16) 0 e (1 ~ b)Yo, (k > rb) k - rb 8 Equation (1-16) can be f u r t h e r s i m p l i f i e d ^ t o Po = _2£_, _ (k>g) (1 k - g To i l l u s t r a t e : 17) A c o r p o r a t i o n pays a d i v i d e n d of $1.00 and has a d i v i d e n d growth of 5% per annum w h i l e i n v e s t o r s r e q u i r e a r e t u r n of 10% p e r annum. A s t o c k bought a t t h i s p r i c e would p r o v i d e d i v i d e n d y i e l d of .$3-rPP = 5% p l u s a c a p i t a l g a i n of 5% per annum $20.00 on the i n c r e a s e i n s t o c k p r i c e . seen by s o l v i n g E q u a t i o n k = 2° + Po ( 1 - 3 ) , g = o. T h i s r e l a t i o n s h i p r e a d i l y can be (1-17) f o r k g In the case o f a c o n s t a n t equation the i n v e s t o r w i t h a (1-18) d i v i d e n d stream p r e v i o u s l y r e f e r r e d t o i n The p a r t i c u l a r m e r i t o f t h i s model f o r t e s t i n g purposes i s t h a t s t o c k p r i c e i s g i v e n i n terms o f c u r r e n t values i n s t e a d o f expected v a l u e s o f b, Y and r . ^The same r e s u l t can be o b t a i n e d using algebra: Di D? D3 (1 + k) (1 + k)2 ( i + it) 3 Do (1 + g) (1 + k) £ t=l (Do (1 + g)2 (1 + k)2 Do (1 + ?-,)*• (1 + k ) t + = Do k - g Do (1 + g)3 (1 + k)3 + 9 G. A l t e r n a t i v e F o r m u l a t i o n s o f Constant S e v e r a l hypotheses, Growth: c o n s i s t e n t w i t h c o n s t a n t r a t e s of growth, have been advanced t o e x p l a i n common s t o c k v a l u e s . of t h e s e adopt t h e d i v i d e n d s , investment e a r n i n g s or d i s c o u n t e d cash f l o w 1. The most important o p p o r t u n i t i e s , stream of approach. D i v i d e n d Approach I t has been p o p u l a r s i n c e t h e time o f J.B. W i l l i a m s t o equate the p r i c e o f a common share p e r p e t u a l stream of dividends. above i l l u s t r a t e s The to t h e p r e s e n t v a l u e o f i t s f u t u r e tendency The Gordon-Shapiro model d i s c u s s e d the d i v i d e n d approach t o v a l u a t i o n . of w r i t e r s o f t h e " D i v i d e n d " s c h o o l i s t o c o n s i d e r the d i v i s i o n o f e a r n i n g s between d i v i d e n d s and r e t e n t i o n s c r i t i c a l to the v a r i a t i o n i n p r i c e o f a common s h a r e . 0. Harkavy concluded I n h i s 1953 s t u d y , t h a t w h i l e d i v i d e n d s a f f e c t p r i c e more i n the s h o r t - r u n than i n t h e l o n g - r u n , " . . . g i v e n two s t o c k s s i m i l a r i n a l l r e s p e c t s b u t d i v i d e n d payout, a h i g h e r p r i c e w i l l be p a i d f o r t h e s t o c k o f t h e company d i s t r i b u t i n g a g r e a t e r p r o p o r t i o n o f i t s earnings i n dividends."^ See Graham, Dodd and C o t t l e , S e c u r i t y A n a l y s i s : P r i n c i p l e s and Technique, 4 t h ed. (New York: McGraw-Hill Book Company, I n c . , 1962); 0. Harkavy, "The R e l a t i o n Between Retained E a r n i n g s and Common Stock P r i c e s f o r L a r g e , L i s t e d C o r p o r a t i o n , " J o u r n a l of F i n a n c e , V I I I (September, 1953), 283-297; J . E . W a l t e r , " D i v i d e n d P o l i c i e s and Common Stock P r i c e s , " J o u r n a l o f F i n a n c e , XI (March, 1956), 29-41; M.J. Gordon, " D i v i d e n d s , E a r n i n g s , and Stock P r i c e s , " Review o f Economics and S t a t i s t i c s , XLI (May, 1959), 99-105; D. Durand, "The Cost of C a p i t a l , C o r p o r a t i o n F i n a n c e and the Theory of Investment: Comment," American Economic Review, XLIX (September, 1959), 639-655; G.R. F i s h e r , "Some F a c t o r s I n f l u e n c i n g Share P r i c e s , " Economic J o u r n a l , LXXI (March, 1961), 121-141; J . L i n t n e r , " D i v i d e n d s , E a r n i n g s , Leverage, Stock P r i c e s and the Supply of C a p i t a l to C o r p o r a t i o n s , " Review o f Economics and S t a t i s t i c s , XLIV (August, 1962), 243-269. 0. Harkavy, I b i d . , 297. 10 2. Investment O p p o r t u n i t i e s To b e s t i s equivalent illustrate t h a t the investment o p p o r t u n i t i e s to the d i v i d e n d M i l l e r w i l l be d e s c r i b e d . ^ opportunities Approach approach approach, t h e model of M o d i g l i a n i and While Solomon adopted an investment approach i n h i s "simple growth" model, he used the Gordon-Shapiro model as the b a s i s f o r h i s "dynamic growth" model which assumes a c o n s t a n t r a t e of r e i n v e s t m e n t r a t h e r than a constant amount of r e i n v e s t m e n t . ^ The investment o p p o r t u n i t i e s approach s t a t e s t h a t the p r i c e of a common share i s determined by the e a r n i n g e x i s t i n g assets power o f the c o r p o r a t i o n ' s and the premium a r i s i n g from the a b i l i t y to make investments y i e l d i n g a r a t e o f r e t u r n g r e a t e r r e q u i r e d by the s h a r e h o l d e r s . To i l l u s t r a t e this o f the f i r m than t h a t approach, let Y ~= b = f r a c t i o n o f income r e t a i n e d and r e i n v e s t e d ; r = perpetual k = shareholders' constant annual income from e x i s t i n g assets; r a t e of r e t u r n on new investment required rate of return; r > k At the end o f y e a r 1, the c o r p o r a t i o n income a t the end o f y e a r 2 o f ( b Y ) r . i n v e s t s bY, which r e t u r n s an At t h i s time, a second i s made c o n s i s t i n g o f bY + b(bYr) o r bY (1 + b r ) . The f i r m investment continues to i n v e s t as shown i n T a b l e 1-1 so t h a t both income and r e i n v e s t m e n t i n c r e a s e over time a t the r a t e b r . M.H. M i l l e r and F. M o d i g l i a n i , " D i v i d e n d P o l i c y , Growth, and the V a l u a t i o n of Shares," J o u r n a l of B u s i n e s s , XXXIV (October, 1961), 411-433. Solomon, Theory of F i n a n c i a l Management, pp. 62-67. 11 TABLE Investment 1-1 O p p o r t u n i t i e s Approach t o Constant Growth End of Constant Year Income Total A Income Income Investment 1 Y - Y 2 Y (bY)r Y ( l + br) 3 Y bY(l + br)r Y(l + br) bY(l + b r ) The annual investment I t 2 1 1 - 1 bY(l + b r ) i s made e q u a l to Itr k (1 + k ) t The n e t b e n e f i t i n y e a r t , t h e r e f o r e , e q u a l s i S i n c e the investment t A ~r^* x t i n year t e q u a l s bY (1 + b r ) £""1, the p r e s e n t v a l u e of the t o t a l net b e n e f i t s e q u a l I bY(l + br)t-l t=l . (r - k)/k (1 + k ) t _r_zJi. { } I b Y k k x - br {1 + b r ) ^ t=l ; 1 k (1 + k ) t 5 The p r i c e of a share under the investment e q u a l s the sum opportunities 2 bY(l + b r ) ^ t Itr t=l Y(l + br) b Y ( l + br) g e n e r a t e s an annual income I r w i t h a p r e s e n t v a l u e a t the time the investment eo r t _ 2 bY approach of the p r e s e n t v a l u e s of the c o n s t a n t income and the 1 12 income from investment P = I t=l = 1 k o p p o r t u n i t i e s , that i s , 2_ (1 + k ) t + { + ^L_ k - br second term e q u a l s zero and r ^ _ k k } ( 1 _ i 9 ) k t h a t r > k, f o r i f r = k, i f r < k, P w i l l (1-19) can be s i m p l i f i e d common f a c t o r { } For growth to o c c u r , i t i s n e c e s s a r y Equation { _ _ k - br the decline. f u r t h e r by t a k i n g out the Y/k, = Y k ( 1 + b(r - k), k - br .ijizja . (1 20) k - br Since D fc = (1 - b ) Y and br = g, e q u a t i o n 3. (1-11) t (1-20) i s e q u i v a l e n t t o (1-17). Stream of E a r n i n g s Approach The v a l u e of a share a l s o can be d e f i n e d as the sum of p r e s e n t v a l u e of f u t u r e e a r n i n g s l e s s the p r e s e n t v a l u e of investments P F I f we the the i n the r e s p e c t i v e year of the e a r n i n g s ; t h a t i s , = i t=l l t " t> (1 + k ) t Y I . 12 the investment _2i) U assume t h a t the c o r p o r a t i o n f i n a n c e s i t s investments through r e t a i n e d e a r n i n g s , ( 1 solely i n p e r i o d s 1, 2, 3,..., •*- In the M&M f o r m u l a t i o n , o u t s i d e f i n a n c i n g can be taken account w i t h o u t a l t e r i n g the r e s u l t . 2 into 13 00 i s bYo, b Y o ( l + br) , b Y o ( l + b r ) bYo(l + b r ) 2 p r e s e n t v a l u e of the t o t a l investment I bYo(l + t=l t _ 1 . The is br)t-l (1 + k ) t w h i l e the p r e s e n t worth of the t o t a l net income i s 00 Z t=l Yo(l + br)*" 1 (1 + k ) t Hence, Po = I t=l Yo(l + b r ) t ~ l - bYo(l + (1 + k ) t Y o ( l - b) I br)t-i t=l (1 + b r ) ^ 1 (1 + k ) t (1-22) which i s e q u i v a l e n t . t o (1-20). 4. Discounted cash f l o w approach T h i s approach equates the p r i c e of a common share to the p r e s e n t v a l u e of a l l f u t u r e net cash flows between the c o r p o r a t i o n and i t s shareholders. income Y t and stock, 2 . t o the c o r p o r a t i o n are the net i n a d e b t - f r e e c o r p o r a t i o n , from E q u a t i n g the s o u r c e s and uses of or In s o u r c e s of funds the s a l e of The uses of funds are f o r i n v e s t m e n t s , t Dj.. The Y t + g D t = Y t t = + 3 I + t D additional I , and d i v i d e n d s , t funds t ~ t (1-23) 1 t o t h e r words, the s h a r e h o l d e r s expect to r e c e i v e a d i v i d e n d f l o w e q u a l to the t o t a l cash flow of the f i r m l e s s the investment costs; 14 hence p r i c e CO p (Yt - i t I t=l (1 + k ) t Assuming, as i n the p r e v i o u s = P + et) (1-24) formulations that & - o - IQ. (1 + k ) t Z t=l which i s the same as the stream of e a r n i n g s H. t Reasons f o r Adopting approach (1-21). Gordon's Model I t might w e l l be asked s i n c e the a l t e r n a t i v e f o r m u l a t i o n s e q u i v a l e n t , what a r e the advantages i n a d o p t i n g formulation. First, w i l l be d i s c u s s e d simple of r , b, and Y which a r e more r e a d i l y a s c e r t a i n e d than expected v a l u e s . expectations Gordon's d i v i d e n d i t i s u s e f u l i n t e s t i n g because i n a form i t i n c o r p o r a t e s c u r r e n t v a l u e s are Hypotheses d e a l i n g w i t h i n Chapter I I I which expands the simple model i n t o an e m p i r i c a l model. Secondly, we an i d e a l world p o i n t e d out have assumed i m p l i c i t l y of c e r t a i n t y . M o d i g l i a n i and M i l l e r section correctly t h a t once the investment p l a n i s g i v e n , d i v i d e n d becomes i r r e l e v a n t . - ' retained earnings affecting i n the p r e v i o u s 3 The. f i n a n c i n g of investment can be or by s a l e a d d i t i o n a l common shares the p r i c e of s h a r e s . of g r e a t e r d i v i d e n d s of t h e i r shares c o u l d accomplish or by p l e d g i n g I f market i m p e r f e c t i o n s to postpone p r e s e n t are r i s k averse, through without the cash the same by s e l l i n g equivalent a portion them as c o l l a t e r a l f o r a l o a n . e x i s t , however, i n v e s t o r s may consumption of d i v i d e n d s . any 13, ' M i l l e r and Investors wishing policy not Assuming t h a t i n v e s t o r s s h i f t i n g of the time p a t t e r n of d i v i d e n d s M o d i g l i a n i , "Dividend wish P o l i c y , " 411-433. into 15 the future, may cause them to attach greater risk to future dividends. Accordingly, the required rate of return k w i l l be increased. The effect of dividend policy on the required rate of return of shareholders w i l l be discussed more fully in the next chapter which presents Gordon's empirical model. CHAPTER I I GORDON'S STOCK VALUATION MODEL Gordon's s t o c k v a l u a t i o n model s t a t e s t h a t t h e p r i c e of a share i s e q u a l t o t h e c u r r e n t d i v i d e n d between the s h a r e h o l d e r s ' growth of t h e d i v i d e n d ; o r Po = po = required d i v i d e d by t h e d i f f e r e n c e r a t e o f r e t u r n and t h e r a t e o f that i s , (2-1) k - rb LLJZJL&O (2-2) k - rb A. Assumptions The model makes t h e f o l l o w i n g assumptions r e g a r d i n g t h e corporation: (1) t h a t i t i s s u e s no new shares; (2) that i t maintains a constant (3) t h a t i t w i l l e a r n a r a t e of r e t u r n , r , on i t s debt-equity ratio; inve s tmen t and (4) that i t w i l l r e t a i n a constant income i n every f u t u r e Accordingly, f r a c t i o n , b, o f i t s period. the d i v i d e n d w i l l grow a t t h e r a t e b r . There i s ample e v i d e n c e t h a t c o r p o r a t i o n s , "particularly engaged i n m a n u f a c t u r i n g , undertake r e l a t i v e l y l i t t l e 16 outside those equity 17 financing."-'- Furthermore, the work of Gordon g i v e s e v i d e n c e t h a t corporations attempt to m a i n t a i n Accordingly, "... a corporation's a constant i t i s q u i t e reasonable future dividends debt-equity ratio. 2 to assume t h a t i n e s t i m a t i n g i n v e s t o r s do not consider the p o s s i b l e f u t u r e s t o c k s a l e s by a c o r p o r a t i o n as b e i n g m a t e r i a l t h a t they expect the c o r p o r a t i o n equity to m a i n t a i n i t s existing and debt ratio." The r e m a i n i n g two assumptions perhaps are more o b j e c t i o n a b l e . While a c o r p o r a t i o n i s u n l i k e l y to r e t a i n a f r a c t i o n b of i t s income Iti every f u t u r e p e r i o d , t h i s i s not important. i s what i n v e s t o r s expect the c o r p o r a t i o n i n v e s t o r w i l l estimate Lintner provide b and The r for future periods. rational The f i n d i n g s of e v i d e n c e t h a t f i r m s f o l l o w a p o l i c y of paying s t a b l e f r a c t i o n of t h e i r normal e a r n i n g s G i v e n b, to do. What i s r e l e v a n t the r e t e n t i o n and as a dividends.^ hence the investment r a t e , a c o r p o r a t i o n i s expected to earn a r e t u r n of r on i t s investment i n every f u t u r e p e r i o d . that r w i l l vary T h i s assumption does not e x c l u d e the i f b varies. I t does e x c l u d e the p o s s i b i l i t y t a k i n g on d i f f e r e n t v a l u e s when b i s c o n s t a n t . hypothesis p o l l e d on possibility The of r behavioral behind t h i s assumption i s t h a t " . . . i f i n v e s t o r s were the change they expect i n the r a t e of p r o f i t a corporation Hl.J. Gordon, "The S a v i n g s Investment and V a l u a t i o n of a C o r p o r a t i o n , " Review of Economics and S t a t i s t i c s , XLIV (February, 1962), 38. The p r e s e n t a t i o n i n t h i s c h a p t e r r e l i e s l a r g e l y on the above a r t i c l e . See M.J. Gordon, " S e c u r i t y and a F i n a n c i a l Theory of Investment," Q u a r t e r l y J o u r n a l of Economics, LXXIV (August, 1960), 472-492, esp. 476-479. o Gordon, Review of Economics and Statistics, (February, 1962), ^ J . L i n t n e r , " D i s t r i b u t i o n of Incomes of C o r p o r a t i o n s among Retained E a r n i n g s , and Taxes," American Economic Review, XLVI (May, 1956), 97-113. 39. Dividends, 18 w i l l e a r n , t h e t y p i c a l r e s u l t w i l l be a frequency mean z e r o and a s m a l l s t a n d a r d d e v i a t i o n . empirical results w i l l d i s t r i b u t i o n with The q u a l i t y of the t u r n i n l a r g e measure on t h e a c c u r a c y o f t h i s speculation."-' B. Interpretation The q u e s t i o n whether the p r i c e o f a s h a r e i s independent d i v i d e n d p o l i c y w i l l depend upon t h e assumption of made w i t h r e s p e c t t o the b e h a v i o r o f r and k as b i s v a r i e d . Case 1: I f r and k a r e independent „ 9 P / 3 b The ( r _ k ) ( k 3° rb) o f b, then y (2-3) c o n d i t i o n when the share's p r i c e i s maximized can be found by s e t t i n g the p a r t i a l d e r i v a t i v e of P w i t h r e s p e c t to b e q u a l t o z e r o , i n which case r equals k. p r i c e i s independent At t h i s p o i n t , a share's o f the r e t e n t i o n r a t e b. w i t h b and c o n v e r s e l y i f r < k, P w i l l I f r > k, P w i l l f a l l w i t h b. rise The f a c t t h a t P w i l l r i s e or f a l l w i t h b when r £ k i s n o t due t o f i n a n c i n g the investment If through r e t e n t i o n b u t t o the p r o f i t a b i l i t y o f investment. funds were r a i s e d p r i c e would s t i l l Case 2; through s a l e w h i l e b was kept change. I f r and k a r e n o t independent or fall is not a constant. c o n s t a n t , the o f b, P w i l l n o t r i s e i n d e f i n i t e l y w i t h b, however, because t h e r a t e of r e t u r n r , Provided there a r e no i n d i v i s i b i l i t i e s i n 5Gordon, Review o f Economics and S t a t i s t i c s , ( F e b r u a r y , 1962), 39 19 the f i r m ' s investment o p p o r t u n i t i e s r w i l l f a l l as b i n c r e a s e s . In t h i s event, = f r - k - b (1 - b) 3P/3b 3r/3bT ^ By — (k - r b ) 2 (2-4) s e t t i n g 3P/3b = 0, we can a l s o s e t the e x p r e s s i o n {r - k - b (1 - b) 3r/3b} when r = k. = 0. When b = 0, p r i c e i s maximized I f r > k a t b = o, P i s maximized a t a p o s i t i v e of b s i n c e as b i n c r e a s e s , r f a l l s negative because 3r/3b i s n e g a t i v e , and b (1 - b) 3r/3b which i s increases i n absolute At b = 1, P = 0 r e g a r d l e s s o f t h e v a l u e o f r and k. the p r o f i t a b i l i t y zero value value amount. Despite o f i n v e s t m e n t , a c o r p o r a t i o n ' s shares w i l l have i f i t i s expected never to pay a d i v i d e n d . Gordon admits, however, t h a t h i s model i s n o t the b e s t means of d e a l i n g w i t h the s i t u a t i o n of a non-dividend In o r d e r paying t o use E q u a t i o n corporation,^ (2-2) to s o l v e f o r the optimum p r i c e we must be a b l e t o observe the v a r i a b l e s . obtained from h i s t o r i c a l d a t a , must be d e r i v e d . Equation & PoZ so t h a t the l e f t While Yo, r and b can be the s h a r e h o l d e r s ' required return (2-2) can be r e w r i t t e n as = side i s equal based on i t s c u r r e n t d i v i d e n d . k - br (2-5) t o d, a c o r p o r a t i o n ' s d i v i d e n d Then a sample o f s i m i l a r of e q u i v a l e n t r i s k can be taken and used t o e s t i m a t e d = a where a 6 Q i s an e s t i m a t e I b i d . , 40 f n . G - a^br of k and a^ should yield corporations the parameters of (2-6) equal 1. 20 Gordon, however, found t h a t a^ was s i g n i f i c a n t l y l e s s than 1.^ But i f k i s a c o n s t a n t , negative f o r a s u f f i c i e n t l y h i g h growth r a t e and t h e share's p r i c e would pass through i n f i n i t y . greater independent o f b r , d c o u l d become I t i s u n l i k e l y , however, t h a t b r i s than k as r would have to be g r e a t e r r > l k w i t h 0 < b < 1, would not l i k e l y future period. Yet according than g.k or a t minimum t o our assumption, investors expect t h i s r a t e o f r e t u r n on investment i n every Moreover, a c o r p o r a t i o n whose r e t u r n on investment exceeded i t s c o s t o f c a p i t a l would d o u b t l e s s f i n a n c i n g u n t i l r = k. Nevertheless, are expected to earn a h i g h there engage i n o u t s i d e a r e some f i r m s which r a t e o f r e t u r n on investment f o r a long time and which do n o t engage i n o u t s i d e f i n a n c i n g whose s h a r e s still s e l l at f i n i t e p r i c e s . An but a l t e r n a t i v e explanation i s t h a t k i s n o t independent o f b r i s an i n c r e a s i n g f u n c t i o n of b r . Gordon suggests t h a t this requirement would be s a t i s f i e d by the e x p r e s s i o n d = Then as b r i n c r e a s e s , a (1 + b r ) ~ l (2-7) a Q the r e q u i r e d d i v i d e n d y i e l d , d, would though not as r a p i d l y and would a s y m p t o t i c a l l y These a l t e r n a t i v e f u n c t i o n s approach f o r d are i l l u s t r a t e d fall zero. below: Dividend Chart 2-1 V a r i a t i o n i n Dividend Y i e l d with Expected Rate o f Growth i n the D i v i d e n d M.J. Gordon, " D i v i d e n d s , E a r n i n g s , and Stock P r i c e s , " of Economics and S t a t i s t i c s , XLI (may, 1959), 99-105. Review 21 S i n c e d = k - b r , the e x p r e s s i o n the o r i g i n a l model Po Po = Yo = i n (2-7) Xft Or -~bJk - br (1 - b) -1 o can be s u b s t i t u t e d i n to g i v e (1 + b r ) l (2-8) a a When b = o, P = Yo (1 - b) — A s o b r i s e s , the m u l t i p l i e r increases a to —1 *o (1 + b r ) l . Taking a the c u r r e n t d i v i d e n d Y o ( l - b) as given, the l a r g e r the expected growth of the d i v i d e n d b r , the h i g h e r p r i c e i n v e s t o r s w i l l pay (2-8) f o r the s h a r e , p r o v i d e d are positive. For t h i s f o r m u l a t i o n to be c o s t of c a p i t a l k must be theoretically the the parameters of sound, the firm's assumed to be an i n c r e a s i n g f u n c t i o n of b r , the expected r a t e of growth i n i t s d i v i d e n d . k - br implies = a (1 + b r ) ~ l that k = a (l + br) _ a Q ak/Sbr and = - = 1 a l + br product (2-9) a ( l + br)"^ ± 1 + when b = o, a (1 + b r ) " " l f a l l s a to pay 1. Assuming a a ^ Q As b and hence br r i s e , > 1, 3k/8br positive. I t f o l l o w s t h a t a-^ can be willing 1 l 0 In (2-9) Q a a a± should e q u a l a p p r o x i m a t e l y w i l l become permanently + (2-10) k w i l l f a l l as b i n c r e a s e s from 0. rises a +*l) 1 Q (1 + b r ) The (2-7) a D Q i s a f i r m ' s c o s t of c a p i t a l . As br thus moderating the i n c r e a s e of k w i t h considered f o r growth i n the "as br. the p r i c e i n v e s t o r s are dividend."^ 'Gordon, Review of Economics and Statistics, (February, 1962), 41. 22 The greater the value of a-^> the larger the price investors are willing to pay for dividend growth. Formerly, under the assumption that k was a constant, price was independent of b when r = k = a . Q the dividend and investment rates. In this case, P depends on When br = o, k = a „ . * o P w i l l change with b because k changes. If r = a . o' Not only does the value of a share change due to the return on investment but also because of the fraction of earnings retained or paid out in dividends. If the assumption that 3k/3br > o is correct, i t follows that there is an optimum price associated with a finite dividend rate when the rate of return is a constant. The optimum dividend or retention rate can be found by differentiating (2-8) with respect to b, 9 p/ 8 b = M l + brlfl [Taj (1 - b) - 7 ] When 3P/3b = o, the expression |— ( •= o. 2 _ n ) Solving for b, b = — ajL + 1 - 7 - — ~ r(a^ + 1) (2-12) Then Po is maximized by this function of b i f r is independent of b. Moreover, the optimum retention rate is an increasing function of the rate of return, r , and of a-^, the price investors are willing to pay .for growth in the dividend, Gordon notes that the proposition that k is an increasing function of br does not imply that Po is a decreasing function of br. From (2-8) Po = Yo (1 - b) ~ ao (1 + b r ) l a 23 i t can be seen that for a given b, share price w i l l always increase through a rise in r and for a given r and a^, Po w i l l rise and then f a l l with an increase in b. C. Assumptions under which k is an Increasing function of br: The basic premise of Gordon's model is that the value of a share is equal to the present value of the future stream of dividends arising from the share. The present value may be arrived at by either of two methods: by discounting the expected value of the dividends at an interest rate which reflects risk or by discounting the certainty equivalent of the future dividends at the pure rate of interest. The second assumption is that the uncertainty of dividend increases with its time in the future. In terms of the standard deviation, a, this means that at the end of year n, an > on - 1. Similarly, on + 1 > on. The effect of increasing uncertainty on k is indeterminate; that i s , k may be less than, equal to, or greater than k + 1. R If however, k n is an increasing function of t then a corporation's t cost of capital k being a weighted average of the k ' s is an t increasing function of the rate of growth in the dividend.^ A mathematical proof of this proposition is provided by Ramesh Gangolli in Gordon, I b i d . , 49-50. Also see H. Chen, "Valuation under Uncertainty," Journal of Financial and Quantitative Analysis, II (September, 1967), 313-325. Chen points out that while the risk of a future dividend increases with time i t is more important that we know the rate at which this risk increases. He shows that i f risk (1) increases at a constant rate over time k = k + \ for a l l t=l, 2, 3, . . . ; (2) increases at a decreasing rate over time, kpk >k3>.. .>k >k .(. ±; or (3) increases at an increasing rate over y t 2 t t t t Deductive argument cannot solve the problem of how the k ' s behave t and i t should be regarded as a question of fact. Substantiation for this proposition must be based on a model incorporating this proposition in explaining common share prices. time, k^<lc2<k^<.. .<k <k . Since Gordon's proposition that k is an increasing function of b is based on the assumption that the k ' s increase with t, either i t must be assumed that the risk of future dividends must increase at an increasing rate or i t must be shown that k increases with b regardless of whether the k ' s increase with t, to substantiate the theory. t 1 + t t CHAPTER I I I REVIEW OF GORDON'S EMPIRICAL INVESTIGATIONS A. L i n e a r Models Gordon's e a r l i e s t e m p i r i c a l work was r e p o r t e d i n h i s paper " D i v i d e n d s , E a r n i n g s and Stock P r i c e s . " 1 I t attempted to e s t a b l i s h whether i n v e s t o r s used e a r n i n g s , d i v i d e n d s or a combination o f the two i n a r r i v i n g a t the v a l u a t i o n o f a s h a r e . The f o l l o w i n g linear f u n c t i o n was used: where = a P = year-end D = dividends paid during year Y = e a r n i n g s p a i d d u r i n g year D E i g h t samples + a P 1 D + a 2 Y (3-1) price c o n s i s t i n g o f f o u r i n d u s t r i e s f o r the y e a r s 1951 and 1954 were used t o e s t i m a t e the parameters of (3-1). i n d u s t r i e s groups used f o r t e s t i n g were Chemicals Steel The (32) , Foods ( 5 2 ) , (34) and Machine T o o l s ( 4 6 ) . I n o r d e r t o o b t a i n samples o f s u f f i c i e n t s i z e some f r i n g e c l a s s i f i c a t i o n s were i n c l u d e d such as p h a r m a c e u t i c a l m a n u f a c t u r e r s under Chemicals and f o r g i n g manufacturers and o t h e r s t e e l f a b r i c a t o r s w i t h the b a s i c p r o d u c e r s under ^•Review of Economics 2 and S t a t i s t i c s , XLI (May, 1959), I b i d . , 100. 25 Steel. 2 99-105. 26 In a d d i t i o n , c o n s i d e r a b l e v a r i a t i o n e x i s t e d among the f i r m s w i t h r e s p e c t to such a t t r i b u t e s as s i z e , p r o f i t a b i l i t y , market s t r u c t u r e s for s u p p l y and demand and presents type of s h a r e h o l d e r . T a b l e 3-1 the l e a s t - s q u a r e s e s t i m a t e s of the parameters, below their s t a n d a r d e r r o r s (the standard d e v i a t i o n of the sample o b s e r v a t i o n s about the r e g r e s s i o n o r e s t i m a t i n g l i n e ) , coefficients (R) and the m u l t i p l e c o r r e l a t i o n the c o e f f i c i e n t s of d e t e r m i n a t i o n TABLE (R ) • 3-1 R e g r e s s i o n of P r i c e on D i v i d e n d and Income Sample 1951 Chemicals Constant Term Coefficient and s t a n d a r d e r r o r of D Y Multiple Correlat i o n Coefficient of determination R z -.8 (5.2) 16.7 (3.1) .93 .865 .1 7.0 (1.5) 5.5 (.9) .90 .810 5.5 6.6 (1.8) 2.0 (.6) .86 .740 Machine T o o l s 2.4 12.0 (1.2) .8 (.5) .90 . .810 -3.0 25.7 (5.2) .3 (3.3) .92 .846 Foods -.4 10.4 (2.2) 5.6 (1.0) .91 .828 Steels 8.7 8.4 (1.7) 2.0 (.8) .94 .884 Machine T o o l s 6.3 5.5 (1.4) 4.1 (.6) .89 .792 Foods Steels 1954 Chemicals -7.0 27 Gordon expected that i f the dividend coefficient is considered an estimate of the rate of the profit the regression statistics could be evaluated as follows: a. Since the dividend yields on good preferred stocks during these years was 4-5% and companies acquired through mergers had been selling at five times earnings before income tax, i t would be reasonable to expect the dividend coefficient being the reciprocal of the dividend yield, to range between 10 and 25; b. the rate of profit (and hence the dividend coefficient) should be ranked according to industry characteristics in the following order: (1) Chemicals were characterized by size, growth and stability; (2) foods represented a stable industry; (3) steels included large companies and was vulnerable to cyclical trends; and (4) machine tools consisted of comparatively small corporations which were cyclically vulnerable; and c. ,Since 1951 and 1954 differed in terms of business expectations, the coefficients between years should reflect the difference. The results for the model incorporating both earnings and dividends were hardly encouraging. The fact that the dividend coefficient is large and statistically significant in seven out of eight samples would appear to discount the earnings hypothesis. Also, the income coefficients except for Chemicals in 1951 were very low as a measure 28 of for the p r i c e i n v e s t o r s p l a c e d on e a r n i n g s . Chemicals v a r i e s widely from -.8 The i n 1951 dividend to 25.7 in coefficient 1954. Because t h e r e i s h i g h i n t e r c o r r e l a t i o n between the independent v a r i a b l e s making the c o e f f i c i e n t s h i g h l y u n s t a b l e t h e r e i s l i t t l e p r e d i c t i v e v a l u e i n t h i s model. If i n v e s t o r s purchase a share of s t o c k f o r i t s e x p e c t e d . f u t u r e d i v i d e n d s t h i s h y p o t h e s i s might be r e p r e s e n t e d by the f o l l o w i n g equation: P = a Q + aiD + a where r e t a i n e d e a r n i n g s 2 (Y - D) the growth i n the d i v i d e n d . per share of common then , b _ " r (Y - D) (Y) Gordon p r e f e r r e d to use (Y - D) (3-2) i s used as a proxy measure of b r , I f B r e p r e s e n t s the book or a s s e t 00 W _ ~ Y - D value /o o\ (3_3) the a b s o l u t e measure of growth (Y - D) r a t h e r than to d e f l a t e r e t a i n e d e a r n i n g s by book v a l u e because p r i c e d i v i d e n d are a b s o l u t e q u a n t i t i e s i n the m o d e l . approach however i s t h a t two companies may 3 A weakness of f i n d a lower this have the same r e t a i n e d e a r n i n g s but have v a s t l y d i f f e r e n t r a t e s of r e t u r n on I n v e s t o r s , i t i s assumed, w i l l and investment. r a t e of growth s t a r t i n g from a h i g h book v a l u e p r e f e r a b l e to a h i g h e r r a t e of r e t u r n based on a low a s s e t v a l u e which w i l l be d i s c o u n t e d more h e a v i l y i n the distant future. The d i v i d e n d c o e f f i c i e n t s proved more r e a s s u r i n g than under the f i r s t model. too l a r g e . 3 The Ibid., Only the 1951 c o e f f i c i e n t f o r machine t o o l s range of v a r i a t i o n was 101. appeared much s m a l l e r than p r e v i o u s l y 29 tested although s t i l l 1954 quite large. S t e e l s - 1951 and machine t o o l s - were low and c h e m i c a l s - 1954 was h i g h . was much The s t a n d a r d error reduced. S i n c e the r e t a i n e d e a r n i n g s c o e f f i c i e n t r e p r e s e n t e d the p r i c e i n v e s t o r s were w i l l i n g to pay f o r d i v i d e n d growth, i t was p r e d i c t a b l e t h a t the c o e f f i c i e n t s s h o u l d be p o s i t i v e . g e n e r a l l y poor, p a r t i c u l a r l y The Otherwise, t h e r e s u l t s were as t h e c o e f f i c i e n t s a r e low. second model d i d p r o v i d e a s u p e r i o r means o f e s t i m a t i n g p r i c e v a r i a t i o n w i t h r e s p e c t t o the d i v i d e n d g i v e n the f i r m ' s r e t a i n e d e a r n i n g s as compared to e a r n i n g s . I t s h o u l d be noted is t h a t the d i v i d e n d c o e f f i c i e n t i n T a b l e 3-2 the sum o f the d i v i d e n d and e a r n i n g s c o e f f i c i e n t s i n T a b l e 3-1. The i n c r e a s e i n d i v i d e n d i n (3-1) causes an e q u i v a l e n t r e d u c t i o n i n r e t a i n e d e a r n i n g s w h i l e under (3-2) t h e r e t a i n e d e a r n i n g s a r e h e l d constant. I n a d d i t i o n , the m u l t i p l e c o r r e l a t i o n and R 2 statistics a r e the same f o r each year i n the two t a b l e s , s i n c e p r i c e i s a l i n e a r f u n c t i o n o f the same v a r i a b l e s . Finally, the e a r n i n g s and r e t a i n e d e a r n i n g s c o e f f i c i e n t s and t h e i r s t a n d a r d e r r o r s a r e the same s i n c e a change i n e a r n i n g s i s the same as a change i n r e t a i n e d earnings with the dividend held constant. Not o n l y a r e the c o e f f i c i e n t s low but i n t h e case o f machine t o o l s - 1951 and c h e m i c a l s - 1954, the c o e f f i c i e n t s a r e n o t s t a t i s t i c a l l y cent s i g n i f i c a n t a t the f i v e per level. The r e t a i n e d e a r n i n g s c o e f f i c i e n t s a r e more encouraging viewed as the p r i c e i n v e s t o r s a r e w i l l i n g d i v i d e n d than as e a r n i n g s c o e f f i c i e n t s . is when to pay f o r growth i n the I f the growth coefficient low, an i n c r e a s e i n d i v i d e n d s w i t h a c o r r e s p o n d i n g d e c r e a s e i n 30 TABLE 3-2 R e g r e s s i o n o f P r i c e on D i v i d e n d and R e t a i n e d E a r n i n g s Constant Term Sample 1951 Chemicals Coefficient and s t a n d a r d error of D Y - D -7.0 15.9 (2.7) .1 12.5 (1.1) Steels 5.5 Machine T o o l s Multiple Correlation R 2 .93 .865 5.5 (.9) .90 .810 8.6 (1.5) 2.0 (.6) .86 .740 2.4 12.8 (1.0) .8 (.5) .90 .810 -3.0 30.0 (2.6) .3 (3.3) .92 .846 Foods -.4 15.9 (1.5) 5.6 (1.0) .91 .828 Steels 8.7 10.4 (1.4) 2.0 (.8) .94 .884 Machine T o o l s 6.3 9.6 (1.2) 4.1 (.6) .89 .792 Foods 1954 Chemicals retained earnings w i l l 16.7 (3.1) • i n c r e a s e the p r i c e o f a share more than when the growth c o e f f i c i e n t i s h i g h e r . The d i v i d e n d h y p o t h e s i s i n Model 2 i s s u p e r i o r i n p r e d i c t i n g how p r i c e w i l l change w i t h t h e d i v i d e n d g i v e n the r e t a i n e d e a r n i n g s than when g i v e n the f i r m ' s e a r n i n g s . The d i v i d e n d c o e f f i c i e n t s are g r e a t e r than f o r Model 1 and the s t a n d a r d e r r o r s a r e l e s s . There a r e c e r t a i n l i m i t a t i o n s , however, i n t h i s k i n d o f model. A s c a l e f a c t o r , p a r t of which i s r e f l e c t e d by the presence of both 31 high-priced and low-priced stocks in the samples help cause correlation between variables and variation in the coefficients among industries. The influence of scale on the coefficients might be reduced by deflating the variables, by book value for instance, or by the use of logs, or by a combination of the two. Secondly, the current values of dividends and earnings in any one year may vary from the normal values resulting from the average over some prior period. Hence a combitiation of current values and past averages for dividends and retained earnings might provide a better model. The absence of other variables such as corporation size, - debt-equity ratio and variability of earnings which the investor may take into account in valuing a share, would bias the retained earnings and dividend coefficients. Lastly, a model using the actual growth rate rather than an index of growth represented by retained earnings might be improvement. Empirically, there are problems, however. an The use of book value as measure of return on investment is questionable because of variation in accounting practice. The use of past values to predict future earnings might be questioned especially i f other variables are used by investors to predict future earnings. Retained earnings are quite unstable and each industry may show a different pattern of variation over time. 32 B. Refinement The refined model next tested by Gordon was: P a W where o + a l w + + a g + a (g-g) 3 2 3 (3-4) 4 P/W = year-end price divided by book value in current year, D/W = average dividend for the prior five years divided by the book value, D/W = current year's dividend divided by book value g = average retained earnings for the prior five years divided by book value, g = current year's retained earnings divided by book value. The assumption is made that in arriving at the current dividend and its growth, investors look at the average over the prior five years and the amount by which the current years values depart from these averages. Deflation by book value was undertaken to eliminate the scale effect although its use is debatable.^ In interpreting the coefficients, i f a^ = a 2 or a 3 = a4 implies that investors ignore the five-year average dividend or growth in dividend in favor of the current values; i f a the current dividend is ignored; i f a^ > a 2 2 = o this implies that this "implies that investors adjust to a change in the dividend with a log, i . e . , elasticity of expectations is less than one."^ the reverse is true. 4 I b i d . , 104 fn. 5 I b i d . , 105. the When a^ < a , of course, 2 / 33 TABLE 3-3 R e g r e s s i o n of P r i c e on D i v i d e n d , Retained E a r n i n g s , Change i n D i v i d e n d , Change i n Retained E a r n i n g s , A l l D e f l a t e d by Book V a l u e . Constant Term Sample 1951 Chemicals C o e f f i c i e n t & s t a n d a r d <e r r o r of D/W D/W-D/W S-R Multiple Correlation R 2 -.23 12.42 (2.63) 9.79 (5.98) 18.74 (5.96) 14.36 (5.60) .80 .640 Foods .04 14.04 (1.04) 8.06 (2.49) 3.16 (1.39) 4.57 (1.58) .90 .810 Steels .15 9.88 (1.05) 6.38 (1.87) 1.45 (1.09) .41 (1.06) .88 .874 Machine T o o l s .12 12.62 (1.17) 5.93 (2.75) .12 (.99) 1.11 (.80) .91 .828 .54 17.38 (2.92) 12.71 (8.93) .12 (6.39) 3.44 (4.78) .79 .624 -.03 15.51 (1.04) 8.74 (2.82) 5.15 (1.66) 5.96 (1.67) .92 .846 Steels .18 9.69 (.99) 3.85 (1.13) 2.02 (.68) 2.85 (.67) .91 .828 Machine T o o l s .05 11.65 (1.16) 6.06 (1.74) 3.70 (1.12) 1.92 (1.04) .87 .757 1954 Chemicals Foods In comparison to T a b l e the d i v i d e n d 3-2 t h e r e i s a c o e f f i c i e n t s whose range of f l u c t u a t i o n among samples has been reduced. Moreover, a l lbut the chemicals s i g n i f i c a n t a t the f i v e per cent l e v e l . a^ > 2 a s l i g h t improvement i n i t can be i n f e r r e d c o e f f i e n t s are S i n c e i n every sample, t h a t i n v e s t o r s w i l l not take an i n c r e a s e i n d i v i d e n d s i n t o account u n t i l the average of d i v i d e n d s has i n c r e a s e d . 34 The growth c o e f f i c i e n t s are d i s a p p o i n t i n g i n that the c o e f f i c i e n t s f o r g are p o o r e r than f o r Y - D i n T a b l e 3-2 of t h e s e are not s t a t i s t i c a l l y samples, growth the change i n growth showing significant. Furthermore, i n f i v e c o e f f i c i e n t s exceeded those f o r average t h a t i n most c a s e s , i n v e s t o r s p r e f e r r e d change i n r e t a i n e d e a r n i n g s over p a s t performance. used do not y i e l d and t h r e e The a current averages r e l i a b l e e s t i m a t e s of what i n v e s t o r s are w i l l i n g to pay f o r r e t a i n e d e a r n i n g s or growth. While t h i s model i s a g r e a t improvement over the f i r s t t h e r e were s e v e r a l ways, Gordon f e l t f a c t o r might be t r e a t e d d i f f e r e n t l y the v a r i a b l e s . due F i v e of the a l s o be The scale through another r e l a t i o n s h i p among v a l u e s are lower than i n T a b l e to the d e f l a t i o n by book v a l u e . might i t c o u l d be improved. model The r e p r e s e n t a t i o n of 3-2 growth improved. C. N o n l i n e a r Model The r e s u l t s of t e s t i n g a n o n l i n e a r model were r e p o r t e d i n Gordon's 1960 paper "The Optimum D i v i d e n d Rate."^ estimating equation including r i s k variables ln(P/B) t = lna Q + g t l n a i + a2ln + a ln S 3 where t (D/B) The new was t + a4ln U (3-5) P t = average of h i g h and low p r i c e s f o r the months September, October and November of y e a r t , B t = book v a l u e per share at end of y e a r t , S l . J . Gordon, "The Optimum D i v i d e n d Rate," Management S c i e n c e s : Models and T e c h n i q u e s , e d i t e d by C. West Churchman and M i c h e l V e r h u l s t (New York: Pergamon P r e s s , 1960). 35 g t = p r o d u c t of c u r r e n t r e t e n t i o n r a t e b = ( Y - D t ) / Y t and the c u r r e n t rate, r = Y /B , t t t t earnings t D t = d i v i d e n d p a i d d u r i n g year S t = s i z e of the c o r p o r a t i o n measured by t o t a l book v a l u e of the common e q u i t y at the end of year t and - i n s t a b i l i t y of p a s t e a r n i n g s measured by the s t a n d a r d d e v i a t i o n of the r e t u r n , r , on common e q u i t y over the p e r i o d 1934-1954. U t, An a d d i t i o n a l r i s k v a r i a b l e c o n s i s t i n g of the r a t i o of net worth p l u s long-term debt to net worth was was included o r i g i n a l l y but d e l e t e d because the c o e f f i c i e n t v a l u e s were u n s a t i s f a c t o r y . ^ D e f l a t i o n by book v a l u e was p r i c e and dividends i n c l u d e d i n the due undertaken to a v o i d c o r r e l a t i o n between to l o w - p r i c e d and h i g h - p r i c e d shares being samples. While the e i g h t samples c o n s i s t e d of the same i n d u s t r i e s and years as used p r e v i o u s l y , the c r i t e r i a used f o r a f i r m ' s d i f f e r e d somewhat, r e d u c i n g the sample listed inclusion sizes: (1) the f i r m must be on a s e c u r i t y exchange; (2) d a t a on income and net worth must be c o n t i n u o u s l y s i n c e 1934; and (3) the d i v i d e n d i n the sample year must be l e a s t 2% of the book v a l u e per s h a r e . published at ' I b i d . , 101. A l s o see M.J. Gordon, The Investment, F i n a n c i n g and V a l u a t i o n of the C o r p o r a t i o n (Homewood, I l l i n o i s : R i c h a r d D. I r w i n , I n c . , 1962), 146-147. The e i g h t samples were s p l i t e v e n l y between p o s i t i v e and n e g a t i v e c o r r e l a t i o n , o n l y t h r e e were s t a t i s t i c a l l y s i g n i f i c a n t a t the f i v e per cent l e v e l and two had the wrong s i g n . 36 TABLE 3-4 . R e g r e s s i o n o f P r i c e on D i v i d e n d , Growth Rate, and U n c e r t a i n t y V a r i a b l e s . C o e f f i c i e n t & Standard Sample E r r o r of Dividend InD/B Growth rate g Size InS .825 (.132) 4.56 (2.29) .077 (.038) -.081 (.104) .757 Foods (49) 1.023 (.063) 5.51 (1.07) .024 (.026) -.283 (.064) .865 S t e e l s (34) .733 (.095) 2.10 (.90) .002 (.029) -.002 (.132) .740 Machine T o o l s (46) .874 (.078) 1.54 (.82) .041 (.042) -.085 (.082) .757 .822 (.130) -.11 (1.92) .088 (.039) -.018 (.100) .792 Foods (45) .953 (.055) 3.87 (1.08) .084 (.024) -.165 (.057) .903 S t e e l s (29) .S35 (.091) 3.71 (.85) .022 (.021) .136 (.098) .846 Machine T o o l s (43) .694 (.081) 3.24 (.87) .028 (.044) -.131 .089 .774 1951 Chemicals (32) 1954 Chemicals (31) Uncertainty InU R2 The a d d i t i o n of s i z e and u n c e r t a i n t y v a r i a b l e s were an improvement All the s i z e c o e f f i c i e n t s had the c o r r e c t s i g n and t h r e e were statistically had significant. the wrong s i g n w h i l e regarded F o r the u n c e r t a i n t y c o e f f i c i e n t , o n l y one two were s t a t i s t i c a l l y the d a t a as s u p p o r t i n g Gordon the hypotheses t h a t p r i c e i s d i r e c t l y r e l a t e d t o s i z e and i n v e r s e l y r e l a t e d Gordon, "Optimum D i v i d e n d significant. t o the i n s t a b i l i t y Rate," 102. of past earning 37 While the d i v i d e n d c o e f f i c i e n t s a 2 a l l but f o o d s - 1951 a r e l e s s than one. a 2 = 1. 1954, are a l l h i g h l y significant, The theory p r e d i c t s t h a t The growth c o e f f i c i e n t s w i t h one e x c e p t i o n , have the r i g h t s i g n and a r e s i g n i f i c a n t . chemicals - The d i v i d e n d and growth c o e f f i c i e n t s a r e an improvement over the r e s u l t s o f the l i n e a r models but c o u l d be improved f u r t h e r . D. The Nolev Model next e m p i r i c a l model employed by Gordon was r e p o r t e d i n h i s paper "The S a v i n g s , Investment, and V a l u a t i o n o f a C o r p o r a t i o n , the b a s i s o f which a r e used i n d e v e l o p i n g Po = Yo (1-b) — was expanded to take of (1 + Chapter I I . Equation (2-8), br) l a i n t o account c o r p o r a t i o n s i z e and i n s t a b i l i t y earnings: where Po = a = l/a s Yo(l-b) a Yo (1-b) ( l + b r ) l a s (l+u) 2 a S 3 a (3-6) Q = Do r = Yo/Bo b = 1 - Do/Yo r b = YcL^JDo B S = index o f s i z e = sum of net p l a n t account and working c a p i t a l u = index of i n s t a b i l i t y o f e a r n i n g s . To a r r i v e a t Do, the n o r m a l i z e d current dividend, i t i s hypothesized t h a t i n v e s t o r s use an e x p o n e n t i a l l y weighted average o f a c o r p o r a t i o n ' s ^Review of Economics and S t a t i s t i c s , XLIV ( F e b r u a r y , 1962), 37-51. 38 past dividends. S i m i l a r l y , i n v e s t o r s take an e x p o n e n t i a l l y weighted average of p a s t e a r n i n g s e a r n i n g s Yo. normalized The to a r r i v e at the n o r m a l i z e d r e t u r n on investment r i s assumed to be r e t u r n on e x i s t i n g a s s e t s , where Bo regard index, u, i s d e f i n e d as the a b s o l u t e to s i g n ) average of the y e a r - t o - y e a r Y / B , over t the p e r i o d 1947 t Sample d a t a was of 1958. The (i.e., The without to the sample y e a r . 1954 to 1957. from the i n d u s t r i a l groups of the Value the end of t = o. change i n r a t e of r e t u r n , d e r i v e d from 48 food and c o r p o r a t i o n s f o r the y e a r s the i s the a c t u a l net worth or book v a l u e per share of s t o c k at the end instability current The 48 machinery f i r m s were s e l e c t e d L i n e Investment Survey at c r i t e r i a employed excluded f i r m s under the following conditions: (1) i f d a t a on e a r n i n g s available since (2) and d i v i d e n d s were not 1947; i f abnormal market i n t e r e s t i n the shares o c c u r r e d d u r i n g the sample y e a r s ; (3) i f the f i r m ' s d i v i d e n d f e l l below 2% of i t s book v a l u e i n two p e r i o d 1951 The normalized to or more y e a r s d u r i n g the 1958. earnings and d i v i d e n d s v a r i a b l e s are d e f i n e d as f o l l o w s : If D{. = 3D t + (1 - B ) D t _ i ; and Y£ = XY t + (1 ~ X)Y*_!. the smoothing c o n s t a n t s implied 3 and X e q u a l one then the i n v e s t o r i s to c o n s i d e r o n l y the most r e c e n t v a l u e s of d i v i d e n d s and 39 earnings, whereas i f 8 and X equal zero, only the normalized earnings and dividends in the prior period is considered. The following combinations of 8 and X were tested on the sample data: (1) 8 = 1.0; (2) 3 = (3) 3 = Values for X = 1.0 (4) 3 = .8; X= .3 .8; X= .7 (5) 3 = .6; X= .5 .8; X= .5 (6) 3 = .6; X= .3 and rb were calculated. The set 3 = .6 and X = .5 was chosen because in every sample i t provided the highest multiple correlation. ^ 1 I n i t i a l values of .05 and .08 times the year-end book value were assigned arbitrarily to 1957. and Y^ respectively for Each subsequent year's values were determined by the equations for Dt and Yt except that D£ was always taken as the greater of the actual dividend or two per cent of B . T The log form of (3-6) was used to yield a linear expression, ln P = lna5 + aAln D + ailn (1 + br) + 1 + a l n (1 + u) + a lnS 2 The dividend coefficient a 3 A (3-7) is included in order that this parameter can be estimated also and is not forced to equal one. The results are presented in Table 3-5. The dividend coefficient is significantly less than one, ranging from .82 to .93 with the standard error in each sample being very small. The significance is that heretofore i t has been assumed that the coefficient equals one, meaning that a doubling of the dividend, other things being equal, would double the price. Gordon suggests several possible explanations for this. 1 0 I b i d . , Appendix B., 50-51. Investors TABLE 3-5 R e g r e s s i o n o f P r i c e on E x p o n e n t i a l l y Averaged D i v i d e n d and Growth Rate and on R i s k V a r i a b l e s * ln P Mean lna5 l n D* Coeff. Mean l n (1 + b r ) Mean Coeff. InS In (1 + u) Mean Coeff. Mean Coeff. R2 FOOD SAMPLE 1954 3.70 (.57) 2.55 (.15) .671 (.494) .83 (.06) .039 (.021) 11.80 (1.49) .031 (.024) -5.49 (1.31) 4.36 (.85) . .071 (.036) .904 1955 3.69 (.59) 2.56 (.13) .672 (.503) .93 (.05) .040 (.021) 9.87 (1.29) .029 (.022) -4.28 (1.23) 4.41 (.84) .055 (.032) .931 1956 3.59 (.54) 2.62 (.14) .654 (.500) .92 (.05) .042 (.020) 8.76 (1.34) .027 (.020) -4.44 (1.35) 4.47 (.84 .027 (.032) .912 1957 3.54 (.52) 2.49 (.12) .600 (.488) .83 (.05) .042 (.018) 9.87 (1.25) .026 (.010) -6.21 (1.20) 4.51 (.85) .065 (.026) . .931 MACHINERY SAMPLE 1954 3.53 (.47) 2.42 (.22) .609 • (.412) 1955 3.62 (.51) 2.57 (.19) 1956 3.67 (.55) 1957 3.36 (.52) .88 (.09) .047 (.025) 4.16 (1.32) .035 (.023) -1.97 (1.61) 3.68 (.73) .122 (.045) .799 .619 (.465) .83 (.07 .045 (.022) 6.07 (1.39) .035 (.020) -2.32 (1.48) 3.76 (.75) .093 (.039) .869 2.41 (.17) .553 (.518) .82 (.05) .054 (.024) 7.68 (1.12) .035 (.019) -1.77 (1.40) 3.87 (.77) .116 (.034) .912 2.23 (.17) .557 (.518) .85 (.05) .055 (.021) 3.91 (1.25) .033 (.017) -4.52 (1.60) 3.98 (.81) .149 (.033) .893 * The s t a n d a r d d e v i a t i o n s and s t a n d a r d e r r o r s o f the means and c o e f f i c i e n t s r e s p e c t i v e l y a r e shown i n p a r e n t h e s e s below t h e mean and c o e f f i c i e n t . 41 may place a lower price relative to dividend on high priced shares than on low priced shares. Alternatively, there may be some normal level for the dividend and investors expect low dividends w i l l more likely rise than w i l l high dividends. Lastly, errors in measurement may bias the coefficient downwards.H The results do show an improvement in s t a t i s t i c a l significance and in the narrower range of fluctuation for the dividend and growth coefficients. The fact that the machinery results are poorer than those for the food sample could be attributed to investors being less confident that the expected rate of growth w i l l be achieved and accordingly placing a lower price on the stock. Alternatively, an inadequate measurement for the expected rate of growth for the 12 machinery sample may have been used. The instability of earnings coefficient has a negative sign and exceeds its standard error for every sample, supporting the hypothesis that price varies inversely with earnings instability. Similarly, the size coefficient has the correct sign in every sample and is significant at the five per cent level in six of eight years. To further validate the results, Gordon examined the food sample and determined that there was no significant bias imparted to the coefficient estimates through the existence of correlation between the squares of the residuals and the growth rate and dividend 13 variables. Although the dependent variable, price, was not 1 1 I b i d . , 46. 1 2 Ibid. •^Ibid., 47. Heteroscedasticity is discussed in P.G. lloel, Introduction to Mathematical Statistics (New York: John Wiley & Sons, Inc., 1947), p. 106. 42 deflated t h i s problem of h e t e r o s c e d a s t i c i t y through the use a p p a r e n t l y was avoided of a l i n e a r e q u a t i o n i n l o g s . A second s t a t i s t i c a l problem i s t h a t of " f i r m e f f e c t s " which a r i s e s when the same sample i s used i n s u c c e s s i v e over time. I f the average of the r e s i d u a l s s i g n i f i c a n t l y from zero i t i s not the e x i s t e n c e of one the model and peculiar the v a r i a n c e bias The of the to each f i r m . to e l i m i n a t e e s t i m a t e of to be excluded the to from increase the dependent v a r i a b l e and possibly independent v a r i a b l e s . ^ * 1 t e s t on f i r m e f f e c t s were h i g h l y the problem and the a c t u a l and possibly the to random d i s t u r b a n c e s but These f i r m e f f e c t s of Kuh's a n a l y s i s of v a r i a n c e determined t h a t for a firm departs or more independent v a r i a b l e s the parameter e s t i m a t e s of use due cross-sections the food samples significant. In order to s e c u r e a c l o s e r correspondence between e s t i m a t e d v a l u e of the dependent v a r i a b l e and also r e v i s e d parameter e s t i m a t e s a d d i t i o n a l v a r i a b l e s might have included i n the model or d i f f e r e n t measurement r u l e s f o r the independent v a r i a b l e s used."*""* T h i s model has price variation. shown g r e a t The promise as an attempt to e x p l a i n c o e f f i c i e n t s f o r growth and d i v i d e n d s are highly s i g n i f i c a n t i n terms of t h e i r s i z e i n r e l a t i o n to t h e i r s t a n d a r d and range of v a r i a t i o n among samples. show a f a i r l y small v a r i a b l e s used have improved the f o r improvement i n the r e s u l t s but treatment of r i s k and there i s s t i l l The stock errors risk room the i n c l u s i o n of leverage S e e Edwin Kuh, "The V a l i d i t y of C r o s s - S e c t i o n a l l y E s t i m a t e d B e h a v i o r E q u a t i o n s i n Time S e r i e s A p p l i c a t i o n s , " E c o n o m e t r i c a , XXVII ( A p r i l , 1959), 202. 1 A 1 5 1962), M . J . Gordon, Review of Economics and 47. Statistics (February, 43 c o u l d be u n d e r t a k e n . Finally, more a c c u r a t e measurement of the variables i s possible. Using the same sample d a t a , Gordon t e s t e d two a d d i t i o n a l models, which he l a b e l e d the "Simlev" and " A d l e v " models. r e s u l t s of these models were r e p o r t e d t o g e t h e r w i t h the model of e q u a t i o n V a l u a t i o n of the (3-6) i n h i s book, "The "Nolev" Investment, F i n a n c i n g , and Corporation.-^ E. The The Simlev Model l o g a r i t h m i c form used to i n c o r p o r a t e f u r t h e r r i s k v a r i a b l e s was ln P where = ln a + aA l n (1+h) P = P r i c e of a common share D = Current br = I — D Growth r a t e of d i v i d e n d = { — ~ ™ } Y = Earnings normalized = Earnings (o/W) t + a i In D + a Q + = Inn + ^ a l n (1 + o/W) 3 l n u + ay InS (3-8) instability Y {-} by e x p o n e n t i a l index W = Y — D — W smoothing (leverage free) = W t t W + Lt net worth + net debt per share = o p e r a t i n g per assets share, h = Debt-equity TT = Operating ratio = L/W . asset l i q u i d i t y index - 7 INV + 5 00A + 3 PE _ - _ _ _ . o "Myron J . Gordon, The Investment, F i n a n c i n g , and V a l u a t i o n of the C o r p o r a t i o n (Homewood, I l l i n o i s : R i c h a r d D. I r w i n , I n c . , 1962). 1 + dividend t t 5 In (1+br) + a Y 0/w) where W + a 2 44 where INV = normal i n v e n t o r y , 00A = other o p e r a t i n g a s s e t s such as d e f e r r e d charges investments i n o t h e r companies, and and and PE = p l a n t equipment net of d e p r e c i a t i o n a l l of which a r e a r b i t r a r i l y weighted a c c o r d i n g degree of liquidity."^ y = Debt m a t u r i t y index = 1 + L / 1 + where L = (current l i a b i l i t i e s ) (long-term pension liabilities) (cash and and L' = the sum debt) + + W L'/W (intermediate-term (liability + r e s e r v e s such as ( p r e f e r r e d stock) government bonds) - (accounts of the items c o m p r i s i n g according to t h e i r m a t u r i t y debt) + receivable) L, weighted so t h a t u 18 increases with S = Size The Simlev - assets - maturity. current dividend coefficients liabilities. were o n l y s l i g h t l y lower f o r the model compared to the Nolev model. dividend versus The use of the an e x p o n e n t i a l l y smoothed average of the current dividend would seem p r e f e r a b l e because of the ease of computation. The coefficients, again s i m i l a r l y , are h i g h l y s i g n i f i c a n t b e t t e r f o r the food sample. performing The measurement of growth appears s l i g h t l y b e t t e r than f o r the Nolev model. The problems of measuring r e t u r n on investment i n the machinery i n d u s t r y remain Ibid., 74-75, Ibid., 80, 162. 163. growth unsolved. TABLE 3-6 Regression 1954 Statistics 1955 f o r the S i m l e v 1956 Model 1957 1958 . Average FOOD SAMPLE 2.488 .170 2.458 .146 2.584 .169 2.553 .134 2.668 .158 2.550 .155 .784 .066 .859 .058 .885 .064 .789 .049 .711 .056 .804 .059 10.972 1.870 10.854 1.508 8.946 1.789 10.114 1.849 10.199 1.930 10.217 1.789 -5.619 -4.442 -3.885 -8.562 -3.661 -5.234 2.127 1.812 2.432 2.201 2.440 2.202 -.522 .159 -.416 .151 -.255 .163 -.343 .120 -.175 .47 -.342 .148 A s s e t l i q . , 35 .322 .197 .343 .181 .175 .202 .285 .156 .164 .186 .258 .184 Debt mat., a§ .008 .462 -.019 .412 -.286 .425 -.247 .374 -.572 .478 -.223 .430 S i z e , a-j .114 .038 .094 .034 .051 .037 .087 .029 .106 .035 .090 .035 .913 .939 .904 .933 .901 .918 Const, term, l n a D D i v i d e n d , a^ Growth, a.2 Earn, inst., Leverage, a a 3 A Coeff. of det., R 2 TABLE 3-6 CONTINUED 1954 1955 MACHINE 1956 1957 1958 Average SAMPLE 2.516 .182 2.533 .176 2.205 .163 2.337 .174 3.019 .176 2.522 .174 .845 .079 .813 .067 .858 .052 .919 .058 .824 .056 .852 .062 7.468 1.415 7.619 1.742 8.819 1.495 4.370 1.618 2.197 2.157 6.095 1.685 -3.112 1.711 -3.317 1.576 -.854 1.638 -3.880 1.862 -.625 1.887 -2.358 -„ 1.735 .119 .149 -.202 .169 .026 .153 .255 .173 .162 .172 .072 .163 Asset l i q . , 3 5 -.400 .370 -.337 .352 -.016 .300 -.094 .321 .602 .312 -.049 .331 Debt mat., a^ -.088 .458 .161 .663 -.628 .495 -1.029 .574 .456 .627 -.226 .563 .082 .047 .101 .047 .158 .040 .117 .045 .048 .047 .101 .045 .851 .880 .913 .890 .881 .883 Const, term, lna Q D i v i d e n d , a^ Growth, a„ Earn, i n s t . , a 3 L e v e r a g e , a^ S i z e , aj Coeff. of det., R 2 47 The r i s k v a r i a b l e s produced instability c o e f f i c i e n t s while having statistically samples. significant I n two f o r two the r i g h t The earnings s i g n are not food samples and t h r e e machinery of the machinery samples the c o e f f i c i e n t i s exceeded by i t s s t a n d a r d e r r o r . fluctuate widely. The In a d d i t i o n , the coefficients c o e f f i c i e n t i s h i g h e r but l e s s than f o r the Nolev Model. without mixed r e s u l t s . significant N e v e r t h e l e s s , Gordon b e l i e v e d t h a t the use of a leverage-free> e a r n i n g s i n s t a b i l i t y measurement v e r s u s a l e v e r e d measurement the r e s u l t s would have been p o o r e r . The l e v e r a g e c o e f f i c i e n t performed f a i r l y w e l l f o r the food sample but p o o r l y f o r the machinery sample. samples had attributed the wrong s i g n . The Four of f i v e machinery l a c k of i n v e r s e c o r r e l a t i o n may to the c o r r e l a t i o n of l e v e r a g e w i t h e a r n i n g s d i r e c t l y , and i n d i r e c t l y levered earnings. through and be instability e a r n i n g s i n s t a b i l i t y based More p l a u s i b l y perhaps, measure p r o f i t a b i l i t y 19 on the l e v e r a g e v a r i a b l e may s e c u r i t y r a t h e r than l e v e r a g e s i n c e secure 20 p r o f i t a b l e f i r m s are more l i k e l y to use debt financing. A better measurement of r e t u r n than r e t u r n on book v a l u e of e q u i t y may be necessary. The o p e r a t i n g a s s e t l i q u i d i t y and debt m a t u r i t y v a r i a b l e s performed p o o r l y and Gordon concludes or n o t h i n g to the model. Only All the s i z e v a r i a b l e performed the samples had 1 9 Ibid., 165. 2 0 Ib_id., 166. 2 1 Ibid., the r i g h t s i g n and 166-167. t h a t they c o n t r i b u t e l i t t l e 21 w e l l as a r i s k variable. e i g h t of t e n samples were 48 statistically significant. This V7as an improvement on the Nolev model for the food sample while the size coefficients for the machinery sample were the same. F. ln P Q = Adlev Model In a + a ln D + a Q ± 2 In (1+br) + a^ ln (l+67w) + + a4 ln (1+h - ih/k) + a$ lnir + ay ln S (3-9) A new leverage variable (1+h - ih/k) was substituted for (1+h) where i = interest on debt and k = rate of return required by investors on a share i f a corporation's leverage and retention rates are both equal to zero. Also, the risk variable u was omitted because of the poor results in the previous model. The leverage coefficient in the food samples performed exceptionally well. Not only did a^ increase in size over the five year period but also the range of variation was reduced while the ratio of size to standard error increased from approximately two in the Simlev model to from three to five. The machinery sample values, however, failed to show improvement. G. In P = Eko Model ln a + a^ InD + a Q + a a 5 3 In (1+br+vq) 2 ln (1+o/W) + a 4 ln (1+h - ih/k) + ln IT + ay ln S + aQ ln (1 + q) (3-10) The Eko model is an expansion of the Adlev model to include outside equity financing. The rate of growth in the dividend, br, TABLE 3-7 Regression 1954 Statistics 1955 f o r t h e A d l e v Model 1956 1957 1958 Average FOOD SAMPLE 2.454 .158 2.435 .142 2.545 .168 2.541 .126 2.632 .150 2.521 .149 .790 .058 .855 .055 .874 .063 .787 .044 .708 .051 .803 .054 12.401 1.640 11.609 1.449 8.959 1.725 10.442 1.535 10.038 1.685 10.690 1.607 Earn. i n s t . , a3 -5.427 1.872 -3.977 1.678 -3.312 2.258 -8.675 1.988 -4.000 2.251 -5.078 2.009 Leverage, a -1.062 .195 -.854 .200 -.617 .223 -.834 .171 -.852 .222 -.844 .202 -.272 .161 .342 .155 .222 .182 .283 .131 .245 .154 .273 .157 .107 .034 .091 .032 .056 .036 .085 .026 .113 .033 .090 .032 .925 .942 .904 .941 .911 .925 Const, term, l n a Q Dividend, Growth, a 2 A A s s e t l i q . , a^ S i z e , aj C o e f f . of d e t . , R 2 1 TABLE 3-7 CONTINUED 1 1954 1955 1956 Average 1957 1958 2.238 .166 2.330 .181 2.975 .178 2.524 .176 .851 .052 .875 .059 .832 .056 .843 .062 MACHINERY SAMPLE Const, term, lna 2.556 .179 c .844 .077 D i v i d e n d , a-^ Grov;th, &2 2.523 .178 .815 .066 7.207 1.375 7.442 1.705 8.846 1.517 3.758 1.638 2.176 2.135 5.886 1.674 -3.163 1.542 -3.351 1.542 -.274 1.650 -4.317 1.992 -.788 1.995 -2.379 1.744 Leverage, a A -.337 .325 -.353 .276 -.096 .274 -.118 .295 .428 .379 -.095 .310 Asset l i q . , -.337 .325 -.250 .314 .061 .283 .052 .331 .666 .334 .038 .317 .076 .045 .106 .044 .142 .039 .131 .046 .064 .046 .104 .044 .857 .878 .909 .882 .879 .881 Earn, i n s t . , a 3 o S i z e , ay Coeff. of det., R 2 51 is increased by the equity accretion rate vq and the stock financing variable q is added where v = fraction of funds invested by new shareholders during a period that accrues to the equity of existing shareholders at the start of the period q = funds raised through outside equity financing as a fraction of the net worth per share. The outside financing rate was measured by N where t-1 W t-1 N = number of shares outstanding W = book value or net worth per share. For the food sample, the outside equity financing rate coefficient ag has the right sign in every year but is not statistically significant in any year and fluctuates widely. of growth variable coefficient a 2 Moreover, the accuracy has been reduced by the addition of vq resulting from correlation between vq and q. This correlation, in turn, has created correlation between the outside financing rate 22 and share price. The'machinery sample again proved to be even worse. The outside equity financing coefficient has the wrong sign in two years and did not exceed its standard error. The growth coefficient was reduced in every year and the ratio to its standard error was reduced in some years. 2 2 I b i d . , 172. TABLE 3-8 Regression S t a t i s t i c s 1954 1955 , f o r the E k o M o d e l t 1956 1957 1958 Average FOOD SAMPLE Const, term, l n a c Dividend, a^ Growth, a 2 Earn, i n s t . , a3 L e v e r a g e , a^ 2.476 .158 2.403 .136 2.663 .185 2.611 .130 2.755 .144 2.582 .151 .803 .059 .883 .053 .892 .070 .764 .046 .672 .050 .803 .056 11.876 1.615 11.515 1.362 7.143 1.875 8.741 1.404 9.248 1.479 9.705 -1.547 -5.164 1.897 -2.953 1.671 -3.117 2.579 -7.850 2.031 -4.051 2.188 -4.627 2.070 -.998 .195 -.588 .217 -.466 .256 -.759 .178 -.781 .216 -.712 .212 A s s e t l i q . , a$ .297 .164 .279 , .156 .204 .206 .306 .138 .300 .149 .277 .163 S i z e , a-j .103 .037 .086 .031 .040 .040 .083 .027 .095 .033 .081 .034 -3.316 1.967 -5.221 1.239 -2.218 1.816 -1.246 1.384 -.649 1.153 -2.530 1.512 .924 .947 .886 .938 .919 .923 S t o c k i s s u e , ag Coeff. of det., R 2 TABLE 3-8 1954 1955 CONTINUED 1956 1957 1958 Average' MACHINERY SAMPLE 2.660 .195 2.543 .182 2.312 .156 2.401 .173 3.012 .178 2.586 .177 .876 .084 .853 .067 .850 .053 .860 .058 .836 .062 .855 .065 4.917 1.227 5.617 1.412 7.744 1.212 3.738 1.216 .742 1.542 4.552 1.322 -2.352 1.685 -2.858 1.600 -.186 1.576 -4.566 1.941 -.588 2.016 -2.110 1.764 .277 .281 -.274 .297 -.038 .292 -.142 .318 .322 .408 .029 .319 -.218 .358 -.169 .324 .069 .274 .029 .322 .646 .341 .051 .324 S i z e , ay .064 .050 .111 .046 .135 .037 .116 .046 .062 .048 .098 .045 S t o c k i s s u e , ag .382 .9S3 -.709 .768 -1.539 .716 -.814 .937 .891 1.103 -.358 .901 .830 .872 .920 .892 .879 .879 Const, term, l n a D D i v i d e n d , a-^ Growth, &2 Earn. i n s t . , a Leverage, a Asset l i q . , 3 4 a5 Coeff. of det., R 2 54 H. Conclusions from E m p i r i c a l F i n d i n g s Of the t h r e e models t e s t e d , the A d l e v model performed b e s t particularly f o r the food sample. While t h e o r e t i c a l l y outside e q u i t y f i n a n c i n g s h o u l d be r e c o g n i z e d , the Eko model d i d not perform as w e l l p o s s i b l y because of the d i f f i c u l t y i s measuring t h a t v a r i a b l e . The f o o d sample r e s u l t s d i v i d e n d , growth and f o r the Adlev model show t h a t the l e v e r a g e v a r i a b l e s are h i g h l y s i g n i f i c a n t have a s m a l l range of f l u c t u a t i o n . the r i g h t s i g n and The remaining exceed t h e i r standard v a r i a b l e s have e r r o r i n every year. Moreover, i n terms of s t a t i s t i c a l s i g n i f i c a n c e a t the f i v e cent l e v e l , the s i z e earnings coefficient i s significant i n s t a b i l i t y i n t h r e e y e a r s and i n two y e a r s . coefficient operating asset l i q u i d i t y With b e t t e r measurement, the e a r n i n g s i n s t a b i l i t y c o u l d be expected modestly w e l l . Only i n every year and it to be stronger. the d i v i d e n d c o e f f i c i e n t s t a b l e over i s not s t a t i s t i c a l l y s i g n i f i c a n t size i n two y e a r s . i n the l a s t y e a r . coefficients lb±d. , 175. the sign i n i n only three years. have the wrong s i g n t h a t the c o e f f i c i e n t s r e l i a b l e e s t i m a t e s of the parameters."23 23 growth r a t e While have the r i g h t asset l i q u i d i t y c o e f f i c i e n t s Gordon concludes The t h r e e y e a r s , then drops u n t i l every year they each are s t a t i s t i c a l l y s i g n i f i c a n t l e v e r a g e and only i s highly significant the f i v e year p e r i o d . performs w e l l i n the f i r s t e a r n i n g s i n s t a b i l i t y and The per i n four years, The machinery sample under the A d l e v model performed coefficient and "do not provide CHAPTER IV FORMULATION AND TESTING OF THE MODEL T h i s chapter present- the model used f o r t e s t i n g and s p e c i f i e s the r e g r e s s i o n v a r i a b l e s and the a l t e r n a t i v e measures used of the v a r i a b l e s . The d a t a and methodology a l s o w i l l be d e s c r i b e d . A. 1. f o r some S e l e c t i o n of V a r i a b l e s B a s i c Model The b a s i c e m p i r i c a l model o f e q u a t i o n (2-8)expresses the dependent v a r i a b l e , p r i c e , i n the f o l l o w i n g f u n c t i o n a l r e l a t i o n s h i p t o the independent P v a r i a b l e s , d i v i d e n d s and the growth r a t e : o = D o ~ (1 + b r ) l a By r e p l a c i n g l / a w i t h ao and a^ w i t h a Q coefficient which i s allowed 2 and by i n c l u d i n g a d i v i d e n d to vary i n s t e a d of being constrained to e q u a l one, the above e q u a t i o n can be m o d i f i e d t o p o = % D o a For t e s t i n g purposes, InP = 2. In a i C 1 + b r )° t " ) 2 4 1 the l o g a r i t h m i c form i s used: 0 a + ai ln D + 2 l n (1 + br) (4-2) Risk Variables R i s k i s d e f i n e d i n t h i s study as the v a r i a b i l i t y o f the c o r p o r a t i o n ' s expected r e t u r n s from investment, due t o u n f o r e s e e n circumstances. These f u t u r e r e t u r n s a r e random v a r i a b l e s w i t h a j o i n t 55 probability 56 distribution. The i n v e s t o r i s assumed to be a b l e to determine s u b j e c t i v e l y the p r o b a b i l i t y d i s t r i b u t i o n ' s v a r i a n c e or d i s p e r s i o n about i t s expected If value.''" the s t a n d a r d d e v i a t i o n of expected index of r i s k , the p r i c e of a share over returns i s considered an time other t h i n g s b e i n g e q u a l , w i l l be a d e c r e a s i n g f u n c t i o n of the p r o b a b i l i t y distribution's dispersion. a. Business variability of r i s k can be of a f i r m ' s o p e r a t i n g income. c o n s i d e r e d as I t a r i s e s from the i t s f u t u r e investments. p r o j e c t s w i l l have d i f f e r e n t p r o b a b i l i t y return. The the a b i l i t y and Business the f i r m ' s e x i s t i n g a s s e t s and investment of Risk: interest nature Different distribtuions r i s k of a d e c l i n e i n o p e r a t i n g income w i l l of the c o r p o r a t i o n to pay the charges endanger on i t s debt d i v i d e n d s to s h a r e h o l d e r s , b. F i n a n c i a l Risk: F i n a n c i a l r i s k a r i s e s from the method of f i n a n c i n g which causes v o l a t i l i t y or a d d i t i o n a l f l u c t u a t i o n s i n the s h a r e h o l d e r ' s e a r n i n g s . The use o f debt f i n a n c i n g may increase the r a t e of r e t u r n to s h a r e h o l d e r s but i t w i l l a l s o i n c r e a s e the variability earnings to its of the expected to the s h a r e h o l d e r s return. i t has, The v a r i a b i l i t y of expected and w i l l be argued, i s r e l a t e d the f i n a n c i a l s t r u c t u r e of the c o r p o r a t i o n b e s i d e s the n a t u r e of investments. c. Size: An s i z e of a f i r m and inverse relationship the s t a b i l i t y s i z e should be r e f l e c t e d G. Illinois: i s p o s t u l a t e d between the of i t s o p e r a t i n g income. While i n the measurement of b u s i n e s s r i s k by David Q u i r i n , The C a p i t a l E x p e n d i t u r e D e c i s i o n (Homewood, R i c h a r d D. I r w i n , I n c . , 1967), Ch. X. 57 reducing the variability of expected earnings, a size variable is included nevertheless on the proposition that investors w i l l consider, independently, the variability of income and size in arriving at their measure of risk. Two companies with historically identical standard deviations of operating income, for example, could, i t is proposed, be in different risk classes i f they differed in size, other things remaining the same. It is conceivable that the shares of large corporations may command a premium because of greater investor interest and greater marketability of the shares. 3. Complete Model If we let u = index of business risk h = index of financial risk S = index of size then our complete empirical model is 2 InP = ln a + 0 ctAln InD + a In (1 + br) + a-jln (1 + u) + 2 (1 + h) + a lnS 5 B. (4-3) Data The historical data used in this study is provided by Standard and Poor's Compustat service. The Compustat tape which was used here contains annual fiiiancial information for approximately nine hundred industrial companies for the period 1946 to 1965. I t should be noted that since ln 1 = o, the use of ln (1+u) and ln (1+h) allows the risk variables to remain positive provided u and h are positive. 2 58 T h i s i n f o r m a t i o n was g a t h e r e d from company r e c o r d s , from S e c u r i t i e s Exchange Commission and from o u t s i d e s o u r c e s . the For the study a t hand, d a t a were taken s e v e n t y - s e v e n companies i n the machinery United States. More w i l l be s a i d on t h i s C. 1. Some of d a t a has been a d j u s t e d by Standard and Poor's f o r g r e a t e r c o m p a r a b i l i t y among f i r m s . for the i n d u s t r y i n the later. Measurement of the V a r i a b l e s Dependent V a r i a b l e - P r i c e (P) The Compustat tape p r o v i d e s annual a b s o l u t e h i g h , low and p r i c e s f o r the companies l i s t e d bid on n a t i o n a l s t o c k exchanges and p r i c e s f o r over-the-counter i s s u e s . close the These p r i c e s a r e g i v e n on a c a l e n d a r - y e a r b a s i s , r e g a r d l e s s of the f i s c a l year-end and have been a d j u s t e d by Standard and Poor's f o r s t o c k s p l i t s and s t o c k d i v i d e n d s except when these occur between a f i s c a l year-end the and c a l e n d a r year-end. For the purpose of t h i s s t u d y , the year-end c l o s i n g p r i c e been chosen. has Arguments can be and have been o f f e r e d f o r o t h e r measures. Y e a r l y averages o f d a i l y average p r i c e s p r o b a b l y would r e c e i v e a l o t of support but these are not r e a d i l y a v a i l a b l e . There i s a l s o 3 support f o r u s i n g the mean of the h i g h and low p r i c e s d u r i n g the y e a r . T h i s i s r e a d i l y a v a i l a b l e on the Compustat tape. attempt Our model i s an to d e s c r i b e those phenomena which determined individual share p r i c e s a t a s p e c i f i c p o i n t i n time r a t h e r than average p r i c e s over -^Charles E. Edwards and James G. H i l t o n , "A Note on the H i g h Low P r i c e Average as an E s t i m a t o r of Annual Average Stock P r i c e s , " J o u r n a l of F i n a n c e , XXI (March, 1966), 112-115. 59 the year. 2. Independent V a r i a b l e s a. Dividends (D). The current per-share y e a r of the c r o s s - s e c t i o n i s used. splits and The data i s adjusted s t o c k d i v i d e n d s on the Compustat tape and p r e f e r r e d s t o c k payments i n l i e u of cash and The d i v i d e n d i n the f o r stock excludes a l s o excludes spin-offs. c u r r e n t d i v i d e n d i s chosen as the b e s t measure of normal d i v i d e n d s on the ground t h a t w h i l e i t i s t r u e t h a t f l u c t u a t i o n s i n dividends occur, t h e r e i s evidence degree of s t a b i l i t y earnings. 4 i n dividends Thus, " n o r m a l i z e d " d i v i d e n d s ) would not be b. t h a t c o r p o r a t i o n s seek a i n the f a c e of r i s i n g or dividends falling (some average of p a s t appropriate. Growth Rate ( b r ) . Growth r a t e s can be c a l c u l a t e d u s i n g v a r i o u s measures i n c l u d i n g d o l l a r s a l e s , net p r o f i t invested, per-share fair on t o t a l capital earnings, t o t a l assets, fixed assets, t o t a l income or r e t a i n e d e a r n i n g s . r a t i o of r e t a i n e d e a r n i n g s "growth" v a r i a b l e s . - * The Increase to p e r - s h a r e i n p r i c e or changes i n the earnings are a l s o p o s s i b l e time p e r i o d from which r e s u l t s might taken f o r the purposes of p r e d i c t i o n might be an average of s e v e r a l p r e v i o u s net be the p r e v i o u s year or years. I n s o f a r as Gordon's model i s concerned w i t h I t s a t t e n t i o n to the growth i n d i v i d e n d s , we w i l l d e f i n e growth as the product of A Cf. Chapter I . A l s o see J . Fred Weston and Eugene F. Brigham, M a n a g e r i a l F i n a n c e , 2nd ed. (New York: H o l t , R i n e h a r t and Winston, 1966), pp. 460-464. J . Fred Weston, The Scope and Methodology of Finance (Englewood C l i f f s , N.J: P r e n t i c e - H a l l ^ Toe.",T9oTTJ','" pp. v x f r = T x y Benjamin Graham, David L. Dodd and Sidney C o t t l e , S e c u r i t y A n a l y s i s : P r i n c i p l e s and Technique, 4th ed. (New York: McGraw-Hill Book Company, I n c . , 1962), p. 235. 5 60 the r a t e o f e a r n i n g s r e t e n t i o n , b and t h e p r o f i t a b i l i t y o f investment, r; t h a t i s , growth, g The Y, = br r e t e n t i o n r a t e i s measured by t h e f r a c t i o n o f "normal r e t a i n e d i n each b = earnings," period: M Y E q u i v a l e n t l y , t h e r e t e n t i o n r a t e , b = 1 - r where - = the payout rate. The p r o f i t a b i l i t y o f investment, r , can be measured i n such ways as (1) r e t u r n on common e q u i t y , E : (2) r e t u r n on t o t a l r = Y = shareholders' Y E + PS W where PS = p r e f e r r e d (3) r e t u r n on t o t a l Y E+PS+D r funds, W: = stock; capital, C: Y C ' where D = n o n c u r r e n t debt; and (A) r e t u r n on t o t a l r The = a s s e t s , A, Y ~ . A r e t u r n on common e q u i t y o r n e t worth measures have a s t r o n g a p p e a l from the v i e w p o i n t o f the s h a r e h o l d e r s , interested who as owners a r e i n the r e t u r n on the money they have i n v e s t e d i n the p a s t . 61 It i s a measure t h a t can be used to compare d i f f e r e n t investments. A l t e r n a t i v e l y , the r e t u r n on t o t a l c a p i t a l or t o t a l measures r e c e i v e s t r o n g support The a f t e r - t a x earnings expense, i n o r d e r i s minimized. should from investment a n a l y s t s . ^ be a d j u s t e d Hence these measures p r o v i d e power of f i r m s w i t h d i f f e r e n t incremental to i n c l u d e i n t e r e s t t h a t the e f f e c t of changes i n c a p i t a l s t r u c t u r e measure of c o r p o r a t i o n performance and Superior to any a c o n s i s t e n t long-term a comparison of the average r a t e s of r e t u r n i s the r a t e of r e t u r n . Without access r e c o r d s , however, i t would be extremely d i f f i c u l t Our tacit earning capital structures. of these or m a r g i n a l t h i s measure. assets to c o r p o r a t i o n to even approximate assumption i s t h a t i n v e s t o r s use average r a t e of r e t u r n based upon the h i s t o r i c an c o s t or book v a l u e of a s s e t s . For t e s t i n g purposes both the r e t u r n on t o t a l a s s e t s and worth were chosen. income and dividends. The f i r s t was the second i n c o n j u n c t i o n w i t h net A Y _ br = Since per-share a first regressed Cf. income b e f o r e respectively. earnings approximation, A n - — — W s u b s t a n t i a l f l u c t u a t i o n s i t was As to o p e r a t i n g Hence, the measurements of growth a r e : Y and used i n c o n j u n c t i o n net are s u b j e c t t o , i n some i n s t a n c e s , felt earnings per on time f o r the p e r i o d 1956 Graham, Dodd and necessary share to 1965 to n o r m a l i z e earnings. f o r each c o r p o r a t i o n were using the linear C o t t l e , S e c u r i t y A n a l y s i s , pp. 462-463. 62 function, Y = t a + bT The n o r m a l i z e d e a r n i n g s , Y, each y e a r o b t a i n e d from The second assumption the t r e n d s t e p was and line. to e l i m i n a t e any b i a s a r i s i n g of a linear, t r e n d . a l s o were f i t t e d The V7as d e f i n e d as the p r e d i c t e d v a l u e i n In a d d i t i o n , two from l o g a r i t h m i c equations f o r each company: ln Y Y = a + b (ln T). t t - a + bT computed t r e n d v a l u e f o r each f i r m ' s n o r m a l i z e d e a r n i n g s taken from whichever e q u a t i o n of the t h r e e p r o v i d e d the b e s t chosen on the b a s i s of m i n i m i z i n g Z(Y - Y ) ; 2 the squared t h a t i s , the sum d e v i a t i o n s between a c t u a l e a r n i n g s and estimated B e s i d e s e l i m i n a t i n g a l i n e a r b i a s , the use of these l o g a r i t h m i c f u n c t i o n s i s supported The was fit, of earnings.^ two by the n a t u r e of e a r n i n g s growth. a r i t h m e t i c s t r a i g h t l i n e r e p r e s e n t s a c o n s t a n t amount of growth per y e a r , whereas the l o g a r i t h m i c s t r a i g h t l i n e s r e p r e s e n t percentage The Our the r a t e of growth. s t a r t i n g p o i n t of the e a r n i n g s t r e n d i s a l s o i n i t i a l assumption determine constant was f u t u r e expected important. t h a t i n v e s t o r s use h i s t o r i c a l d a t a to v a l u e s of d i v i d e n d s , growth and A c c o r d i n g l y , the t r e n d e q u a t i o n was risk. changed to cover a p e r i o d up ^ P r o p e r l y , goodness of f i t i s based upon the t r e n d l i n e w i t h the lowest s t a n d a r d e r r o r of e s t i m a t e . Since _ „ JZ (y - Yj 2 v n - k (n - k) was the same f o r each t r e n d l i n e the use of z(Y - Y) i s equivalent. T h i s t o p i c i s t r e a t e d at l e n g t h i n Mordecai E z e k i e l and K a r l A. Fox, Methods of C o r r e l a t i o n and R e g r e s s i o n A n a l y s i s . 3rd ed. (New York: John Wiley" & Sons, I n c . , 1959), Ch. V I I . 63 to and i n c l u d i n g the c r o s s - s e c t i o n y e a r . The actual period covered should the average b u s i n e s s c y c l e but f i n a n c i a l information deplete trend the sample. equation; s e c t i o n year. on be s h o r t enough so that l a c k of the Compustat tape vzould not A ten y e a r p e r i o d was The seriously chosen f o r each y e a r ' s t h a t i s , from t - 9 to t where t was the cross- machinery sample, o r i g i n a l l y c o n s i s t i n g of s e v e n t y - s e v e n f i r m s , had been reduced to f i t y - s i x the 1956-1965 t r e n d e q u a t i o n s were used. ten y e a r s , long enough to encompass By companies when taking the p e r i o d back an a d d i t i o n a l t h i r t e e n companies were d e l e t e d leaving a sample of f o r t y - t h r e e f i r m s . Both o p e r a t i n g and net income (income b e f o r e income or e a r n i n g s b e f o r e were t e s t e d taxes and p r e f e r r e d and for t h e i r explanatory f i x e d charges) common dividends powers. c. Business Risk (u): The s e l e c t i o n of a sample c o n s i s t i n g of one i n d u s t r y or more a c c u r a t e l y , a group of c l o s e l y r e l a t e d i n d u s t r i e s i s an attempt c o n t r o l f o r the v a r i a t i o n i n share p r i c e due to b u s i n e s s to risk. A pure "homogeneous r i s k c l a s s " i s however, u n l i k e l y to e x i s t where the number of companies i n any comprising with l i k e an i n d u s t r y c l a s s exceeds one. sample, w h i l e m a n u f a c t u r i n g s i m i l a r p r o d u c t s technology r e t a i n d i f f e r e n c e s as a r e s u l t among o t h e r of s e r v i n g d i f f e r e n t g e o g r a p h i c a l varying Companies areas or market segments, things, maintaining degrees of p r o d u c t d i v e r s i f i c a t i o n or q u a l i t y , or having different abilities of management. B u s i n e s s or o p e r a t i n g operating r i s k r e l a t e s to the v a r i a b i l i t y income or e a r n i n g s b e f o r e i n t e r e s t and taxes. of A useful 64 measure o f t h i s r i s k , u, i s t h e s t a n d a r d d e v i a t i o n " of income, Y; that i s , u = f (0y) As u i n c r e a s e s , t h e d e s i r a b i l i t y t o most i n v e s t o r s of t h e share o f common s t o c k t o which u a t t a c h e s d e c l i n e s and t h e p r i c e , t h i n g s r e m a i n i n g unchanged, Two measures and (1) U (2) U where Y W w i l l be r e d u c e d . of b u s i n e s s r i s k were t e s t e d : Y w average income over a t e n - y e a r p e r i o d net worth. The f i r s t measure, c a l l e d used i n t e s t s by Barges the " c o e f f i c i e n t of v a r i a t i o n , " has been and B e n i s h a y x u and f r e q u e n t l y i s recommended as a measure o f r e l a t i v e r i s k by f i n a n c i a l w r i t e r s . " ^ measure was used by Gordon P other (see Chapter I I I ) . The second Both a r e d e s i g n e d t o f A l t e r n a t i v e measures of d i s p e r s i o n such as skewness might a l s o have been used but a r e beyond the scope o f t h i s s t u d y . C f . Fred D. A r d i t t i , " R i s k and t h e Required Return on E q u i t y , " J o u r n a l o f F i n a n c e , XXII (March, 1967), 19-36. 9 of A l e x a n d e r Barges, The E f f e c t o f C a p i t a l S t r u c t u r e on t h e Cost C a p i t a l (Englewood C l i f f s , New York: P r e n t i c e - H a l l , I n c . , 1963). H a s k e l B e n i s h a y , " V a r i a b i l i t y i n E a r n i n g s - P r i c e R a t i o s of C o r p o r a t e E q u i t i e s , " American Economic Review, L I (March, 1961), 81-94. 1 0 Hc.F. Stephen H. A r c h e r and C h a r l e s A. D'Ambrosio, B u s i n e s s F i n a n c e : Theory and Management (New York: The M a c M i l l a n Company; London: C o l l i e r - M a c M i l l a n L i m i t e d ; 1966), and James C. Van Home, F i n a n c i a l Management and P o l i c y (Englewood C l i f f s , New J e r s e y : P r e n t i c e - H a l l I n c . , 1968). 65 account f o r t h e i n f l u e n c e o f f i r m s i z e on t h e measurement o f business r i s k . the I n t h e homogeneous r i s k c l a s s r e f e r r e d t o above, b u s i n e s s r i s k o f each f i r m would be t h e same. d. F i n a n c i a l R i s k : (h) As a proxy f o r f i n a n c i a l r i s k , we chose two measures r e f l e c t i n g the to and long-term debt p a y i n g a b i l i t y of a f i r m ; h o l d debt i n i t s c a p i t a l t h a t i s , the c a p a c i t y structure: (1) times - f i x e d charges - earned = o p e r a t i n g income f i x e a charges (2) debt-equity r a t i o . Unfortunately the d a t a on f i x e d charges was u n a v a i l a b l e on t h e Compustat tape f o r most f i r m s i n the machinery the sample so g r e a t l y sample and d e p l e t e d t h a t the f i r s t measurement was abandoned. With r e s p e c t t o t h e d e b t - e q u i t y r a t i o , long-term debt was chosen i n t h e numerator. P r e v i o u s t e s t s by M o d i g l i a n i and M i l l e r i n c l u d e d p r e f e r r e d s t o c k s i n c e both p r e f e r r e d s h a r e h o l d e r s and bondholders r e c e i v e payment b e f o r e r e s i d u a l e a r n i n g s may be distributed to common s h a r e h o l d e r s . to include current l i a b i l i t i e s , in the numerator e. long-term debt and p r e f e r r e d Size (S): to measure s i z e , such as t o t a l book v a l u e common e q u i t y , t o t a l o f n e t p l a n t account and working assets l e s s current l i a b i l i t i e s , market v a l u e of e q u i t y . of dollars. calculate. shares of the l e v e r a g e v a r i a b l e . Numerous ways e x i s t of A s e p a r a t e t e s t was conducted capital, book v a l u e of i n v e s t e d c a p i t a l and T h i s study used t o t a l assets i n m i l l i o n s The c h o i c e was based on expediency - i t i s simple to There a r e no apparent one measure over a n o t h e r . t h e o r e t i c a l grounds to favor 66 D. Methodology The machinery i n d u s t r y f o r the p e r i o d 1956 s e l e c t e d f o r t e s t i n g purposes. work which covered the p e r i o d utility i n d u s t r y and others, 1954 to 1958. classified a v a i l a b l e on general I t was Poor's as f o l l o w s : been chosen There was a s e v e n t y - s e v e n , whose The firms are machine t o o l s ( 8 ) , handling (8), i n d u s t r i a l ( 6 ) , s p e c i a l t y ( 1 6 ) , steam g e n e r a t i n g (11), (4) (5). n e c e s s a r y to s e t c e r t a i n c r i t e r i a f o r a f i r m ' s i n c l u s i o n i n the sample. information would r e s u l t . ( 6 ) , c o n s t r u c t i o n and m a t e r i a l s industrial electrical A ten year p e r i o d was the Compustat tape. m e t a l f a b r i c a t i n g (13), o i l w e l l and the a t t e n t i o n has l a r g e number of companies, t o t a l l i n g by Standard and agricultural Unlike relatively l i t t l e i n the hope t h a t a d d i t i o n a l i n f o r m a t i o n f i n a n c i a l d a t a was was Thus t h i s study extends Gordon's devoted to the machinery i n d u s t r y . sufficiently to 1965 To a f f o r d c o m p a r a b i l i t y on a company had y e a r p e r i o d o t h e r w i s e the to be f i r m was between y e a r s , financial a v a i l a b l e i n each y e a r of the deleted from the sample. ten Moreover, s i n c e l o g a r i t h i m s were used, the v a r i a b l e s f o r each f i r m were r e q u i r e d to have v a l u e s The greater than zero. m u l t i p l e r e g r e s s i o n a n a l y s i s was performed by the U.B.C. TRIP program at the Computing C e n t r e . A separate routine required of the e a r n i n g s t r e n d f o r the l e a s t - s q u a r e s fitting was regression. CHAPTER V RESULTS AND In the i n i t i a l select fit t e s t s , the most important o b j e c t i v e s were t o the a p p r o p r i a t e trend period f o r normalized earnings. defined CONCLUSIONS and t o choose t h e c u r v e o f b e s t For t h i s purpose, the v a r i a b l e s were as f o l l o w s : P = year-end p r i c e i n c r o s s - s e c t i o n D = current br = growth r a t e of d i v i d e n d = Y - D A Y = normalized earnings i n c r o s s - s e c t i o n A = t o t a l assets u = index of b u s i n e s s dividend year i n cross-section year year a t book v a l u e risk = C y / ? ( c o e f f i c i e n t of v a r i a t i o n ) Cy Y s t a n d a r d d e v i a t i o n o f n e t income about trend = = average o f n e t income from t-9 to t where t i s cross-section h line year = index of f i n a n c i a l = L/E L = long-term debt E = book v a l u e o f common S = s i z e o f the f i r m i n m i l l i o n s of d o l l a r s o f t o t a l 67 risk equity asset 68 A. Regression Results The sample estimates of the regression statistics are shown in Table 5-1. The coefficient values in each year represent the influence on price that investors attribute to each variable. The dividend coefficient ranges in magnitude from .5671 in 1965 to .8463 in 1956 and averages ,7088. This means that for a cross-section of firms in 1956, for example, a 100% change in the dividend of a stock is associated with an 85% change in the price of that stock. The coefficients of the other variables can be similarly interpreted although the particular logarithmic form of the growth, business risk and financial risk variables complicates the analysis. The dividend, growth and size coefficients performed well. statistically The dividend coefficient was "highly significant," that i s , statistically significant at the 1% level and had the expected sign indicated by the theory in every year. The growth coefficient has the expected sign in every year and is highly significant in eight of the ten years while the size coefficient is significant at the 5% level in eight of ten years including six years where i t is significant at the 1% level and has the correct sign in a l l years. at the 10% level. In one year, size is significant The growth coefficient fluctuates considerably, however, from a high of 10.2215 in 1956 to a low of 1.9181 in 1965. The drastic decline after 1962 both in magnitude and ratio of coefficient to its standard error may indicate a disenchantment on the part of investors with "growth" in the stock market. TABLE 5-1 R e g r e s s i o n S t a t i s t i c s f o r Ln P = l n a 0:3 l n (1 + 1956 1957 1958 1959 u) + 0 4 1960 Q + ct^ l n D + a l n (1+h) + a 1961 5 2 I n (1 + b r ) + InS 1962 1963 1964 1965 2.4222 .2078 2.4886 .1006 2.5068 .1296 2.6916 .1970 Average MACHINERY SAMPLE, n=43 C o n s t a n t , In a D D i v i d e n d , a-^ Growth, a2 1.8561 .1601 2.3755 .1803 2.2224 .1880 2.3696 .1820 .8051 .0577 a .7065 .0773 10.2215 2.2990 3 7.7367 1.8480 a 7.3805 1.6293 a 8.2272 2.0462 Financial Risk, 0 4 S.E .7635 .3106 S i z e , ct^ .0590 .0428 .1165 .0362 R2 .8106 .8613 b .2648 .2509 .5364 .2338 a .4788 .1732 .1163 .0350 a -.0206 .2921 b .1098 .03S0 a .8082 .8957 a b c .6706 .0915 a .8240 .0583 a a 7.2825 2.1055 a 8.5411 2.0838 a 3.3269 1.3872 a a 9.7356 2.1529 a .3525 .2599 a a •8137 .0736 .1159 .1406 .6235 .0877 .5831 .0788 a .0786 .1508 a a .8463 .0867 Business Risk, 0 3 2.6198 .1962 2.0085 .1946 .350?c .1791 -.0360 .2920 a .1525 .0396 .7788 a .1660 .1456 .0420 .2757 .4536 .1149 .1176 .3063 -.3426 .2845 -.2275 .1678 .0768° .0417 .0976 .0384 .7283 .7536 s i g n i f i c a n t a t t h e .01 l e v e l s i g n i f i c a n t a t the .05 l e v e l s i g n i f i c a n t a t t h e .10 l e v e l b .1090 .0213 .8983 .6480 .0752 a 2.5519 2.1234 .3053 .1470 b -.3103 .1909 b .1381 .0278 .7995 a ,5671 .0934 2.3561 .1736 a .7088 .0780 1.9181 2.3181 5.9222 1.9993 .0346 .1861 .2378 .1773 -.2554 . .2441 .0490 .2573 ,1562 .0352 .7027 a .1132 .0356 .8037 70 The business and financial risk coefficients performed poorly. Neither coefficient was significant at the 5% level and both, at times, carried unexpected signs. The coefficient for business risk was positive in every year while the coefficient for financial risk was negative in six years. The coefficient of determination, R , which is the ratio of explained variance to total variance of the dependent variable is considered high for cross-sectional regression. It averages .8037 over the ten-year period, with a range of .7027 to .8957. In the previous test net income before preferred and common dividends was used to normalize earnings and normal earnings in turn was used in the measurement of growth. Since net income should be associated with the rate of return on net worth, W, rather than on total assets, the growth variable was changed to Y where W W W = book value of common equity and preferred stock. Table 5-2 presents the regression statistics. There is l i t t l e change in the dividend, growth and size coefficients. They have the expected sign in every year and the dividend coefficient is highly significant in every year. The growth coefficient is highly significant in seven years out of ten years and significant at the 5% level in another, while assets are highly significant in eight years and significant at the 10% level in another year. This is a slight improvement in significance. One notable change is the decrease in the fluctuation of the growth coefficient which ranges from 1.5636 to 7.7929. TABLE 5-2 R e g r e s s i o n S t a t i s t i c s f o r Ln P = l n a Q + In D + a 2 In (1+br) + a ln(l+u) + 3 Y — D Y — D a A l n ? l + h ) + a r InS A f t e r Change i n Growth V a r i a b l e from b r = H n = 43 Constant, l n a Q D i v i d e n d , a-^ Growth, ct Business Risk, a 1957 1958 1959 1960 1961 1962 1963 1964 1965 2.4290 .1679 1.8820 .1521 2.2079 .1817 2.3943 .1725 2.0530 .1798 2.6452 .1862 2.4094 .1991 2.5101 .1002 2.5284 .1262 2.7096 .1963 6.9011 1.3302 a .8180 .0709 a .8073 .0557 a .7165 .0742 3 5.6S06 1.2334 a 5.8653 1.1892 a 6.1985 1.3944 .0650 .1417 .1110 .1349 .4156 .2519 F i n a n c i a l R i s k , 0:4 .4586 .2770 -.0127 .2346 .2603 .2251 Size, 0 5 .0556 .0403 .1157 .0350 R2 .8318 .8701 3 . 1956 .8538 .0818 2 to — - — ,w A J a .1179 .0339 a a ,.4569 .1681 a -.2904 .2822 .1085 .0368 a .9022 .8204 a b c .5946 ' .0741 a .6222 .0853 7.7929 1.4942 a 5.9456 1.5479 .3287° .1697 -.3473 .2721 a .1441 .0375 .8021 a a .6757 .0882 a .8211 .0593 a 7.0063 1.5279 a 2.2474 1.0485 ..1159 .1434 .0601 .2656 -.1090 .3034 -.6319 .2805 b .0739° .0404 .0988 .0369 a .7429 .7716 s i g n i f i c a n t a t t h e .01 l e v e l s i g n i f i c a n t a t t h e .05 l e v e l s i g n i f i c a n t a t the .10 l e v e l a b .6463 .0756 a 1.5636 1.4808 .5686 .0926 Average 2.3769 .1662 a .7124 .0758 1.6957 1.5898 5.0897 1.3836 a .3032 .1491 b .0157 .1864 .2326 .1729 -.3230° .1738 -.3678 .1926 c -.2938 .2322 -.1657 .2474 .1362 .0280 a .4485 .1179 .1078 .0216 .8954 a .7978 .1517 .0357 .7062 a .1110 .0346 .8140 72 The business risk coefficients overall, are slightly lower in magnitude with the same level of significance. in sign. There is no improvement Financial risk, however, has the sign predicted by the theory in eight out of ten years but is significant at the 5% level in only one of those years and significant at the 10% level in two others. The coefficient of determination showed slight improvement to .8140 over ten years. An alternative measure of business risk next was tested by changing u to u W The results are presented in Table 5-3. There was no significant change in the dividend, growth, financial risk and size coefficients. The R values also were very 2 close to previous results, averaging .8129 over the testing period. Business risk as an explanatory variable appeared to have less influence than the l i t t l e i t had before. Although one year had the expected sign, the fluctuation of the coefficient over the years studied increased considerably, with a range of -.2715 to 2.7266. The use of net income in deriving normalized earnings also affects the measurement of business risk. The theory indicates that the variability of earnings applies to net operating income; that i s , net income before income taxes, fixed charges and depreciation. Accordingly, in the next test, operating income was used in conjunction with the risk and growth proxies u and br - W Y - D A TABLE 5-3 Regression Statistics for Ln P = lna Q + cx-^ In D + ct ln (1+br) + ct In (1+u) + 2 3 0v 0"Y otA In (1+h) + 015 InS After Change in Business Risk Variable from u = - ~ to —* -> Y w 0 n=43 Constant, lna Q Dividend, Growth, or-2 1956 1957 1958 1959 2.4376 .1635 1.8946 .1528 2.2912 .1707 2.4574 .1717 .7878 .8535 . .0696 .0794 a 6.0950 1.2752 2.0992 .1725 a ,8010 .056S a .6974 .0749 a 5.6627 1.2162 a 5.7381 1.4690 a 6.8462 1.3545 . 1960 2.5972 .0977 2.5644 .1227 2.7423 .1829 2.4169 .1599 .9120 1.0582 .0672 1.8386 -.1108 .3031 -,6363 .2818 .0270 .2364 .2653 ..2318 -.3538 «.3171 .2908 , .2738 Size, 0 5 .0552 .0402 .1174 .0355 R2 .8319 .8677 a b c 2.4329 .1811 c .4584° .2757 .8112 2.6524 .1835 2.1142 1.1565 b Financial Risk,0:4 .8985 Average 5.7857 1.5867 2.6683 1.1667 a 1965 a 2.0937 1.8569 .1102 .0378 1964 7.3587 1.5564 a .0210 .7918 a 1963 .6190 .0838 .5823 .0730 .3869 .7751 ,1115 .0342 1962 a a Business Risk, 0:3 a 1961 a .6700 . .0851 a 6.9556 1.5213 .1440 .0378• .0747 .0405 .8001 .7436 a c significant at the .01 level significant at the .05 level significant at the .10 level a .7960 .0574 b b a 1.5863 1.1220 -.3163 .1753 a .5615 .0889 a .7000 .0740 1.8969 1.6654 4.8571 1.4369 a 2.5226 1.0575 b -.2715. 1.3186 1.3241 1.1755 c -.3595 .1888 c -.3012 .2315 -.1644 .2489 .1036 .0218 .8940 .6320 .0712 .6457 1.6025 2.7266 .7349 .0973 .0368 .7713 a a .1379 .0273 .8045 a .1479 .0360 .7065 a .1100 .0348 .8129 74 The growth proxy i n c l u d e s the r a t e of r e t u r n on t o t a l a s s e t s w h i l e the o t h e r v a r i a b l e s were l e f t unchanged. are p r e s e n t e d i n Table The regression s t a t i s t i c s 5-4. Over the ten-year p e r i o d , the d i v i d e n d c o e f f i c i e n t s l i g h t l y J b w e r , averaging every year. g e n e r a l l y lower and 1965, the magnitude of the growth c o e f f i c i e n t . a b s o l u t e l e v e l s were evidenced p a r t i c u l a r l y when the c o e f f i c i e n t the c o e f f i c i e n t was and .6706, but remained h i g h l y s i g n i f i c a n t significant significant became n e g a t i v e . a t the 5% i n o n l y two other years. The a t the 5% l e v e l i n e i g h t out of the ten y e a r s . at s l i g h t l y h i g h e r i n most y e a r s but size significant tests, remained r i s k v a r i a b l e s d i d not show improvement e i t h e r . f o r f i n a n c i a l r i s k was having the expected coefficient s i g n i n s i x y e a r s but not b e i n g B u s i n e s s r i s k had significant f o r b u s i n e s s r i s k was The about the same as i n p r e v i o u s the 5% l e v e l i n any of the y e a r s . s i g n i n f i v e y e a r s but was in a t the 1% l e v e l i n o n l y f i v e y e a r s ranged coefficient The In a d d i t i o n , coefficient The in The use of o p e r a t i n g income i n the growth v a r i a b l e c o n s i d e r a b l y reduced 1964 ranged the statistically expected i n none of t h e s e y e a r s . significant The a t the 5% l e v e l i n o n l y three years. To determine whether the poor r e s u l t s f o r r i s k were caused the use of u = O y / W , the same model was coefficient of v a r i a t i o n was that i s , Y used t e s t e d except as the proxy t h a t the f o r business risk, by TABLE 5-4 Regression Statistics for Ln P = l n a + a-^ 'In D + a 0 cu ln (1+h) + ln (1+br) + 0 3 ln (1+u) + 2 InS After Change to Operating Income with u = -~ and br = W n=46 Constant, lna Q Dividend, Growth, a 2 Business Risk, 0 3 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 2.2045 .2529 1.7033 .2401 2.4379 .2469 2.6406 .2613 1.7678 .2591 2.6422 .2381 2.4450 .2081 2.4567 .1292 2.3029 .1606 2.7316 .2005 .7335 .0879 a .7417 .0702 3.9339 1.0171 a 2.8276 .7298 a .7843 .0643 a 2.0340 .7891 a .6071 .0781 a ,6140 .0834 b 2.5643 .8423 a 3.0750 .8299 -.7484 1.0038 -.2792 1.1210 -.9063 .9548 -1.2969 1.0312 3.0859 1.2724 .6074 .3693 .2479 .2677 .3134 .2581 -.0549 .3132 -.3036 .3170 Size, 0:5 .0679 .0512 .1312 .0428 R .7306 .8217 Financial Risk, a 2 4 " A a ,1069 .0400 .0912 .0447 a .8619 .7552 a b c b a .6477 .0862 a b .1702 .0450 .7438 a a .6317 .0844 1.9302 .7660 b 2.4841 .7183 1.2616 1.2260 -.3089 1.0681 1.8876 .9124 4.1315 1.5138 .1356 .3218 -.3515 .2859 -.2389 .1829 .0601 .0440 .0865 .0379 .6994 .7386 significant at the .01 level significant at the .05 level significant at the .10 level a ,7364 .0606 a •9154C a .5400 b b .1202 .0239 .8585 a .6472 .0729 a .5626 .0840 Average 2.3332 .2197 a .6706 .0772 -.1659 .7497 1.9424 .7690 a .7804 1.5512 .7607 1.1655 -.3493C .1836 -.3044 .2325 .0298 .2732 .1728 .0273 .1583 .0324 -.1747 .7080 .7806 a .6881 a .1165 .0389 .7678 76 As Table 5-5 shews, the coefficient for business risk performed poorly. Only three years had the sign indicated by the theory compared to five years in Table 5-4 and only one year was significant compared to three years previously. In neither case did the business risk coefficient have the correct sign in the year in which i t was significant. There was, however, a considerable reduction in the range of fluctuation over the years. More importantly, the use of the coefficient allowed the growth coefficient to "improve." of variation In a l l ten years, compared to eight years previously, growth has the expected sign. In addition, eight of the years are significant, being one more than before. The range of fluctuation is slightly reduced as well. Comparison of Table 5-2 with 5-3 and Table 5-4 with 5-5 indicates that there is a slight advantage in using ay/* instead of ay/W as a business risk proxy. Using the same model reported i n Table 5-4, the financial risk proxy was changed from h = L/E to h where = L + P.S. + C.L. ———————-— E P.S. = book value of preferred stock C.L. = current l i a b i l i t i e s . The results tabulated in Table 5-6 show no appreciable improvement in the performance of this risk coefficient nor in the effects on any other variable. compared to previous tests Although one more year has the expected sign, none of the years are significant at the 5% level The range, however, was slightly reduced. TABLE 5-5 Regression Statistics for Ln P = lna Q + aj_ In D + a ln (1+br) + a 2 3 ln (1+u) + °Y 0:4 ln (1+h) + 0 5 InS After Change to Operating Income with u = -= n=46 Constant, lna D Dividend, a. Growth, a 1957 1958 1959 1960 1961 1962 1963 2.2257 .2677 1.6426 .2569 2.3029 .2752 2.6515 .2769 1.9180 .2843 2.7063 .2438 2.4623 .2328 2.3921 .1541 .7355 .0907 a 3.6805 .9375 2 Business Risk, a 1956 3 .7465 .0709 a .7802 .0649 2.8001 .7151 a 2.0977 .8283 a .6001 .0798 a b 2.36l4 .8717 a .5986 .0887 a .6458 .0891 a 3.2535a .8924 1.9654b .7808 .6296 .0852 2.4280a .7538 -.1658 .3040 .0677 .3129 .0527 .3117 -.3609 .3146 .4853 .3861 .1676 .3333 -.1013 .3125 Financial Risk, 0 4 .5662 .3619 .2602 .2700 .3529 .2642 -.1199 .3159 -.2300 .3310 .1546 .3245 -.3540 .2861 Size, 0.5 .0700 .0512 .1365 .0424 .0523 .0438 .0856 .0383 R .7289 .8216 .6934 .7387 2 3 a .1170 .0406 .0977 .0434 a .7536 .8589 a b c b .1478 .0461 .7173 a a significant at the .01 level significant at the .05 level significant at the .10 level 1964 .7380 .0623 a .6464 .0771 1.3444b .5326 .7779 .6331 .4263 .2442. .8725 .3909 -.2240 .1868 .1239 .0247 .8545 Average 2.1986 " 2.6664 .2380 .2049 c b 1965 a b -.2800 .1923 a .1752 .0287 .7685 a .5767 .0882 2.3166 .2435 a .6697 .0797 .0412 .7547 2.0750 .7700 .2843 .3990 .1728 .3309 -.2712 .2362 .0145 .2769 .1597 .0322 .6901 a .1166 .0391 .7626 - TABLE 5-6 Regression Statistics for Ln P ctA ln (1+h) + a n=46 Constant, lna 1956 o Dividend, 2.1212 .2560 3 l n a + 0 a l n D + 1 a 2 ^ n ( 1 + b r ) + a 3 l n ( 1+u ) + OY 5 InS After Change to Operating Income with u = — and h = W TH-P +r T S E ,1957 1958 1959 1960 1961 1962 1963 1964 1965 Average 1.6556 .2368 2.3926 .2486 2.6473 .2546 1.8020 .2509 2.6173 .2304 2.5080 .2040 2.4893 .1284 2.3366 .1645 2.7169 .2055 2.3287 .2180 .7128 .0875 a .7386 .0672 a Growth, (*2 3.5783 .9857 a 2.8206 .7217 3 Business Risk, 0:3 -.5817 1.0059 -.2004 1.1155 -1.0405 .9805 -1.3003 1.0304 3.0540 1.2681 Financing Risk, 0 4 .3133 .2543 .2427 .1953 .0120 .1987 -.0349 .2042 -.2062 .2115 Size, ct5 .0824 .0502 .1267 .0419 R2 .7229 .8247 a .7657 .0646 l„9799 .8034 b .1300 .0403 .8568 a a .6072 .0781 a .6129 .0836 a .6390 .0875 2.5719 .8416 a 3.0981 .8288 a b .0909 .0442 .7552 b .1705 .0449 .7440 a a .6546 .0883 a .7522 .0600 1.9304 .7681 b 2.4412 .7277 a .8889 .5472 1.2737 1.2296 -.3718 1.1010 1.9040 .9273 4.1710 1.5557 .0464 .2536 -.1480 .2532 -.1223 .1525 -.2015 .1765 a a .1623 .7337 b .0656 .0462 .0761° .0405 .1164 .0255 .6983 .7310 .8548 a significant at the .01 level b significant at the .05 level c significant at the .10 level .6662 .0746 a a .1709 .0309 .7682 a .6206 .0850 a .6770 .0776 .3053 .7819 1.9452 .7740 .7976 1.5767 .7706 1.1791 .1303 .2022 .0032 .2102 .1256 .0363 .6781 a .1155 .0401 .7634 79 B. Conclusions The purpose of this thesis was to determine whether a stock valuation model based upon the dividend formulation of Myron J . Gordon provides an adequate explanation of the variation in stock prices over an extended period of time. It can be concluded that the empirical results support the theory that investors mainly consider the current dividend, its expected rate of growth and its risk in determining the price of a share. Tests conducted on a sample taken from the machinery industry, showed that on average over a ten-year period, between 76% and 81% of the total variance in share price was explained by the model. The lowest R value in any year was .6781, 2 while the highest value was .9022. The coefficients of dividends, growth and size were statistically significant at the 5% level or better in most of the years tested. The dividend coefficient, every year. in particular, was highly significant in Furthermore, except for the growth coefficient years, these coefficients in two had the expected sign indicated by the theory. In terms of stability, only the growth coefficient fluctuated widely. The change in absolute level and stability of growth can be partly explained by the measurements used for corporate earnings or return on investment. The most important reason, however, may be changing investor valuation of growth in the stock market. Except for a short period in early 1962, the stock market has been an expansionary phase since 1960. The tests show that after 1962, however, there was a drastic decline in the growth coefficient which corresponds to the market's reassessment of "growth stocks." 80 That this decline continued until 1965 probably relates to the industry's prospects rather than to growth expectations for the overall market. The good performance of the size variable is a mixed blessing. The fact that size appeared to be highly correlated with both financial and business risk may have contributed to the failure of the other risk variables. More importantly, the lack of statistical significance in most years would indicate that the measurement of risk was at fault. In particular, measures of business risk other than the standard deviation of income might be more successful. There is also a strong possibility that in assessing risk, investors consider such factors as quality of management, which is not derived from the balance sheet or income statement of the corporation. Lastly, i t is possible that the machinery industry, i t s e l f , is not broadly representative of the stock market. Although the model proved generally successful in predicting share price variation, its usefulness to investors for security selection is limited. Cross-section averages for an industry may ignore conditions peculiar to certain companies within the industry. Omission of other important determinants of stock prices common to an industry also is possible i f less likely. A more common problem is that of accurate measurement of the variables. Assuming the problem of measurement can be overcome i t is probable that the nature of the relationship between variables w i l l change from year to year and this study indicates this is frequently the case. The weight attached to growth in dividends and earnings was found to be particularly vulnerable to change over time. Lastly, 81 the mechanistic use of past or current earnings - even i f normalized to the extent that its values deviate from investors expectations limit the model's usefulness. The main value of Gordon's model is in specifying the variables important to stock valuation and in clarifying the nature of the relationships. To this extent, this model is worthy of study by investor and corporation officer alike. 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An investigation of Gordon's common stock valuation model Smith, Patrick John 1968
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