UBC Theses and Dissertations

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UBC Theses and Dissertations

Tests of determinants of optimal capital structure Portman, Nicholas Francis 1983

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T E S T S O F D E T E R M I N A N T S O F O P T I M A L C A P I T A L S T R U C T U R E b y N I C H O L A S F R A N C I S P O R T M A N B . C o m m . ( H o n s . ) , D a l h o u s i e U n i v e r s i t y , 1 9 8 1 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E ( 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 F A C U L T Y O F G R A D U A T E S T U D I E S D e p a r t m e n t O f C o m m e r c e A n d B u s i n e s s A d m i n i s t r a t i o n W e a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d T H E 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 A p r i l 1 9 8 3 © N i c h o l a s F r a n c i s P o r t m a n , 1 9 8 3 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 n/fin i i A b s t r a c t T h i s paper p r o v i d e s an e x a m i n a t i o n of the r e l a t i o n s h i p between c a p i t a l s t r u c t u r e and a number of f i r m c h a r a c t e r i s t i c s . A s y n o p s i s of the t h e o r y and e v i d e n c e on c a p i t a l s t r u c t u r e t o d a t e i s p r o v i d e d . A model i s d e v e l o p e d which p o s i t s t h a t c a p i t a l s t r u c t u r e i s p o s i t i v e l y r e l a t e d t o l i q u i d i t y , f i r m s i z e , the r e l a t i v e amounts of s u b o r d i n a t e d and p r i o r i z e d d e b t , and n e g a t i v e l y r e l a t e d t o o p e r a t i n g l e v e r a g e , s a l e s v a r i a b i l i t y , and b a n k r u p t c y c o s t s . T e s t s of the model were performed i n a r e g r e s s i o n c o n t e x t , w i t h the l o g a r i t h m of the d e b t - t o - e q u i t y r a t i o as the dependent v a r i a b l e . The c h a r a c t e r i s t i c s used as independent v a r i a b l e s were degree of o p e r a t i n g l e v e r a g e , v a r i a n c e of s a l e s , i n d u s t r y c l a s s , f i r m s i z e , the p r o p o r t i o n of s e c u r e d t o unsecured d e b t , a l i q u i d i t y measure (c a s h t o t o t a l a s s e t s ) , and a number of p r o x i e s f o r o p e r a t i n g l e v e r a g e ( a c c o u n t s r e c e i v a b l e , i n v e n t o r y and net p l a n t , t o t o t a l a s s e t s ) . Dummy v a r i a b l e s were i n t r o d u c e d t o check f o r the i n f l u e n c e of i n d u s t r y c l a s s , c o n v e r t i b l e debt and p r e f e r r e d s on c a p i t a l s t r u c t u r e . C a p i t a l s t r u c t u r e was found t o be s i g n i f i c a n t l y n e g a t i v e l y r e l a t e d t o l i q u i d i t y , i n d u s t r y c l a s s , o p e r a t i n g l e v e r a g e , and s i g n i f i c a n t l y p o s i t i v e l y r e l a t e d t o the r a t i o s u b o r d i n a t e d t o o t h e r l o n g term d e b t . S i z e and s a l e s v a r i a b i l i t y were found t o have no i n f l u e n c e on f i n a n c i a l l e v e r a g e . F i r m s which had i s s u e d p r e f e r r e d s t o c k had h i g h e r debt r a t i o s . C o n v e r t i b l e debt tended t o a c t l i k e e q u i t y . Table of Contents Abstract L i s t of Tables L i s t of Figures I. CAPITAL STRUCTURE: THEORY AND EVIDENCE TO DATE I I . A SIMPLE MODEL OF CAPITAL STRUCTURE I I I . METHODOLOGY AND RESULTS LITERATURE CITED APPENDIX A - LIST OF COMPANIES SAMPLED 6 iv L i s t of Tables Regression Results Variance Decomposition Industry Regressions Industry Regressions Continued V L i s t of Figures 1. Expected Normal Plot, A l l Cases, 1981 & 1976 Data 49 2. Expected Normal Plot, Cases 69 & 241 Deleted, 1981 & 1976 Data 5 0 3. Expected Normal Plot, A l l Cases, 1971 & 1966 Data 51 1 I. CAPITAL STRUCTURE; THEORY AND EVIDENCE TO DATE In a world where c a p i t a l markets are both . complete and p e r f e c t , the r e l a t i v e amounts of r i s k y debt and e q u i t y used f o r f i n a n c i n g have no e f f e c t on f i r m v a l u e . 1 As f i n a n c i a l leverage i n c r e a s e s , s t o c k h o l d e r s demand higher r e t u r n s to compensate them f o r b e a r i n g i n c r e a s e d r i s k . Hamada examined the e f f e c t of f i n a n c i a l leverage on the systematic r i s k of e q u i t y . 2 Hamada assumed that the MM p r o p o s i t i o n h e l d . He a d j u s t e d stock r e t u r n s to what they would have been had the f i r m not been l e v e r e d , and then regressed the e s t i m a t e s of r e t u r n s (observed and adjusted) a g a i n s t estimates of the systematic r i s k of the l e v e r e d and unlevered f i r m s . The r e s u l t s showed that leverage e x p l a i n e d between 21 and 24 percent of observed systematic r i s k . Hamada measured the systematic r i s k of h i s observed and a d j u s t e d r e t u r n s . He found the standard d e v i a t i o n of h i s s y s t e m a t i c r i s k measure to be lower f o r the a d j u s t e d r e t u r n s , f o r each i n d u s t r y . T h i s suggested that w i t h i n each i n d u s t r y , a l l e q u i t y f i n a n c e d firms tended to face the same l e v e l s of s y s t e m a t i c r i s k , but f i r m s c o u l d have chosen to have more systematic r i s k i f they i n c r e a s e d f i n a n c i a l l e v e r a g e . C h i -1 Joseph E. S t i g l i t z , "On the I r r e l e v a n c e of Corporate F i n a n c i a l P o l i c y , " American Economic Review, December 1974. 2 Robert S. Hamada, "The E f f e c t of the Firm's C a p i t a l S t r u c t u r e on the Systematic Risk of Common Stocks," J o u r n a l of Finance, June 1966. 2 squared tests suggested that variation in systematic r i s k within ri s k classes was less than that in the whole sample. This again suggested similar underlying c a p i t a l i z a t i o n rates for firms within each industry, but d i f f e r i n g amongst risk classes. F i n a l l y , Hamada found that the F-ratio of variance between industries was less for the observed systematic risk measures than for the adjusted ones. Between industries, systematic risk measures have similar v a r i a b i l i t y , when compared to the v a r i a b i l i t y of systematic r i s k measures of unlevered firms. These re s u l t s tend to support the MM hypothesis. The inclusion of corporate and personal income taxes leaves th i s conclusion unchanged for the individual f i r m . 3 Firms induce equityholders to switch to holding bonds by of f e r i n g them higher y i e l d s . These higher yi e l d s compensate equityholders for their loss of tax savings from the reduction in their equity positions. There are some investors who are taxed at too high a rate for the tax savings from corporate borrowing to be s u f f i c i e n t to offset the increase in personal taxes resulting from the switch. Firms w i l l be ind i f f e r e n t to issuing debt or equity when the increase in firm value from issuing debt equals zero. This occurs when the increase in corporate tax shield from debt issue i s offset by the increased y i e l d offered to the investor to induce him to switch drom equity to debt. M i l l e r ' s theory suggests that there e x i s t s an optimal c a p i t a l structure for a l l firms taken together, but the ind i v i d u a l firm w i l l find 3 M.H. M i l l e r , "Debt and Taxes", Journal of Finance, May 1977. 3 t h a t d e b t s t r u c t u r e d o e s n o t m a t t e r . " O n e a r g u m e n t t h a t s u g g e s t s f i r m s d o i n d e e d f a c e a n o p t i m a l c a p i t a l s t r u c t u r e c o n c e r n s i n f o r m a t i o n a s y m m e t r y . 5 I n s i d e r s e n g a g e i n f i n a n c i a l s i g n a l l i n g i n o r d e r t o p r o v i d e i n f o r m a t i o n t o s h a r e h o l d e r s a b o u t t h e n a t u r e o f t h e f i r m ' s b u s i n e s s r i s k a n d p r o f i t a b i l i t y . B y g i v i n g c o r r e c t s i g n a l s c o m p r i s i n g p o s i t i v e i n f o r m a t i o n , m a n a g e r s e n s u r e t h a t f i r m v a l u e i s m a x i m i z e d . T h i s a r g u m e n t h o l d s , g i v e n a n a p p r o p r i a t e i n c e n t i v e s t r u c t u r e f o r m a n a g e r s . H o w e v e r , i t m a y b e i n t h e i n t e r e s t o f s t o c k h o l d e r s t o m a k e s i d e p a y m e n t s t o m a n a g e r s , t h e r e b y i n d u c i n g t h e m t o m a k e t h e w r o n g s i g n a l s . T h i s c a n l e a d t o r e s u l t s w h i c h a r e i n c o n s i s t e n t w i t h f i r m v a l u e m a x i m i z a t i o n . A p o t e n t i a l l y i m p o r t a n t e l e m e n t i n c a p i t a l s t r u c t u r e t h e o r y i s b a n k r u p t c y c o s t s . T h e s e d e a d w e i g h t l o s s e s w i l l l e a d t o t h e v a l u e o f a b a n k r u p t f i r m b e i n g l e s s t h a n t h e n e t p r e s e n t v a l u e o f e x p e c t e d f u t u r e c a s h f l o w s t o t h e f i r m . A s a f i r m t a k e s o n m o r e d e b t , t h e p r o b a b i l i t y o f b a n k r u p t c y i n c r e a s e s . T h e f i r m w i l l o n l y i s s u e d e b t u n t i l t h e m a r g i n a l b e n e f i t f r o m u s i n g m o r e d e b t e q u a l s t h e i n c r e a s e i n e x p e c t e d b a n k r u p t c y c o s t s . B a n k r u p t c y c o s t s c a n b e c l a s s e d a s e i t h e r d i r e c t o r i n d i r e c t , a n d t h e d i s t i n c t i o n s e t f o r t h b y W a r n e r w i l l b e * R i c h a r d B r e a l e y a n d S t e w a r t M y e r s , P r i n c i p l e s o f C o r p o r a t e  F i n a n c e , M c - G r a w H i l l , I n c . , T o r o n t o , 1 9 8 1 , C h a p t e r 1 8 . 5 A n d r e w H . C h e n a n d E . H a n K i m , " T h e o r i e s o f C o r p o r a t e D e b t S t r u c t u r e : A S y n t h e s i s " , J o u r n a l o f F i n a n c e , M a y 1 9 7 9 . 6 J e r o l d B . W a r n e r , " B a n k r u p t c y C o s t s : S o m e E v i d e n c e " , J o u r n a l  o f F i n a n c e , M a y 1 9 7 7 . 4 f o l l o w e d h e r e . 6 D i r e c t b a n k r u p t c y c o s t s r e f e r t o l e g a l , a c c o u n t i n g , t r u s t e e , a n d o t h e r p r o f e s s i o n a l f e e s , t h e v a l u e o f m a n a g e r i a l t i m e s p e n t a s s e s s i n g t h e b a n k r u p t c y , c o u r t c o s t s , a n d t h e d i s b u r s e m e n t s b y t h e t r u s t e e a n d o t h e r a g e n t s o f t h e c o u r t . I n d i r e c t c o s t s i n c l u d e l o s t s a l e s , l o s t p r o f i t s , l o s s o f i n t a n g i b l e a s s e t s , t h e o p p o r t u n i t y c o s t o f f u n d s t i e d u p d u e t o l e g a l p r o c e e d i n g s , a n d t h e c o s t o f c r e d i t o r s t i m e . A n i d e a l e x a m i n a t i o n o f t h e e f f e c t s o f b a n k r u p t c y c o s t s o n t h e c a p i t a l s t r u c t u r e d e c i s i o n o f t h e f i r m w o u l d i n c l u d e a n a l y s i s o f t h e e x a n t e e x p e c t e d c o s t s o f b a n k r u p t c y a t t h e t i m e w h e n m a n a g e m e n t i s m a k i n g t h e r e l e v a n t d e c i s i o n s . U n f o r t u n a t e l y , e x a n t e e x p e c t e d b a n k r u p t c y c o s t s a r e n o t d i r e c t l y o b s e r v a b l e . T w o a u t h o r s s u g g e s t t h a t d i r e c t b a n k r u p t c y c o s t s , a s a p e r c e n t a g e o f f i r m v a l u e , a r e n e g a t i v e l y r e l a t e d t o f i r m s i z e . B a x t e r f o u n d t h a t f o r a s s e t r e a l i z a t i o n s u n d e r $ 5 0 0 0 0 , t h e r a t i o o f a d m i n i s t r a t i v e c o s t s t o t o t a l a s s e t r e a l i z a t i o n w a s 2 5 . 7 % , w h e r e a s f o r r e a l i z a t i o n s o v e r $ 5 0 0 0 0 , t h e r a t i o w a s 1 9 . 9 % . 7 I n c o n t r a s t t o B a x t e r ' s e x a m i n a t i o n o f p e r s o n a l b a n k r u p t c i e s , c o n c e n t r a t e d o n t h e l i q u i d a t i o n c o s t s o f a s a m p l e o f p u b l i c l y t r a d e d r a i l r o a d c o m p a n i e s , a n d h i s s t u d y a l s o s u g g e s t e d t h a t t h e r e l a t i v e d i r e c t c o s t s o f b a n k r u p t c y d e c l i n e a s f i r m s i z e i n c r e a s e s . 8 F o r e x a m p l e , W a r n e r f o u n d b a n k r u p t c y c o s t s a s a 7 N e v i n s D . B a x t e r , " L e v e r a g e , R i s k o f R u i n a n d t h e C o s t o f C a p i t a l " , J o u r n a l o f F i n a n c e , 1 9 6 7 . 8 J e r o l d B . W a r n e r , O p . C i t . 5 p e r c e n t o f m a r k e t v a l u e a t t h e d a t e o f b a n k r u p t c y t o b e 9 . 1 % a n d 6 . 6 % f o r t h e t w o s m a l l e s t r a i l r o a d s , a n d 2 . 7 % a n d 1 . 7 % f o r t h e t w o l a r g e s t . I n a d d i t i o n t o b a n k r u p t c y c o s t s , w h i c h m a y w e l l b e s m a l l , t h e r e a r e c o s t s o f f i n a n c i a l d i s t r e s s , w h e n t h e f i r m i s o n t h e v e r g e o f b a n k r u p t c y . T h e c o s t s o f f i n a n c i a l d i s t r e s s i n c l u d e t h e r e d u c t i o n o f f i r m v a l u e d u e t o b o n d h o l d e r s t o c k h o l d e r c o n f l i c t s , a n d t h e b o n d i n g a n d m o n i t o r i n g c o s t s a s s o c i a t e d w i t h d e b t c o v e n a n t s . 9 T h e i n c l u s i o n o f c o s t s o f b a n k r u p t c y a n d f i n a n c i a l d i s t r e s s t e n d s t o s u p p o r t t h e t r a d i t i o n a l v i e w t h a t t h e r e i s a n o p t i m a l d e b t s t r u c t u r e w h i c h m i n i m i z e s t h e w e i g h t e d a v e r a g e c o s t o f c a p i t a l . 1 0 S c h w a r t z a n d A r o n s o n a r g u e d t h a t w i t h o u t f r i c t i o n l e s s c a p i t a l m a r k e t s , f i r m s w o u l d d e v e l o p o p t i m a l c a p i t a l s t r u c t u r e s w h i c h w o u l d a p p e a l t o v a r i o u s s e g m e n t s i n t h e m a r k e t f o r f u n d s . 1 1 T h e s e o p t i m a l c a p i t a l s t r u c t u r e s w o u l d b e d e v e l o p e d i n l i g h t o f t h e f i r m ' s o p e r a t i o n a l a n d a s s e t c h a r a c t e r i s t i c s . T h e y s u g g e s t e d t h a t f i r m s i n t h e s a m e i n d u s t r y w o u l d h a v e s i m i l a r a s s e t s t r u c t u r e s a n d f a c e s i m i l a r l e v e l s o f b u s i n e s s r i s k , a n d 9 M . H . J e n s e n a n d W . H . M e c k l i n g , " T h e o r y o f t h e F i r m : M a n a g e r i a l B e h a v i o r , A g e n c y C o s t s a n d O w n e r s h i p S t r u c t u r e " , J o u r n a l o f F i n a n c i a l E c o n o m i c s , O c t o b e r 1 9 7 6 . 1 0 R i c h a r d B r e a l e y a n d S t e w a r t M y e r s , O p . C i t . , p . 3 9 6 . 1 1 E l i S c h w a r t z a n d J . R i c h a r d A r o n s o n , " S o m e S u r r o g a t e E v i d e n c e i n S u p p o r t o f t h e C o n c e p t o f O p t i m a l C a p i t a l S t r u c t u r e " , J o u r n a l  o f F i n a n c e , M a r c h 1 9 6 7 . 6 consequently would e x h i b i t s i m i l a r c a p i t a l s t r u c t u r e s . Furthermore, f i r m s i n d i f f e r e n t i n d u s t r i e s would have d i f f e r r i n g c a p i t a l s t r u c t u r e s . In an e f f o r t to t e s t t h i s theory, they sampled four i n d u s t r i e s i n 1928 and 1961. They took three samples of e i g h t f i r m s i n each i n d u s t r y i n each year. The i n d u s t r i e s examined were r a i l r o a d s , e l e c t r i c and gas u t i l i t i e s , mining, and i n d u s t r i a l s . They used a one way ANOVA t e s t f o r d i f f e r e n c e s i n the mean e q u i t y to t o t a l a s s e t s r a t i o f o r a l l sample means. Common e q u i t y was seen as a r e s i d u a l c l a i m a n t , and v a r i a t i o n i n common e q u i t y was f e l t to be more c r u c i a l than v a r i a t i o n i n p r i o r c l a i m s . Schwartz and Aronson concluded t h a t i n n e i t h e r 1961 or 1928 was there any s t a t i s t i c a l d i f f e r e n c e i n f i n a n c i a l s t r u c t u r e s w i t h i n any c l a s s of f i r m s . They d i d f i n d s i g n i f i c a n t i n t e r - i n d u s t r y d i f f e r e n c e s i n both 1928 and 1961 f o r a l l samples. Schwartz and Aronson maintained that i n d u s t r y f i n a n c i a l s t r u c t u r e does change i n response to v a r i a t i o n i n the environment. For example, they suggested t h a t over time, r a i l r o a d s became l e s s l e v e r a g e d . T h i s was because of i n c r e a s e d c o m p e t i t i o n from other forms of t r a n s p o r t and the s u s c e p t i b l i t y of r a i l r o a d s to v a r i a t i o n i n b u s i n e s s c y c l e s . They i m p l i c i t l y a s s e r t that f i r m s f a c i n g higher l e v e l s of b u s i n e s s r i s k tend to reduce t h e i r degree of f i n a n c i a l l e v e r a g e . Nonetheless, i t appeared to them that f i n a n c i a l s t r u c t u r e s were s t a b l e over time. U n f o r t u n a t e l y , they d i d not t e s t t h i s h y p othesis s t a t i s t i c a l l y . T h e i r examination was by i n s p e c t i o n , which l e d 7 them t o c o n c l u d e t h a t f i n a n c i a l c a p i t a l s t r u c t u r e s changed g r a d u a l l y i n response t o e n v i r o n m e n t a l c h a n g e . 1 2 S c o t t c r i t i c i z e d Schwartz and Aronson on s e v e r a l grounds. He argued t h a t Schwartz and Aronson o n l y sampled f o u r i n d u s t r i e s , and t h e i r c h o i c e of i n d u s t r i e s b i a s e d t h e i r r e s u l t s . R e g u l a t i o n of r a i l r o a d s and u t i l i t i e s may w e l l have l e d t o s i m i l a r c a p i t a l s t r u c t u r e s w i t h i n each i n d u s t r y . F u r t h e r m o r e , they t e s t e d f o r e q u a l i t y amongst a l l group means, but d i d not conduct p a i r w i s e comparisons of means between i n d u s t r y groups. S c o t t went on t o p e r f o r m t e s t s s i m i l a r t o t h o s e of Schwartz and Aronson, u s i n g a l a r g e r sample of u n r e g u l a t e d f i r m s , and asked how many i n t e r i n d u s t r y d i f f e r e n c e s were s i g n i f i c a n t . He e x p l i c i t l y assumed a r e l a t i o n between the b u s i n e s s r i s k and the f i n a n c i a l r i s k of f i r m s , and t h a t i n d u s t r y g r o u p i n g s c o r r e s p o n d e d t o g r o u p i n g s by b u s i n e s s r i s k . U s i n g one way ANOVA t e s t s , h i s c o n c l u s i o n s gave the same r e s u l t s as t h o s e of Schwartz and Aronson. He argued t h a t s i g n i f i c a n t i n t e r - i n d u s t r y v a r i a t i o n i n e q u i t y r a t i o s was due t o management a d j u s t i n g f i n a n c i a l s t r u c t u r e i n response t o the the l e v e l of b u s i n e s s r i s k f a c e d by the f i r m , w h i c h d i f f e r e d among i n d u s t r i e s . No such d i f f e r e n c e s i n i n t r a - i n d u s t r y e q u i t y r a t i o s c o u l d be found, i n d i c a t i n g t h a t f i r m s i n the same i n d u s t r y f a c e s i m i l a r l e v e l s of b u s i n e s s r i s k . Remmers, S t o n e h i l l , W r i g h t and B e e k h u i s e r (RSWB) found t h a t 1 2 D a v i d F S c o t t , J r . , "Evidence on the Importance of F i n a n c i a l S t r u c t u r e " , F i n a n c i a l Management, Summer 1972. " 8 Scott's test was biased for two reasons. 1 3 F i r s t , they said that by increasing the number of industries in the sample, he added two groups which exhibited extreme equity r a t i o s because of unusual p r o f i t a b i l i t y and growth. Unfortunately, they stated nothing further in thi s regard: the claim remains unsubstantiated. In the second instance, RSWB raise the issue of sample size again. Scott used 77 firms, with two industries comprised of four firms each, and two industries of five companies. RSWB calculated debt ra t i o s in the same industries, using larger samples, and found that t h e i r ratios were considerably d i f f e r e n t from Scott's. However, they neither explain t h e i r comparison procedure, nor provide their r e s u l t s . In their own tests, RSWB attempted to expand on previous work by looking at c a p i t a l structure as a function of both size and business r i s k , in an international context. They assumed that within an industry, firms face similar environments, and hence va r i a t i o n of sales and earnings amongst firms are correlated. This gave them grounds for proxying business risk by industry c l a s s . They posited that size i s a determinant of fi n a n c i a l structure because the d i v e r s i f i c a t i o n of product l i n e s by large firms reduces firm r i s k , permitting the firm to increase f i n a n c i a l leverage. RSWB pointed out that there may be 1 3 Lee Remmers, Arthur S t o n e h i l l , Richard Wright and Theo Beekhuisen, "Industry and Size as Debt Ratio Determinants in Manufacturing Internationally", Financial Management, Summer 1974. 9 other reasons for the high c o r r e l a t i o n of intra-group equity r a t i o s , such as similar technology and asset structures, for example. RSWB's sample consisted of firms in the Fortune 500 (1971) l i s t . A firm was included in the sample i f i t was in an industry which comprised at least twenty companies. They took sample debt ratios for the years 1966, 1970, and 1971, and using an F-test, they detected no differences among sample group means. They did say that some industries not reported on in their paper did have s i g n i f i c a n t l y d i f f e r e n t debt r a t i o s , but these were not at t r i b u t a b l e to va r i a t i o n in business r i s k . The elimination of these unusual industries biased their results in favour af accepting the n u l l hypothesis. Their international tests led to the conclusion of significant, i n t e r - industry differences in debt rat i o s for industries in France and Japan, but none in the United States, Norway, or the Netherlands. They postulated that the results for France were due to special conditions prevalent there. In t h e i r tests for size as a determinant of f i n a n c i a l structure, RSWB s p l i t an international sample into three groups of equal numbers, according to t o t a l sales. With one exception, they accepted the n u l l hypothesis at the 95% confidence l e v e l . In round four of thi s debate, Scott and Martin suggested that RSWB's choice of Fortune 500 firms was too l i m i t i n g : i t led 1 4 David F. Scott, J r . , and John D. Martin, "Industry Influence on F i n a n c i a l Structure", Financial Management, Spring 1975. 10 to homogeneity in the sample. 1 0 Scott and Martin also asserted that RSWB's use of the debt to t o t a l assets r a t i o was inappropriate for measuring leverage because of the degree of s u b s i t u t a b i l i t y of prior claims for one another. This had also been pointed out by Schwartz and Aronson. This s u b s t i t u t a b i l i t y i s e s p e c i a l l y notable in the case of preferred stock and debt. Another of the c r i t i c i s m s l e v e l l e d against RSWB i s that their r e s u l t s may have been erroneous due to the assumptions necessary for their tests. S p e c i f i c a l l y , the conditions of equality of variance across industries, and normality, may have been vi o l a t e d . In t h e i r experiment, Scott and Martin used non parametric tests which did not require the assumptions of equal variance and normality. They asserted that an i n f l u e n t i a l point which represents a "firm that i s unusually highly levered or a firm not levered at a l l may materially d i s t o r t the computation of the mean debt r a t i o [or equity r a t i o ] for a pa r t i c u l a r i n d u s t r y " . 1 5 So, they used a non-parametric ANOVA test for differences in equity r a t i o s amongst industries, where equity r a t i o was defined as common equity divided by t o t a l assets. The sample was composed of non-regulated industries. Scott and Martin found s i g n i f i c a n t differences among industries' mean equity r a t i o s for each of the years in the period 1967 to 1972. They also tested for differences based on the ranking of equity r a t i o s , the results of which supported th e i r previous findings. 1 5 Ibid., p68. 11 T h e y u s e d b o t h n o n - p a r a m e t r i c a n d F t e s t s i n t h e i r e x a m i n a t i o n o f t h e r e l a t i o n b e t w e e n s i z e a n d e q u i t y r a t i o s . L i k e R S W B , t h e y g r o u p e d f i r m s i n t o t h r e e e q u a l c l a s s e s , a c c o r d i n g t o s i z e . T h e y f o u n d s i g n i f i c a n t d i f f e r e n c e s a m o n g t h e g r o u p s i n a l l t e s t s . T h e i r t e s t o f s i z e f o c u s s e d o n t o t a l a s s e t s , w h e r e a s R S W B s i z e m e a s u r e w a s t o t a l s a l e s . F e r r i a n d J o n e s t e s t e d t h e e f f e c t s o f i n d u s t r y c l a s s , b u s i n e s s r i s k , a n d o p e r a t i n g l e v e r a g e u p o n f i n a n c i a l l e v e r a g e . 1 6 T h e y r e a s o n e d t h a t o p e r a t i n g l e v e r a g e i s i m p o r t a n t b e c a u s e i t r e f l e c t s e a r n i n g s v a r i a b i l i t y , w h i c h t h e y f e l t s h o u l d b e n e g a t i v e l y r e l a t e d t o f i n a n c i a l l e v e r a g e . T h e y u s e d t h e d e b t t o e q u i t y r a t i o b e c a u s e o f " c o n c e p t u a l s i m p l i c i t y a n d t h e v a r i a b l e ' s a b i l i t y t o m o r e c o m p l e t e l y r e f l e c t a f i r m ' s t o t a l r e l i a n c e o n b o r r o w e d f u n d s " . 1 7 F e r r i a n d J o n e s g r o u p e d f i r m s i n t o i n d u s t r i e s b y u s i n g b o t h S I C c o d e s a n d p r o d u c t l i n e s , a n d j u s t b y S I C c o d e s . T h e y t e s t e d f o r a n i n d u s t r y e f f e c t u s i n g b o t h m e t h o d s o f g r o u p i n g . T h e y m e a s u r e d s i z e b y t o t a l s a l e s , t o t a l a s s e t s , a v e r a g e t o t a l a s s e t s a n d a v e r a g e t o t a l s a l e s . A v e r a g e s w e r e c o m p u t e d u s i n g d a t a f r o m t h e m o s t r e c e n t f i v e y e a r p e r i o d . T h e c o e f f i c i e n t s o f v a r i a t i o n i n s a l e s , a n d i n p r e - t a x i n c o m e , a s w e l l a s t h e s t a n d a r d d e v i a t i o n s o f s t a n d a r d i z e d s a l e s g r o w t h a n d s t a n d a r d i z e d c a s h 1 6 M i c h a e l G . F e r r i a n d W e s l e y H . J o n e s , " D e t e r m i n a n t s o f F i n a n c i a l S t r u c t u r e : A N e w M e t h o d o l o g i c a l A p p r o a c h " , J o u r n a l o f  F i n a n c e , J u n e 1 9 7 9 . 1 7 I b i d . , p 6 3 3 . 1 2 flow growth were used to proxy business r i s k . To compute these measures of business r i s k , annual data for the most recent f i v e years was used. Degree of operating leverage (DOL) was defined as the r a t i o of the percentage variance in EBIT to the percentage variance in sales. DOL was also proxied by the r a t i o of fixed assets to t o t a l assets and average fixed assets to t o t a l assets for a five year period. In t h e i r examination of c a p i t a l structure, F e r r i and Jones grouped firms according to debt structure, using a c l u s t e r i n g algorithm. They used an asymmetric uncertainty c o e f f i c i e n t to test for industry e f f e c t s , then used multivariate discriminant analysis to see i f they could d i s t i n g u i s h between the c l u s t e r s , in examinations of the other hypotheses. Unfortunately, the nature of the cl u s t e r i n g introduced bias into the second t e s t . The discriminant test i s biased by the somewhat a r b i t r a r y choice of boundaries for the groups of firms. For t h i s reason, the F e r r i and Jones technique i s not employed in th i s paper. F e r r i and Jones found some support for the existence of relationships between f i n a n c i a l structure and siz e , industry c l a s s , and operating leverage, but none between debt r a t i o and income v a r i a t i o n . They found SIC codes to give stronger results in industry groupings than did SIC codes combined with product l i n e s . Using 1976 data, they found that either h i s t o r i c a l or current data could be used in discriminating e f f e c t i v e l y amongst groups of debt r a t i o s . However, using 1974 r a t i o s , both h i s t o r i c and current data were necessary for e f f e c t i v e discrimination amongst groups. They contended that t h i s was due 13 to the differences in economic conditions during the two periods. In the expansion of 1976, debt was readily available to marginal firms, whereas in the 1974 recession, these same marginal firms were unable to finance through debt. Operating leverage discriminated amongst debt classes in both 1974 and 1976 when average fixed assets to average t o t a l assets was used as the discriminator, but the e l a s t i c i t y of EBIT with respect to sales was only an e f f e c t i v e discriminator for the 1976 data. The e f f e c t of the degree of operating leverage on r i s k , and hence on firm market value, was examined in an e a r l i e r study by L e v . 1 8 He defined operating leverage as the r a t i o of fixed to variable costs. Lev's model postulated that higher earnings v o l a t i l i t y would occur for firms with lower variable costs per product. Within a r i s k c l a s s , such as a homogeneous industry, the higher the fixed costs, the higher the v a r i a b i l i t y of returns to stockholders, hence the higher the t o t a l and systematic r i s k of common stocks. He noted that t h i s was analagous to the argument that increased f i n a n c i a l leverage leads to larger standard deviation of stock returns. To test t h i s hypothesis, Lev regressed t o t a l operating costs on sales, for the e l e c t r i c u t i l i t y , s t e e l , and o i l producer industries, for the years 1949 to 1968. He used the slope of these regressions as estimates of average variable costs per 1 8 Baruch Lev, "On the Association Between Operating Leverage and Risk", Journal of F i n a n c i a l and Quantitative Analysis, September 1974. ~~~ 1 4 u n i t o f o u t p u t . H e a s s u m e d n o c h a n g e s i n t h e p r o d u c t i o n f u n c t i o n s o v e r t h e s a m p l e p e r i o d , a n d f o u n d t h e a s s u m p t i o n t o b e b o r n e o u t , i n g e n e r a l , b y c r o s s v a l i d a t i o n t e s t s . H e t h e n u s e d t h e s t a n d a r d d e v i a t i o n o f s t o c k r e t u r n s a n d t h e s t o c k ' s b e t a a s i n d e p e n d e n t v a r i a b l e s i n a r e g r e s s i o n i n w h i c h h i s a v e r a g e v a r i a b l e c o s t e s t i m a t e w a s t h e d e p e n d e n t v a r i a b l e . H i s l o w R -s q u a r e d s t a t i s t i c s , w h i c h r a n g e d f r o m . 0 5 t o . 3 8 , s u g g e s t e d t h a t t h e d e g r e e o f o p e r a t i n g l e v e r a g e w a s n o t t h e o n l y v a r i a b l e w h i c h a f f e c t e d r i s k . H o w e v e r , s i n c e a l l b u t o n e o f h i s c o e f f i c i e n t s w e r e s i g n i f i c a n t a t t h e . 0 5 l e v e l , t h e r e l a t i o n s h i p b e t w e e n r i s k a n d o p e r a t i n g l e v e r a g e w a s c o n f i r m e d . T h e c o e f f i c i e n t s w e r e n e g a t i v e i n a l l c a s e s . L e v a r g u e d t h a t t h e o n l y c a s e o f l a c k o f s i g n i f i c a n c e w a s d u e t o t h e h e t e r o g e n e i t y o f t h e f i r m s i n t h e i n d u s t r y i n q u e s t i o n , t h e o i l i n d u s t r y . I n a r e c e n t s t u d y , M a r s h f o c u s s e d o n t h e i s s u a n c e o f d e b t a n d e q u i t y b y B r i t i s h f i r m s b e t w e e n 1 9 5 9 a n d 1 9 7 0 . 1 9 T a r g e t d e b t r a t i o s w e r e p r o x i e d b y t h e a v e r a g e d e b t r a t i o o v e r t h e s a m p l e p e r i o d . M a r s h e x p l a i n e d a n d p r o v i d e d r e f e r e n c e s f o r t h e a r g u m e n t s t h a t t r e a s u r e r s t e n d t o t h i n k i n t e r m s o f b o o k r a t h e r t h a n m a r k e t v a l u e s , t h a t c o v e n a n t s t e n d t o b e w r i t t e n i n t e r m s o f b o o k v a l u e s , a n d t h a t b o o k v a l u e s o f d e b t a n d e q u i t y a r e m o r e c l o s e l y t i e d t o a s s e t s a l r e a d y o w n e d b y t h e f i r m , a n d d o n o t c a p i t a l i z e t h e f u t u r e c a s h f l o w s o f a s s e t s t h e f i r m i s e x p e c t e d 1 9 P a u l M a r s h , " T h e C h o i c e B e t w e e n E q u i t y a n d D e b t : A n E m p i r i c a l S t u d y " , J o u r n a l o f F i n a n c e , M a y 1 9 7 7 . 2 0 I b i d . , p 1 3 1 . 1 5 to a c q u i r e . 2 0 Using these reasons, he argued persuasively for the use of book values. Marsh f e l t that size would be a factor influencing target debt r a t i o s because of economies of scale in f l o t a t i o n costs of security issues. Measures of s i z e , operating leverage, and asset composition were included to attempt to proxy the e f f e c t of v a r i a t i o n in target r a t i o s over time which had not been picked up by the h i s t o r i c average debt r a t i o s . Marsh found that the choice between issuance of debt or equity depended upon the state of the market and h i s t o r i c a l stock prices in such a way that firms appear to have target ra t i o s of short and long term debt and equity to t o t a l assets. Furthermore, these target le v e l s were found to be functions of company size , expected bankruptcy costs and asset structure. In imperfect c a p i t a l markets, with p o s i t i v e bankruptcy and d i s t r e s s costs, there appears to be j u s t i f i c a t i o n for the arguments that si z e , asset structure, industry c l a s s , business r i s k , bankruptcy costs, d i s t r e s s costs, and operating leverage a f f e c t c a p i t a l structure. 16 I I . A SIMPLE MODEL OF CAPITAL STRUCTURE The objective of this section i s to derive a theoretical model of optimal c a p i t a l structure. The model posits c a p i t a l structure as a function of the l i q u i d i t y of a firm's assets, i t business r i s k , s i z e , bankruptcy costs, and the leve l s of subordinated and p r i o r i z e d debt claims. The model assumes ri s k neutral valuation with a probability density P(s), where s i s defined to l i e in the closed i n t e r v a l from s to s. In an Arrow-Debreu context, s V= Jjx(s)Q(s)ds, where Q(s) i s the vector of Arrow-Debreu prices, and X(s) i s the vector of state contingent cash flows. This implies that s j fo,(s)ds=l/( 1+Rf ) , or \( l / ( 1+Rf )Q(s)ds=1 . I 5 This i s equivalent to stating that the price of a r i s k l e s s security which provides a payoff of 1 in every state would be 1 / (1+Ri), where Rf i s the rate of return on a r i s k l e s s asset. In the context of ri s k neutral valuation, (l+Rf)Q(s) i s treated as a p r o b a b i l i t y d i s t r i b u t i o n , so that s (1+Rf)Q(s)=P(s) and ^>(s)ds=1. This provides 1 7 r X ( s ) P ( s ) d s s w h i c h i s e q u i v a l e n t t o t h e A r r o w - D e b r e u p r i c i n g m o d e l s e t o u t a b o v e . 2 1 S u p p o s e t h a t t h e p r o c e e d s o f a f i n a n c i n g a r e p l a c e d i n t o a r i s k l e s s a s s e t , L , s u c h a s c a s h , w h i c h e a r n s n o r e t u r n , a n d a r i s k y p r o j e c t w h i c h p r o v i d e s s t a t e c o n t i n g e n t c a s h f l o w s . L e t c a s h f l o w s f r o m t h e r i s k y p r o j e c t , d e n o t e d C , b e d e f i n e d a s ( 1 ) C = X + g ( s - e ) , w h e r e s ( 2 ) e = j s P ( s ) d s . s I n t h i s c a s e , E ( C ) = X , w h e r e X i s a s c a l e p a r a m e t e r r e f l e c t i n g t h e s i z e o f t h e f i r m ( h a v i n g n o r e l a t i o n t o X ( s ) d e f i n e d a b o v e ) , a n d % = g % , w h e r e g i s a p a r a m e t e r r e f l e c t i n g b u s i n e s s r i s k . A m o r e p r e c i s e d e f i n i t i o n o f b u s i n e s s r i s k w i l l b e g i v e n l a t e r . L e t b a n k r u p t c y c o s t s , d e n o t e d B , h a v e t h e f o r m B = a g + b X w i t h ^ B / ^ X = b > 0 . T h i s i s c o n s i s t e n t w i t h e v i d e n c e t o d a t e , a s d i s c u s s e d i n C h a p t e r 1 , w h i c h s u g g e s t s t h a t r e l a t i v e , p e r c e n t a g e b a n k r u p t c y c o s t s d e c r e a s e w i t h i n c r e a s e s i n f i r m s i z e . F u r t h e r m o r e , l e t 2 1 F o r a d i s c u s s i o n o f c o n t i n g e n t c l a i m s p r i c i n g , s e e T h o m a s E . C o p e l a n d a n d J . F r e d W e s t o n , F i n a n c i a l T h e o r y a n d C o r p o r a t e P o l i c y , A d d i s o n W e s l e y , D o n M i l l s , O n t a r i o , 1 9 7 9 . 18 t=marginal corporate- tax rate, F=the face value of debt outstanding,Vl=the value of the levered firm, Vu=the value of the unlevered firm, Ve=the value of equity, and Vd=the value of debt outstanding. In t h i s context, the state contingent after (corporate) tax flows to various > security holders are given below: STATE CONTINGENT CASH FLOWS SECURITY STATE L+X+g(s-e)<F L+X+g(s-e)>F BONDS EQUITY TOTAL L+(1-t)(X+g(s-e))-B 0 L+(1-t)(X+g(s-e))-B L+(1-t)(X+g(s-e))-(1-t)F L+(1-t)(X+g(s-e))+tF Define z as being that state for which L+X+g(z-e)=F, so that (4) z=(F-L-X)/g+e The values of debt, equity, and the levered firm are: Vd= V 3= S =([L+(1-t)(X+g(s-e))-B]P(s)ds + ^FP(s)ds, or =L5p(s)ds + (l-t)^(X+g(s-e))P(s)ds - B^P(s)ds +F^P(s)ds,and (5) Vd 5 * I J Ve= [L+(1-t)(X+g(s-e))-(1-t)F]jp(s)ds, or s . * i ( 6 ) V e = ( L - ( 1 - t ) F ) J p < s ) d s + ( 1 - t ) ( ( X + g ( s - e > ) P ( s ) d s , a n d 19 (7) Vl=L^P(s)ds + (1-t)^(X+g(s-e))P(s)ds + tF^P(s)ds - BJPUMS, which i s Ve + Vd. Since Vu=L^P(s)ds + (1-t)j(X+g(s-e))P(s)ds, (7) can be written as 1 s * 1 (8) Vl=Vu-B\P(s)ds+tF)P(s)ds which i s the value of the unlevered firm, less expected bankruptcy costs, plus the tax sh i e l d of debt. Noting that ^z/^)F=l/g, ^z/^L=-l/g, ^z/&g=-(F-L-X)/g, ^z/^X=-l/g, and ^Vu/^F=0, i t can be shown that s" ^V1/&F = -B(^z/^F)P(z) + t^P(s)ds - tFOz/^F)P(z) s = t^P(s)ds - [(B+tF)/g]P(z) This gives the f i r s t order condition for a maximum, s (9) t^P(s)ds - [(B+tF)/g]P(z) = 0. The second derivative i s >Vl/c)F 2 = -tOz/c)F)P(z) " [(B+tF)/g 2]P' (z) - (t/g)P(z) = -(2t/g)P(z) - [(B+tF)/g 2]P'(z). 20 = -(2t/g)P(z) - [(B+tF)/gZ]P'(z). This provides the second order condition for a maximum, (10) -(2t/g)P(z) - 0/g 2)(P'(z))[B+tF] <0. As an example, assume that s i s defined to l i e between s and £5, so that P(S)=1/W, where w=s-s. This i s the uniform case, which s a t i s f i e s the condition that P'(z)^0. The f i r s t , order condition (9) becomes t(s-z)l/w - [(B+tF)/g]/w = 0 or (11) "s-z -tF/g =B/tg. Substituting from (4) into (11) gives s - [(F-L-X)/g)+e] - F/g = B/tg, which reduces to (12) F* = -B/2t + (g/2)(s-e) + (L+X)/2. But s-e ="s-1/2(s"+s_) =1/2(S-S) =1/2W, so that (12) can be rewritte (13) F* = -B/2t + gw/4 + (L+X)/2 and substituting from (3), the value of the levered firm is maximized when (14) F* = -(ag+bX)/2t + gw/4 +(L+X)/2, which i s equivalent to (15) F* = [(tL+(l/2)tgw-ag)+(t-b)X]/2t, which reduces to (16) F* = {tL+g[(1/2)tw-a]+(t-b)X}/2t. We assume t>>b, and (l/2)tw<a. Equation (14) provides the comparative s t a t i c s results given below. (17) ^F*/£)L=l/2>0. Each d o l l a r of l i q u i d i t y , L, added, allows a f r a c t i o n a l increase in F. which i s consistent with the theory set forth i s Chapter 1. )>0, 21 (19) V*/^ X = -b/2t+1/2 = (1/2) (t-b)>0, since b<<t by assumption, again consistent with theory and evidence described in Chapter 1 . F e r r i and Jones showed that the e l a s t i c i t y of F* with respect to firm size i s greater than unity. That i s (dF*/>X)(X/F*)>1 or (20) \ F * / ^ X > F * / X . Substituting (19) into (20) gives (1/2t)(t-b)>F*/X. Using (15) gives d / 2 t ) ( t - b ) X > (1/2t)[tL+g((1/2)tw-a)] + (1/2t)(t-b)X, or (l/2t)[tL+g((l/2)tw-a)] < 0, or g((1/2)tw-a) < -tL, hence (1/2)tw-a < -tL < 0, so that (21) )F*/9g = -a/2t + w/4 = (1/2t) ( (1/2 ) wt-a )<0 as i s shown above. Firms facing more business r i s k issue less debt, again supported by the material presented in Chapter 1. The rest of t h i s chapter of the thesis deals with expanding the model, as set forth above, to include two le v e l s of debt: subordinated and unsubordinated debt. Denote Ff as the face value of senior debt, and Fj as the face value of junior (unsubordinated) debt. Further, l e t bankruptcy costs be defined for senior debt as Bf=afg+bfX, and for junior debt as Bj=ajg+bjX The state contingent after (corporate) tax cash flows to the various security holders are as given below: 22 STATE CONTINGENT CASH FLOWS STATE SECURITY L+X+g(s-e)<Ff Ff^L+X+g(s-e)<Ff+Fj Fj+Ff^L+X+g(s-e) SENIOR L+(1-t)(X+g(s-e))-Bf Ff Ff BONDS JUNIOR 0 L+(1-t)(X+g(s-e)-(1-t)Ff-Bj Fj BONDS EQUITY 0 L+(l-t)(X+g(s-e)-(l"t)(Ff+Fj) TOTAL L+(l-t)(X+g(s-e))-Bf L+(1-t)(X+g(s-e))+t(Ff+Fj) L+(1-t)(X+g(s-e))+tFf-BJ Denoting Vf as the value of senior debt, Vj as the value of junior debt, x=(Ff-L-X)/g+e, and y=(Ff+Fj-L-X)/g+e, then i t can be shown that X ~ Vf=^[L+(1-t)(X+g(s-e))-Bs]P(s)ds + Ff|p(s)ds, or £ x -x X * (22) Vf=-Bf}P(s)ds + (L+(1-t))^P(s)ds + FfJP(s)ds, and S 5 X (23) Vj=Bj^P(s)ds + (L+(1-t))^P(s)ds + Fj^P(s)ds - (1-t)Ff\P(s)ds 23 and s * (24) Ve=(L+(1-t)) j u + g ( s - e ) ) P ( s ) d s - (1 - t ) (Ff +F j )5P( S )ds. In t h i s case, s Vu = ^ (L+( 1-t)) (X+g(s-e) ) P ( s ) d s , so t h a t Vl=Vu + F f j p ( s ) d s - B f j P ( s ) d s + F j ) P ( s ) d s - B j J P ( s ) d s * I 1 _ y - ( 1 - t ) F f J p ( s ) d s - ( 1 - t ) ( F f + F j ) ^ P ( s ) d s , or X ^ (25) Vl=Vu - B f ( p ( s ) d s - B j ( p ( s ) d s + t F f j p ( s ) d s + t F j ^ P ( s ) d s , i * * T Equation (25) s t a t e s t h a t the value of the l e v e r e d f i r m i s equal to the value of the unlevered f i r m , l e s s expected bankruptcy c o s t s , p l u s the tax s h i e l d s a s s o c i a t e d with j u n i o r and s e n i o r debt. Note that "c)x/^Ff=i/g, , f3x/^Fj = 0,V/^Ff=l/g, ^y/9Fj = l / g , ^Vu/^Ff=Vu/r)Fj = 0. -^ V l / ^ F f = - ( B f / g ) P ( x ) + (Bj/g)P(y) + t ^ P ( s ) d s - ( t F s / g ) P ( x ) - ( t F j / g ) P ( y ) - ( B j / g ) P ( y ) , and \vi/b Fj=-(Bj/g)P(y) + t ^ P ( s ) d s - t F j P ( y ) / g . Y These give the f i r s t order c o n d i t i o n s 24 (26) tjp(s)ds - (P(x)/g)(Bf-Bj+tFf) - (P(y)/g) (Bj+tFj) =0, and s (27) t^P(s)ds - (P(y)/g)(Bj+tFj)=0. The second order derivatives are: ^V l / ^ F f 2 = ( l / g 2 ) P ' ( x ) ( - B f + B j - t F f ) - ( l / g 2 ) P ' ( y ) ( B j + t F j ) -(2t/g)P(x) ^ V l / d F f Fj=-(1/g 2)P'(y)(Bj+tFj) - (t/g)P(y) ^ V l / ^ F j 2 = - d/g 2)P'(y)(Bj+tFj) - (2t/g)P(y) The second order condition requires that the determinant of > 2V1/^ Ff 2 ^ Vl/^)Fft>FJ j 1 >0. ^VIAFOFJ V v i / ^ F j j / Substitute A=(1/g 2)P'(x)(-Bf+Bj-tFf), B=(-2t/g)P(x), C=(-l/g 2)P'(y)(Bj+tFj), and D=(-t/g)P(y). By substitution, the second order condition may be rewritten (A+B+C)(C+2D)-(C+D)(C+D)>0 (A+B)(C+2D)>DD Again, i f the uniform case i s used, P'(x)=P'(y)=0, so that A=C=0, and 2BD>DD or 2B<D since D<0. Expanding the last inequality, -(4t/g)P(x)<-(t/g)P(y) or 4P(x)>P(y), which holds in the uniform case. Continuing the uniform case further, equation (26) can be rewritten as (28) t(s-x)l/w - (l/gw(Bf-Bj+tFf) - (1/gw)(Bj+tFj) =0. 2 5 R e c a l l i n g t h a t x = ( F f - L - X ) / g + e a n d s - e = ( 1 / 2 ) w , ( 2 8 ) i s e q u i v a l e n t t o t F f = - B f - t F j + g [ ( l / 2 ) t w - t ( F f - L - X ) / g ] w h i c h r e d u c e s t o ( 2 9 ) F j * = g w / 2 - 2 F f + L + X - B f / t S i m i l a r l y , e q u a t i o n ( 2 7 ) c a n b e w r i t t e n a s t ( s - y ) 1 / w - ( 1 / g w ) ( B j + t F j ) = 0 , w h i c h r e d u c e s t o ( 3 0 ) F j * = ( l / 2 ) ( L + X + ( l / 2 ) g w ) - ( l / 2 t ) B J . S o l v i n g s i m u l t a n e o u s l y , i t c a n b e s h o w n t h a t ( 3 1 ) F j * = ( 1 / 3 ) ( L + X + ( l / 2 ) g w ) + ( l / 3 t ) ( B f - 2 B j ) . F o r e a s e o f e x p o s i t i o n , d e f i n e M = 1 / 3 ( L + X + ( 1 / 2 ) g w ) . S u p p o s e t h a t B f = B j = B , t h e n F f * = F j * = M - B / 3 t , w i t h V f * / ^ ( . ) =^F j * / } ( . ) • A s s u m i n g e q u a l b a n k r u p t c y c o s t s f o r j u n i o r a n d s e n i o r d e b t g i v e s t h e f o l l o w i n g c o m p a r a t i v e s t a t i c s r e s u l t s f o r ( 3 1 ) a n d ( 3 2 ) : ( 3 3 ) ~^Ft*/}X = 1 / 3 - ( l / 3 t ) X = ( l / 3 ) [ l - ( t / X ) ] > 0 w h i c h i m p l i e s t h a t l a r g e r f i r m s h a v e m o r e o f b o t h f o r m s o f d e b t . ( 3 4 ) ^ F f*/3L = 1 / 3 > 0 , w h i c h i m p l i e s t h a t m o r e l i q u i d f i r m s h a v e m o r e o f b o t h t y p e s o f d e b t . ( 3 5 ) > F f * / $ g = ( i / 3 ) w - a / 3 t = ( 1 / 3 t ) [ ( w t / 2 ) - a ] < 0 s i n c e ( w t / 2 ) - a < 0 , a s s h o w n a b o v e . F i r m s w i t h m o r e c a s h f l o w v o l a t i l i t y h a v e l e s s o f b o t h k i n d s o f d e b t . ( 3 6 ) > F f * / ^ t = B / 3 t > 0 w h i c h s h o w s t h a t m o r e h e a v i l y t a x e d f i r m s h a v e m o r e o f b o t h t y p e s o f d e b t . T h e s e a r e a l l c o n s i s t e n t w i t h t h e p r e d i c t i o n s o f t h e m o d e l i n i t s s i m p l e r f o r m . N o w a s s u m e t h a t B j = 2 B f . T h i s a s s u m p t i o n i s n o t 26 unreasonable, at least in Canadian courts. Trustees get paid a maximum percentage rate of the cash or cash equivalents paid to unsecured c r e d i t o r s . E s s e n t i a l l y , the secured creditors have an opportunity to get their security back before the trustee can take a share of the pie. This maximum can be overruled by the courts. Under t h i s assumption, (31) and (32) can be rewritten as (37) F j * =(1/3)(L+X+(l/2)gw) - Bf/t, and (38) Ff* =(1/3)(L+X+(l/2)gw). These give the following comparative s t a t i c s r e s u l t s : (40) ^)Ff*/^X= 1/3 >0 and (41) V j V ^ X =1/3 - bf/t =(1/3)[l-(3bf/t)]^0. Larger firms are expected to have more senior debt, but w i l l only issue more junior debt i f s i s less than 1/3 of the tax rate, or very small. This i s consistent with evidence presented in Chapter 1. (42) 3.Ff*/)L = F j * / L =1/3 >0, as before. (43) >f*/<)g =w/6 >0 and (44) Vj/^9 = w/6 - a f / t =(l/3t)[(wt/2)-3as] <0 since wt/2<as as shown above. Riskier firms issue more senior debt and less junior debt. Riskier firms issue more senior debt and less junior debt. (45) Vf*/&t=0 and (46) >j*/c)t=Bf/t >0, so that as the tax rate increases, there i s an increasing incentive for firms to issue more junior debt. 27 To examine the effects of X,g,t and L on c a p i t a l structure as a whole, the p a r t i a l derivatives for Ff* and F j * must be added together. Under the assumption of constant bankruptcy costs, the results are simply twice those given for Ff*. That i s , larger firms, more l i q u i d firms, and firms facing higher tax brackets a l l issue more debt, c e t e r i s paribus. Increased operating leverage decreases the r e l a t i v e reliance on debt financing. Furthermore, by adding (29) and (30), i t can be shown that the p a r t i a l s of Ff* with respect to F j * are i d e n t i c a l to the p a r t i a l s of F j * with respect to Ff*. If we now examine the p a r t i a l s for Bj=2Bf, (47) ^(Ff*+Fj*)/)x =2/3-bs/t =(2/3)[l-(3bs/2t)^0. Size e f f e c t i s once again linked to the tax rate, and w i l l be pos i t i v e i f bankruptcy costs are small. (48) \(Ft*+Fj*)/£) L =2/3 >0, which i s consistent with previous r e s u l t s . (49) ^Ff*+Fj*)/£) g =( l/3t) (wt-3as) <0 since tw<3as, as shown abov Once again, as business r i s k increases, f i n a n c i a l leverage declines. (50) ^(Ff*+Fj*)/>t = Bf/t >0. This i s consistent with results to date. If the tax rate for junior debt i s p o s i t i v e , then the marginal value of issuing more debt declines as the tax rate increases. Business r i s k w i l l now be defined more c a r e f u l l y , as comprising: (51) Industry r i s k : the r i s k inherent in the environment in which 28 the firm i s operating, and v a r i a b i l i t y of earnings before interes and taxes (EBIT). The variance of EBIT has two components: (52) Sales v a r i a b i l i t y and (53) E l a s t i c i t y of EBIT with respect to sales. To show that VAR(EBIT) has two components, assume EBIT=Revenue-Fixed Costs-Variable Costs. Suppose the firm s e l l s Q units of product at price P. Variable per unit cost of production i s denoted V, while F represents fixed production costs. VAR(EBIT)=VAR(PQ-VQ-F) =VAR[(P-V)Q] =(P-V)(P-V)VAR(Q) DOL= (P^Q-V>Q) /P}CJ= (P-V) /P These f i n a l results are consistent with evidence to date. The next chapter sets out the hypotheses generated by the model, and the results of the tests of those hypotheses. 29 I I I . METHODOLOGY AND RESULTS The model in chapter two implies that a number of factors influence the c a p i t a l structure of the firm. The n u l l hypotheses to be tested are l i s t e d below: H1: L i q u i d i t y has no eff e c t on the firm's financing decision, from (48). H2: Operating leverage i s not related to f i n a n c i a l leverage, from (49) and (53). H3: Firms issuing junior debt do not have larger debt-to-equity r a t i o s , from (40), (41), (43), and (44). The model implied that some firms may have increased incentives to issue either junior or senior debt. Doing so would enable them to have higher debt-to-equity r a t i o s than otherwise. H4: The degree of f i n a n c i a l leverage i s not affected by firm s i z e , from (47). H5: Sales variance i s unrelated to f i n a n c i a l structure, from (49) and (52). H6: Preferred stock has the same influence on c a p i t a l structure as that of common stock, to be discussed below. H7: Convertible debt has the same e f f e c t on c a p i t a l structure as does common stock, to be discussed below. H8: Firms' c a p i t a l structures are not affected by time, to be discussed below. H9: Capital structure i s not influenced by the industry in which a firm operates, from (49) and (51). Cross sectional regression was used to attempt to f i t the model DEBTEQ=A+BiXi, where A i s the intercept term, Xi i s the 3 0 i t h i n d e p e n d e n t v a r i a b l e , a n d B i i s t h e r e g r e s s i o n c o e f f i c i e n t c o r r e s p o n d i n g t o t h e i t h i n d e p e n d e n t v a r i a b l e . T h e d e c i s i o n v a r i a b l e s a r e : 1 . C M T A = ( C a s h + M a r k e t a b l e S e c u r i t i e s ) / T o t a l A s s e t s . 2 . A R T A = A c c o u n t s R e c e i v a b l e / T o t a l A s e t s . 3 . I N V T A = I n v e n t o r y / T o t a l A s e t s . 4 . N T P T A = N e t P l a n t / T o t a l A s e t s . T h i s i n c l u d e s a l l p h y s i c a l a s s e t s u s e d f o r p r o d u c t i o n . 5 . S U B S E C = S u b o r d i n a t e d D e b t / O t h e r L o n g T e r m D e b t . 6 . S I Z E = T o t a l A s s e t s . 7 . D O L = E l a s t i c i t y o f E B I T w i t h r e s p e c t t o s a l e s . 8 . V A R = S t a n d a r d i z e d v a r i a n c e o f s a l e s . 9 . P F D D U M = D u m m y v a r i a b l e , f o r p r e f e r r e d s h a r e s o u t s t a n d i n g . 1 0 . C O N V D U M = D u m m y v a r i a b l e , f o r c o n v e r t i b l e d e b t . 1 1 . Y R D U M = D u m m y v a r i a b l e f o r s a m p l e y e a r . 1 2 - 2 5 . D 1 - D 1 4 = D u m m y v a r i a b l e s f o r i n d u s t r y c l a s s e s . T h e h y p o t h e s e s a s l i s t e d a b o v e c a n b e r e s t a t e d i n t e r m s o f t h e r e g r e s s i o n c o e f f i c i e n t s , a n d t h e s e a r e g i v e n b e l o w . H 1 : B 1 = 0 . H 2 : B 2 = B 3 = B 4 = B 7 = 0 . H 3 : B 5 = 0 . H 4 : B 6 = 0 . H 5 : B 8 = 0 . H 6 : B 9 = 0 . H 7 : B 1 0 = 0 . H 8 : B 1 1 = 0 . H 9 : B 1 2 = B 1 3 = B 1 4 = B 1 5 = B 1 6 = B 1 7 = B 1 8 = B 1 9 = B 2 0 = B 2 1 = B 2 2 = B 2 3 = B 2 4 = B 2 5 = 0 . 31 R a n k i n g o f t h e i n d u s t r y S I C n u m b e r s w a s f e l t t o h a v e b e e n m e a n i n g l e s s , s o t h e u s e o f S I C c o d e s a s a n i n d e p e n d e n t v a r i a b l e i n a r e g r e s s i o n s e t t i n g w o u l d h a v e b e e n i n a p p r o p r i a t e . D u m m y v a r i a b l e s w e r e c r e a t e d f o r f o u r t e e n o f t h e f i f t e e n i n d u s t r i e s . U s i n g f i f t e e n d u m m y v a r i a b l e s w o u l d h a v e l e d t o a n i l l -c o n d i t i o n e d X - m a t r i x w h i c h c o u l d h a v e b e e n p a r t i t i o n e d i n t o a n i d e n t i t y m a t r i x , h e n c e t h e i r i n c l u s i o n w o u l d h a v e p r o v i d e d n o m o r e i n f o r m a t i o n t h a n i f t h e y h a d n o t b e e n u s e d a t a l l . H o m o g e n e i t y a m o n g s t f i r m s i n a g i v e n i n d u s t r y i s n e c e s s a r y i f t h e i n d u s t r y c l a s s m e t h o d o l o g y i s t o w o r k w e l l . H o w e v e r , s a m p l i n g i n d u s t r i e s o n t h e t h e b a s i s o f h o m o g e n e i t y , u s i n g s o m e a p r i o r i s p e c i f i e d r a t i o n a l e , w o u l d h a v e i n t r o d u c e d b i a s i n t o t h e s a m p l e . F u r t h e r m o r e , i f t e s t s t a k e n o v e r a r a n d o m s a m p l e o f i n d u s t r i e s d o n o t s h o w a s t r o n g r e l a t i o n s h i p b e t w e e n c a p i t a l s t r u c t u r e a n d i n d u s t r y c l a s s , t h e n i n d u s t r y c l a s s w i l l n o t b e u s e f u l i n p r e d i c t i n g o r d e t e r m i n i n g o p t i m a l c a p i t a l s t r u c t u r e . I f i n d u s t r y g r o u p i n g s a r e t o p r o v i d e m a n a g e m e n t a n d i n v e s t o r s w i t h u s e f u l i n f o r m a t i o n , t h e n t h e g r o u p i n t o w h i c h a n y p a r t i c u l a r f i r m f a l l s m u s t b e r e a d i l y i d e n t i f i e d . S I C c o d e s p r o v i d e t h i s e a s e o f g r o u p i n g a n d i d e n t i f i c a t i o n . S o t h e i n d u s t r i e s u s e d w e r e t h o s e f o r w h i c h s u f f i c i e n t d a t a w a s a v a i l a b l e w i t h i n S I C g r o u p i n g s . D a t a f o r t h e s a m p l e w a s d r a w n f r o m t h e C o m p u s t a t A n n u a l a n d Q u a r t e r l y t a p e s o f 1 9 8 2 . B e a r i n g i n m i n d t h a t i n d u s t r y c l a s s w a s t o b e u s e d a s a n i n d e p e n d e n t v a r i a b l e , f i r m s w e r e c h o s e n i f t h e y w e r e i n a n i n d u s t r y w h i c h h a d m o r e t h a n e l e v e n e n t r i e s o n t h e q u a r t e r l y t a p e . T h e r e w e r e 1 5 o f t h e s e i n d u s t r i e s , 32 consisting of 212 companies, in the sample. A l i s t of firms and industries i s included in the appendix. Firms which became bankrupt before February 28, 1983, were excluded from the sample. Observations for which DEBTEQ<0 were dropped from the sample. These firms could have introduced considerable unreasonable noise into the data. For example, consider two firms with p o s i t i v e debt outstanding, but one of which has s l i g h t l y negative equity, while the other has s l i g h t l y p o s i t i v e equity. Their debt rat i o s would appear at opposite ends of the real l i n e , whereas in an absolute sense they had almost i d e n t i c a l c a p i t a l structures. It has been shown that f i n a n c i a l r a t i o s deteriorate as firms approach bankruptcy. 2 2 To attempt to control for impending bankruptcy by the introduction of another dummy variable would require the determination of some cutoff point. This cutoff point would be set at some time before bankruptcy when the firm's f i n a n c i a l ratios began to deteriorate, which would have been when the impending bankruptcy would have begun to have had an e f f e c t on the firm's balance sheet. The cutoff point would be a r b i t r a r y , and a source of bias. So a l l firms which have become bankrupt before February 28 1983 were deleted from the 2 2 Edward I. Altman, "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy", Journal of Finance, September, 1978 and William H. Beaver, "Market Prices, F i n a n c i a l Ratios, and the Prediction of F a i l u r e " , Journal of Accounting Research, Autumn 1968. 33 sample. In order to ensure a large enough sample, each firm was used twice, data was taken from both 1981 and 1976. This assumed that over a period of f i v e years, firms were able to change the i r c a p i t a l structures. A s t a t i s t i c a l test for independence of the 1981 and 1976 data was considered to be inappropriate. If a firm was at i t s optimal debt r a t i o in 1976, then i t may well be that i t was at the same optimal c a p i t a l structure in 1981. YRDUM, a dummy variable, which was set equal to 1 i f the observation was made in 1976, and 0 otherwise, was included as a check for the influence of sample date. A l l the variables used in these tests were book values, as reported on the Compustat tapes. Book values were used for the reasons given in Chapter 1: treasurers tend to think in terms of book values; book values of debt and equity are more cl o s e l y t i e d to the book value of assets since they do not c a p i t a l i z e expected cash flows from assets that w i l l be acquired in the future; covenants are written in terms of book values. Any noise introduced by the use of book values was assumed to be random. No expectation of d i r e c t i o n of bias could be formulated. For instance, management may choose measures of determining sales, or the reported book value of marketable s e c u r i t i e s , to minimize income taxes, or maximize accounting earnings, or to portray some desired l e v e l of assets or 2 3 Jack Clark Francis, Investments: Analysis and Management, Third E d i t i o n , McGraw H i l l Book Company, Toronto, 1980. 34 l i a b i l i t i e s . 2 3 So there may be incentives for management to manipulate book values. It was beyond the scope of t h i s thesis to construct market values for debt and equity. Furthermore, for many of the other assets, i t would have been extremely d i f f i c u l t to measure market values. Indeed, for p r a c t i c a l purposes, book values of many of the variables were the only reasonable proxies for market values. Adequate descriptions of these assets, such as plant, would not have been available from which to derive market values. Also, the uniqueness of c e r t a i n assets would have made them es p e c i a l l y d i f f i c u l t to price, either d i r e c t l y or by proxy. The f i r s t independent variable, CMTA, was a measure of l i q u i d i t y of the firm's asset structure. Financial leverage was expected to increase as a result of increases in l i q u i d i t y . The less l i q u i d assets, e s p e c i a l l y NTPTA, may have had a reverse e f f e c t on l i q u i d i t y , and hence be associated with a negative c o e f f i c i e n t . ARTA, INVTA and NTPTA were used as proxies for operating leverage, since they represent fixed costs. This also led to the expectation of negative c o e f f i c i e n t s for these variates. ARTA,INVTA,NTPTA, DOL, and VAR were examined to see i f they were independent. As i s shown below, they are non-collinear. SUBSEC was a measure of subordinated to other long term debt. The model posited that i t should have a positive c o e f f i c i e n t , under the assumption of small bankruptcy costs which were the same for both senior and subordinated debt. The simpler model predicted that SIZE would be p o s i t i v e l y 3 5 r e l a t e d t o f i n a n c i a l l e v e r a g e . T h e m o r e c o m p l i c a t e d m o d e l p r e d i c t e d t h e c o e f f i c i e n t o f S I Z E t o b e e i t h e r p o s i t i v e o r n e g a t i v e , d e p e n d i n g u p o n t h e r e l a t i v e m a g n i t u d e o f b a n k r u p t c y c o s t s . P r e v i o u s s t u d i e s f o u n d S I Z E t o b e p o s i t i v e l y r e l a t e d t o t h e f i n a n c i a l l e v e r a g e , s o l a r g e r f i r m s w e r e e x p e c t e d t o a s s u m e m o r e f i n a n c i a l l e v e r a g e . D O L w a s f i r s t m e a s u r e d a s t h e s i m p l e a v e r a g e o f t h e p e r c e n t a g e c h a n g e i n e a r n i n g s b e f o r e i n t e r e s t a n d t a x e s t o t h e p e r c e n t a g e c h a n g e i n s a l e s . I t w a s t a k e n o v e r a l l t h e q u a r t e r s i n t h e f i v e y e a r s p r i o r t o t h e d a t e a s s o c i a t e d w i t h t h e b a l a n c e s h e e t d a t a , e x c e p t i n g t h o s e c a s e s w h e r e t h e r e w e r e n o s a l e s . T h e r e s u l t a n t D O L m e a s u r e s h o w e d a c o e f f i c i e n t o f v a r i a t i o n o v e r 1 , 0 0 0 , 0 0 0 d u e t o t r e m e n d o u s v a r i a b i l i t y i n t h e d a t a , a n d n o t j u s t a f e w e x c e p t i o n a l o b s e r v a t i o n s . S o m e f i r m s h a d m i n i s c u l e c h a n g e i n s a l e s , b u t r e l a t i v e l y l a r g e c h a n g e s i n e a r n i n g s , w h i c h l e d t o s o m e v e r y l a r g e n u m b e r s . C o n s e q u e n t l y , D O L w a s r e d e f i n e d a s t h e s l o p e o f t h e s i m p l e r e g r e s s i o n o f E B I T o n s a l e s o v e r t h e r e l e v a n t f i v e y e a r p e r i o d . T h i s i s t h e m e a s u r e t h a t a p p e a r s i n t h e r e s u l t s g i v e n b e l o w . V A R w a s t a k e n t o b e t h e s a m p l e s t a n d a r d d e v i a t i o n o f s a l e s d i v i d e d b y t h e s a m p l e m e a n o f s a l e s , a g a i n o v e r a f i v e y e a r p e r i o d . T h e s a m p l e s i z e s v a r i e d f r o m 2 2 t o 5 0 a c r o s s i n d u s t r i e s . S i n c e v a r i a n c e i s u n d e r e s t i m a t e d f o r s m a l l s a m p l e s , i t w a s f e l t t h a t s a m p l e v a r i a n c e w a s a m o r e a p p r o p r i a t e m e a s u r e t h a n p o p u l a t i o n v a r i a n c e . D i v i d i n g b y t h e s a m p l e m e a n m a d e a l l o w a n c e f o r d i f f e r e n c e s i n t h e a v e r a g e l e v e l o f s a l e s a m o n g s t c o m p a n i e s . T h e d e f i n i t i o n s c h o s e n f o r D O L a n d V A R a r e s t a n d a r d 36 f i n a n c i a l r a t i o s . 2 " PFDDUM and CONVDUM were dummy v a r i a b l e s used as checks on the d e f i n i t i o n of DEBTEQ. The c o e f f i c i e n t s of both v a r i a b l e s were expected to be zero. Preferreds and c o n v e r t i b l e s were included because they can act l i k e both debt and e q u i t y . Both c o n v e r t i b l e s and pr e f e r r e d s are l i k e debt i n that they require f i x e d i n t e r e s t payments. C o n v e r t i b l e s are l i k e e q u i t y i n that c o n v e r t i b l e bondholders have the option of t u r n i n g t h e i r s e c u r i t i e s i n t o r e s i d u a l c l a i m s . P r e f e r r e d stockholders are r e s i d u a l claimants i n that they do not receive dividends u n t i l a f t e r debtholders have been pa i d . The dependent v a r i a b l e was defined as t o t a l assets l e s s equity d i v i d e d by e q u i t y . Debt-to-equity was used rather than d e b t - t o - t o t a l assets because i t was f e l t to encompass more info r m a t i o n . F e r r i and Jones recognized that i t s a t i s f i e s both sides i n the dispute about whether c a p i t a l s t r u c t u r e i s more pro p e r l y measured using debt or equity d i v i d e d by t o t a l a s s e t s . 2 5 Equity was the sum of common stock, p r e f e r r e d stock, and c o n v e r t i b l e debt. This d e f i n i t i o n of DEBTEQ was chosen so that the v a r i a b l e would contain as much information as p o s s i b l e about c a p i t a l s t r u c t u r e . P r e l i m i n a r y r e g r e s s i o n runs were examined to see which of three d e f i n i t i o n s of DEBTEQ gave the smallest t - s t a t i s t i c s for the c o e f f i c i e n t s of PFDDUM and CONVDUM. The other p o s s i b l e 2 f t Richard Brealey, and Stewart Myers, Op. C i t . , pp 586-587. 2 5 M. G. F e r r i and Wesley H. Jones, Op. C i t . 37 d e f i n i t i o n s for equity were common stock, and common stock less preferred stock. The chosen d e f i n i t i o n was f e l t to contain the most information about preferreds and convertibles and their r e l a t i o n to c a p i t a l structure. A l l the non-dummy independent variables were standardized. This was to reduce the p o s s i b i l i t y of roundoff errors when inverting the X'X matrix. If the determinant of the X'X matrix i s near zero, or the variables d i f f e r considerably in scale, there i s a serious danger of roundoff e r r o r s . 2 6 So that the results could be e a s i l y interpreted, the dependent variable was not standardized. For example, unstandardized data should not lead to an intercept term which i s s i g n i f i c a n t l y negative, since t h i s i s not observable in firms which are going concerns. Because the magnitude of DEBTEQ was r e l a t i v e l y close to that of the standardized independent variates, i t was f e l t that the use of standardized independent varibles would aid in the interpretation of the r e s u l t s . Preliminary results suggested that the assumption of constant variance necessary in a regression setting was being v i o l a t e d . From a s t a t i s t i c a l point of view, heteroscedasticity was observed and had to be corrected. In p a r t i c u l a r , the size of the residuals increased with DEBTEQ, and the expected normal p r o b a b i l i t y plot of residuals was a steep curve of p o s i t i v e and decreasing slope. The ideal expected normal plot i s a forty--2 6 John Neter and William Wasserman, Applied Linear S t a t i s t i c a l Models, Richard D. Irwin Inc., Homewood, I l l i n o i s , 1974, p34/. 38 f i v e degree straight l i n e . To compensate for these violations of normality, DEBTEQ was transformed. The new dependent variable, LNDE, was taken to be the logarithm to base e, of DEBTEQ. A decrease in equity both decreases the denominator and increases the numerator, so that a change in financing policy has a double e f f e c t . DEBTEQ i s concave to the o r i g i n , with respect to equity. The derivative of the logarithm of the debt-to-equity r a t i o as defined, with respect to preferred stock, is negative i f the average equity to t o t a l assets r a t i o i s greater that 1/2. For the sample, the r a t i o was .48. An examination of the c o r r e l a t i o n matrix indicated that SIZE and VAR were highly correlated (.7946). An a u x i l i a r y regression showed that VAR=.79458(SIZE). Average sales and sales variance were not s i g n i f i c a n t l y correlated. The intercept was not forced to zero, but the regression results gave an intercept term of n i l . This regression was highly s i g n i f i c a n t , with a R-squared s t a t i s t i c of .63 and a F-ratio of 75.19. A new variable, NEWVAR, was formed, which equalled VAR-.79548(SIZE),so as to separate the ef f e c t s of size and sales variance. The regression results are given in Table 1. Each column gives the c o e f f i c i e n t s for a d i f f e r e n t regression. The f i r s t column corresponds to the output from the f u l l set of data from 1976 and 1981. 3 9 T a b l e I - R e g r e s s i o n R e s u l t s 1 9 8 1 r 1 9 7 6 D A T A A l l C a s e s A l l C a s e s C a s e s 6 9 , 2 4 1 D e l e t e d 1 9 7 1 , 1 9 6 6 D A T A A l l C a s e s C a s e s 3 8 , 2 3 6 D e l e t e d I n t e r c e p t . 4 6 - . 0 4 . 4 4 . 0 4 . 0 4 C M T A - . 2 2 * * * - . 2 1 * * * - . 2 4 * * * - . 2 4 * * * - . 2 5 * * * A R T A - . 0 7 - . 1 7 * * * - . 0 7 - . 0 6 - . 0 7 I N V T A - . 1 2 - . 1 7 * * * - . 1 1 - . 2 2 * * - . 2 3 * * N T P T A - . 3 1 * * * - . 1 7 * - . 3 1 * * * - . 2 3 * * - . 1 9 S U B S E C . 1 2 * * * . 1 3 * * * . 1 2 * * * 1 ^ * * * . 1 1 * * * S I Z E - . 0 2 . 0 3 - . 0 1 - . 0 5 - . 0 4 D O L - . 0 3 - . 0 6 - . 0 5 N E W V A R . 0 3 . 0 4 . 0 1 P F D D U M . 1 3 * * * . 2 6 * * * . 1 2 * * * . 4 0 * * * . 3 8 * * * C O N V D U M . 0 0 . 0 8 . 0 0 . 1 5 . 1 5 Y R D U M - . 0 5 - . 0 7 - . 0 5 . 1 0 . 1 0 D1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 1 0 D1 1 D1 2 D 1 3 D 1 4 - . 5 2 * * * - . 8 3 * * * _ 7 5 * * * - * 4 8 * * * - . 3 8 * - . 6 4 * * * - . 0 2 _ 4 4 * * * - * . 8 9 * * * - . 7 3 * * * - ! 7 4 * * * . 0 1 . 4 9 * - . 4 7 * * * - . 4 9 * * - . 8 3 * * * - . 7 4 * * * - 4 7 * * * - ' . 3 7 * - . 5 7 * * * . 0 0 - . 4 7 * * * - " . 8 8 * * * - . 7 0 * * * - . 7 1 * * * . 0 6 . 5 2 * * - . 4 6 * * * - . 6 0 * * - . 6 9 * * * - . 3 6 - . 7 3 * * * - . 5 6 * * * - . 6 1 * * * - . 4 9 * - . 4 5 * * - . 8 9 * * * - . 6 8 * * * - . 6 2 * * . 4 6 . 3 9 - . 3 4 _ 5 7 * * * - ^ 5 9 * * * - . 2 7 - . 7 5 * * * - . 5 6 * * * - . 5 6 * * * - . 5 3 * * _ 5 4 * * * - . 8 4 * * * - . 6 3 * * * - . 5 7 * * * . 4 3 . 3 1 - . 3 0 F - R A T I O P ( T A I L ) 1 4 . 6 7 6 . 0 0 0 1 6 . 1 1 . 0 0 0 1 5 . 7 4 5 . 0 0 0 1 1 . 7 5 1 . 0 0 0 1 2 . 5 7 4 . 0 0 0 • I N D I C A T E S B O N F E R R O N I S I G N I F I C A N C E A T . 1 0 L E V E L • • I N D I C A T E S B O N F E R R O N I S I G N I F I C A N C E A T . 0 5 L E V E L * * * I N D I C A T E S B O N F E R R O N I S I G N I F I C A N C E A T . 0 1 L E V E L 40 Bonferroni j o i n t confidence inter v a l s were used to enable simultaneous testing of a l l the regression c o e f f i c i e n t s . In essence, the p r o b a b i l i t y associated with the Bonferroni interval requires taking the two t a i l p robability derived from the t-s t a t i s t i c for each c o e f f i c i e n t , and d i v i d i n g that t - s t a t i s t i c by the number of regression c o e f f i c i e n t s . The f i r s t hypothesis cannot be supported: i t appears that firms with more l i q u i d i t y do not have higher debt r a t i o s . The s i g n i f i c a n t l y negative c o e f f i c i e n t of CMTA implies t h i s surprising r e s u l t . This may have been due to firms experiencing downturns in earnings, which would have led to decreased retained earnings, hence lower equity, while at the same time cash flows would have decreased. If t h i s were the case, then one would expect the c o e f f i c i e n t to be closer to zero, or less s i g n i f i c a n t , or both, during periods of economic growth. During expansionary periods, firms would face growing cash flows, in general. Retained earnings would not be expected to decrease during these times, nor would cash be drawn down due to reduced cash flows. To see i f economic climate might be inducing the negative c e f f i c i e n t for CMTA, simi l a r regressions were run on 1971 and 1966 data. These r e s u l t s indicate that that the inverse rela t i o n s h i p between CMTA and LNDE i s permanent. The c o e f f i c i e n t of CMTA may have been due to c o l l i n e a r i t y . However, when a l l the variables with which CMTA had an absolute value of simple c o r r e l a t i o n of more than .20 were deleted from 41 t h e m o d e l , t h e c o e f f i c i e n t f o r C M T A r e m a i n e d s i g n i f i c a n t l y n e g a t i v e . F u r t h e r m o r e , i n a n a l l s u b s e t s c o n t e x t , C M T A w a s a l w a y s a m o n g t h e f i r s t v a r i a b l e s i n c l u d e d i n t h e r e g r e s s i o n ( u s i n g t h e B M D P p a c k a g e P : 9 R ) , a n d t h e s i g n o f i t s c o e f f i c i e n t w a s a l w a y s n e g a t i v e . I n a f u r t h e r e f f o r t t o t e s t f o r c o l l i n e a r i t y , e s p e c i a l l y a m o n g t h r e e o r m o r e v a r i a t e s , t h e B e l s l e y , K u h a n d W e l s h t e c h n i q u e o f v a r i a n c e d e c o m p o s i t i o n w a s u s e d . T h i s p r o c e d u r e r e q u i r e s s t a n d a r d i z i n g t h e X - m a t r i x t o u n i t c o l u m n l e n g t h . P r i n c i p l e c o m p o n e n t s a n a l y s i s i s t h e n u s e d t o b r e a k t h e X - m a t r i x d o w n i n t o e i g e n v a l u e s a n d c o r r e s p o n d i n g o r t h o g o n a l e i g e n v e c t o r s . T h e e i g e n v e c t o r s a r e t h e n d e c o m p o s e d a s s h o w n i n T a b l e 2 . 42 Table II - Variance Decomposition Variance(Bi) Lj 1 2 3 4 5 6 7 8 9 10 1 1 Nj 1 .88 .01 .05 .03 .30 .00 .02 .02 .01 .00 .00 .00 1 .0 1 .32 .02 .12 .17 .27 .00 .09 .02 .07 .00 .03 .05 1 .4 1 .27 .13 .21 .06 .08 .00 .06 .03 .10 .01 .01 . 1 1 1 .5 1 .04 .15 .31 .26 .14 .00 .01 .05 .04 .03 .00 .01 1 .8 1.01 .31 .10 .19 .12 .04 .02 .19 .08 .03 .04 .09 1.9 .95 .08 .05 .06 .01 .03 .03 . 1 1 .04 .02 .02 .06 2.0 .88 .08 .02 .04 .01 .03 .10 .37 .07 .07 .09 .31 2.1 .81 .10 .07 .01 .02 .15 .09 .07 .12 .27 .17 .24 2.3 .77 .01 .03 .15 .01 .02 .42 .02 .34 .09 .06 .07 2.4 .73 .00 .10 .02 .01 .06 .14 .01 .08 .32 .36 .06 2.6 .65 .04 .00 .01 .00 .66 .01 .10 .04 .15 .21 .00 2.9 Lj i s the square root of the j t h eigenvalue. Nj i s the j t h condition index. This i s equal to the square root of the largest eigenvalue divided by the square root of the jt h eigenvalue. 4 3 E a c h r o w o f T a b l e 2 c o r r e s p o n d s t o a n e i g e n v a l u e . . T h e f i n a l c o l u m n o n t h e r i g h t s i d e o f t h e t a b l e g i v e s t h e c o n d i t i o n i n d e x a s s o c i a t e d w i t h e a c h e i g e n v a l u e . E a c h o f t h e o t h e r c o l u m n s c o r r e s p o n d s t o o n e o f t h e o r i g i n a l X - v a r i a t e s . T h e i t h c o n d i t i o n i n d e x i s t h e r a t i o o f t h e s q u a r e r o o t o f t h e l a r g e s t e i g e n v a l u e t o t h e s q u a r e r o o t o f t h e i t h e i g e n v a l u e . A h i g h c o n d i t i o n i n d e x i s a s s o c i a t e d w i t h c o l l i n e a r i t y . B e l s l e y , K u h a n d W e l s h s u g g e s t t h a t w e a k d e p e n d e n c i e s a r e f o u n d w h e n i n d i c e s r e a d b e t w e e n 5 a n d 1 0 , w h e r e a s m e a s u r e s o f 3 0 t o 1 0 0 i n d i c a t e s e v e r e i l l - c o n d i t i o n i n g . T h e l a r g e s t c o n d i t i o n i n d e x i n t h i s c a s e i s 2 . 9 , w h i c h g i v e s n o i n d i c a t i o n o f c o l l i n e a r i t y . I n t h e r e s t o f t h e t a b l e , t h e i , j t h e n t r y g i v e s t h e a m o u n t o f v a r i a n c e o f t h e j t h X - v a r i a t e d e s c r i b e d b y t h e i t h e i g e n v e c t o r . C o l l i n e a r i t y i s d i a g n o s e d i f a l a r g e p o r t i o n o f t h e v a r i a n c e o f t w o o r m o r e X - v a r i a t e s i s a s s o c i a t e d w i t h t h e s a m e e i g e n v e c t o r . P u t a n o t h e r w a y , i f t w o o r m o r e v a r i a n c e d e c o m p o s i t i o n p r o p o r t i o n s i n t h e s a m e r o w a r e l a r g e , t h e n t h e s a m e e i g e n v e c t o r i s e x p l a i n i n g t h e v a r i a n c e o f t h e n o n -o r t h o g o n a l X - v a r i a t e s c o r r e s p o n d i n g t o t h e l a r g e v a r i a n c e d e c o m p o s i t i o n p r o p o r t i o n s . B e l s l e y , K u h a n d W e l s h s u g g e s t t h a t a g o o d c u t o f f p o i n t f o r t h e v a r i a n c e - d e c o m p o s i t i o n p r o p o r t i o n s i s . 5 0 , a n d t h a t d i s c r e p e n c i e s u s u a l l y s h o w u p w i t h p r o p o r t i o n s b e i n g a b o u t . 8 0 o r s o . I n T a b l e 2 , t h e r e i s n o c a s e i n w h i c h t w o p r o p o r t i o n s a s s o c i a t e d w i t h a n y o n e c o n d i t i o n i n d e x e x c e e d . 3 5 , s o t h a t t h e r e i s l i t t l e o r n o c o l l i n e a r i t y i n t h e d a t a ; t h e c o l u m n s o f t h e X - m a t r i x a r e o r t h o g o n a l . T h i s - s u p p o r t s t h e 4 4 contention that VAR and DOL are independent as postulated in (52) and (53). The proxies for degree of operating leverage, ARTA, INVTA, and NTPTA, a l l have negative c o e f f i c i e n t s . This i s consistent with lower f i n a n c i a l leverage for firms with high operating leverage, so the second n u l l hypothesis i s rejected. The in d i v i d u a l c o e f f i c i e n t s are not a l l s i g n i f i c a n t . The lack of significance of ARTA and INVTA could be due to d i f f e r e n t industries having d i f f e r e n t types of receivables and inventories. d i f f e r e n t firms. Write-off procedures for accounts receivable w i l l vary amongst industries, as w i l l accounts receivable and inventory turnover. Consequently, the extent to which these variables measure fixed costs w i l l vary amongst industries. Plant i s a fixed cost for a l l the firms, so i t should be a better proxy for operating leverage than ARTA or INVTA. SUBSEC has a s i g n i f i c a n t and positive c o e f f i c i e n t , which i s consistent with the theory that firms which s a t i s f y certain conditions have higher debt r a t i o s . The extent to which junior debt w i l l be used depends on taxes, bankruptcy costs, and operating leverage. Tax rates were not examined in t h i s experiment, so that the influences on SUBSEC cannot be properly determined. SUBSEC was regressed against ARTA, INVTA, NTPTA, SIZE, DOL, and NEWVAR. The R-squared s t a t i s t i c was less than .01, and each t - s t a t i s t i c was less than 1.0. The data was extremely skewed, with only 68 cases being non-zero, so regression was perhaps an 45 inappropriate way to test the relationship in question. Transformations indicated by the expected normal plot to correct the error variance were the logarithmic or the square root transformations. The f i r s t was impossible since many of the observations was 0.0, and the second was shown to be inappropriate. In Chapter 2, firms were shown to be i n d i f f e r e n t to issuing senior or subordinated debt i f each kind of debt had similar bankruptcy costs. However, i f junior debtholders faced higher bankruptcy costs, junior debt would be issued i f taxes were s i g n i f i c a n t l y p o s i t i v e . The i n s i g n i f i c a n t c o e f f i c i e n t of SIZE leads to r e j e c t i o n of the fourth n u l l hypothesis, that larger firms have larger debt-to-equity r a t i o s . Other studies consistently found SIZE to be p o s i t i v e l y related to f i n a n c i a l leverage. This unexpected result could be due to sampling bias: the Compustat Quarterly In d u s t r i a l Tape comprises firms on the Standard and Poor's 400 I n d u s t r i a l Index, and some other large firms. It could be that once firms reach a certain si z e , there i s no longer any e f f e c t of size on the financing decision. It may also be that the size ef f e c t was swamped by the industry e f f e c t . If there are optimal scales within industries, then the size e f f e c t may be part of the industry e f f e c t . The c o e f f i c i e n t for DOL i s i n s i g n i f i c a n t , causing acceptance of the n u l l hypothesis. However, with the deletion of o u t l i e r s , t h i s variable does become s i g n i f i c a n t at the l e v e l of .10, using Bonferroni confidence l i m i t s . 46 The c o e f f i c i e n t of NEWVAR i s i n s i g n i f i c a n t , leading to acceptance of the hypothesis that sales variance has no re l a t i o n to f i n a n c i a l leverage. This i s contrary to the prediction of the model developed in Chapter 2. It may be that sales v a r i a b i l i t y was measured imperfectly. For example, suppose two firms had i d e n t i c a l sales of 50, 100, and 150 over three periods. Further, assume that one firm grew over the period, with t o t a l assets of 100, 200 and 300 over the three periods. The second firm i s assumed to have constant size of 200 over the three periods. The measures of v a r i a b i l i t y w i l l be the same for both firms, that i s , they have the same standard deviations and same average sales. The firm which grows over the period has sales which are a constant percentage of si z e . One measure of v a r i a b i l i t y which would compensate for the scale e f f e c t would be the standard deviation of the ra t i o of sales to t o t a l assets (the t o t a l assets turnover r a t i o ) . This value would be 0 for the growth firm, and .125 for the constant size firm. Unfortunately, Compustat does not provide balance sheet data on a quarterly basis. However, the measure was computed on the basis of annual data. The c o e f f i c i e n t s for a l l the variables were unchanged in sign from previous regressions. The c o e f f i c i e n t for the standard deviation of sales turnover was i n s i g n i f i c a n t , having a t - s t a t i s t i c of less than one. When i n f l u e n t i a l points, had been deleted, the c o e f f i c i e n t remained i n s i g n i f i c a n t . The insignificance of CONVDUM in the regression indicates that the dependent variable i s well s p e c i f i e d with respect to 47 convertible debt acting l i k e equity. However, PFDDUM i s s i g n i f i c a n t l y p o s i t i v e , even though preferreds are already being treated l i k e equity. Perhaps the reason for t h i s l i e s in the nature of preferred dividends. Preferred shareholders are only e n t i t l e d to dividends after debtholders' claims have been s e t t l e d . However, their claims have an upper bound. If earnings are more than enough to make interest payments and preferred dividends, then the excess must either be paid to common shareholders or be retained. Earnings that are retained are subject to f i r s t claim by debtholders during the next period. In t h i s context, debtholders would prefer that equity be issued solely in the form of preferreds and not at a l l in the form of common stock. It may be that lenders f e e l that future interest payments are more secure when preferred equity i s issued, so that firms who issue preferreds are able to issue more debt. YRDUM i s not s i g n i f i c a n t , as predicted. Twelve of fourteen industry c o e f f i c i e n t s are s i g n i f i c a n t . The regression results are consistent with an industry class e f f e c t , which contradicts the Modigliani-Miller hypothesis. Debt rat i o s are similar within r i s k classes, indicating that there are factors which influence firms' c a p i t a l structure decisions. Three expected normal p r o b a b i l i t y plots are provided in Figures 1, 2 and 3. These correspond respectively to the f u l l sample with no deletions, with case 241 deleted, and with cases 241 and 69 deleted, respectively. Case 241 i s i d e n t i f i e d in 48 Figure 1 as the case with the largest positive standardized residual. Case 69 has the largest negative standardized residual in Figures 1 and 2. Cases 69 and 241 are arguably o u t l i e r s and should be deleted from the sample. When these cases are deleted, the expected normal plot of Figure 3 i s close to the i d e a l , which i s a p o s i t i v e l y sloped f o r t y - f i v e degree straight l i n e . Case 69 was Kaiser Steel, which has large holdings in Kaiser Resources. Kaiser Resources was petitioned for bankruptcy in B r i t i s h Columbia in 1982. Case 241 i s Bowater Corp., whose f i n a n c i a l statements have been translated from pounds to d o l l a r s . Bankruptcy and currency translation are exceptional occurances, and support the contention that these two observations should be deleted from the sample. 49 Figure 1 - Expected Normal P l o t , A l l Cases, 1981 & 1976 Data NORMAL PROBABILITY PLOT OF RESIDUALS + .... + . ... + .. .. + ....-•-.. .. + .... + .... + ....+ E X P E C T E D N 0 R M A L V A L U E 2.7 1 .8 .90 0.0 .90 •1.8 •2 . 7 * * * * * * •....•....+... .+ .... + .... + .. .. + .. .. + . ...+ -.90 -.30 .30 .90 1.5 -1.2 -.60 O.O .60 1.2 50 F i g u r e 2 - Expected Normal P l o t , Cases 69 & 241 D e l e t e d , 1981 & 1976 Data NORMAL PROBABILITY PLOT OF RESIDUALS E X P E C T E D N 0 R M A L V A L U E 2 . 7 + 1.8 .90 0.0 . 90 1.8 - 2 . 7 51 F i g u r e 3 - Expected Normal P l o t , A l l Cases, 1971 & 1966 Data N O R M A L P R O B A B I L I T Y P L O T O F R E S I D U A L S ...+....+....+....+....+....+....+....+....+....+.... * 2 . 7 + * + * * * * E * * X 1 . 8 + * * + P * * . E * C » T * * E . 9 0 + * * + D * * ** N * * 0 * * R 0 . 0 + * + M * * A * * L . * * * * V - . 9 0 + * * + A . * * L * * U . * * E * - 1 . 8 + * * + * * * * * * - 2 . 7 + * • + » . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . - 1 . 5 - . 5 0 . 5 0 1 . 5 2 . 5 - 2 . 0 - 1 . 0 0 . 0 1 . 0 2 . 0 52 The regression re s u l t s for the revised sample are given in the second column of Table 1. In no cases do the signs of the c o e f f i c i e n t s change, but the DOL becomes s i g n i f i c a n t , and takes the sign predicted by the model. The o u t l i e r s did introduce a s l i g h t d i s t o r t i o n of the c o e f f i c i e n t s , but they appear to be stable with or without the o u t l i e r s . A variable selection technique was employed to see i f the model had been c o r r e c t l y s p e c i f i e d . The subset of variables which had the Cp s t a t i s t i c which was close s t , in absolute terms, to the number of variables in the subset, was that selected as the best subset. To calculate the Cp s t a t i s t i c , f i r s t take the r a t i o of the residual sum of squares from the reduced model (using a subset of variables) to the residual mean square for the f u l l model. Subtract from t h i s the difference between the number of variables in the f u l l model less twice the number of variables in the subset. The expected value of Cp i s the number of variables in the reduced equation. The chosen equation had nineteen variables, including the intercept. The f u l l model had twenty-six. The Cp s t a t i s t i c for the best subset was 18.81. Three c o e f f i c i e n t s , for the variables INVTA, DOL, and YRDUM, were i n s i g n i f i c a n t at the Bonferroni j o i n t confidence l e v e l of .05. More importantly, the signs of a l l the c o e f f i c i e n t s were consistent with those of Table 1. Furthermore, in the computer output, for a l l subsets examined, the c o e f f i c i e n t s of a l l the s i g n i f i c a n t variables in Table 1 had the same signs. This i s consistent with the e a r l i e r findings that there i s no c o l l i n e a r i t y in the data. 53 Regressions were next run for each industry, using a l l cases. The results are given in Table 3 and Table 4. The tables l i s t the c o e f f i c i e n t s for each regression, followed by a * i f the c o e f f i c i e n t had a t - s t a t i s t i c which was s i g n i f i c a n t at the .05 l e v e l . 54 T a b l e I I I - I n d u s t r y R e g r e s s i o n s D1 D2 D3 D4 D5 D6 D7 D8 INTERCEPT -.52 -.79 -1 .63 -.49 -.15 -.39 .42 .03 CMTA -.78 -.09 -.13 -.19 -.24 -.15* -.33 -.25 ARTA -.97 .24 -.29 .24 -.04 .07 .09 -.46* INVTA -.47 .31 .13 -.43 -.70* -.49 -.21 -.21 NTPTA -1 .00 .09 -.39 -.14 -.50 -.24 -.30 -.81* SUBSEC .61 .46 .22* .18 N.A. .21* .58* .14* SIZE -.85 -.26 -2.82 -.78 .09 .21 -.01 -.09 DOL .03 -.03 -.09 -.03 -.05 -.06 -.05 .12 NEWVAR -.90 -1.31 4.51 .07 -.03 -.10 -.03 -.31 PFDDUM 1.18* .23 .19 .34* .17 • 19 .46* .36 CONVDUM .23 .18 -.28 .03 -.28* . 1 1 -.20 -.36 YRDUM -.83 -.25 -.06 .00 .14 .13 .12 -.24 R-SQUARED .91 .51 .69 .54 .36 .69 .56 .52 F-RATIO DF P(TAIL) 3.60 1 1,4 . 1 1 1 .31 11,4 .31 2.38 11,12 .08 2.60 1 1 ,24 .02 1 .42 10,25 .23 4.38 1 1 ,22 .00 4.17 1 1 ,36 .00 2.77 1 1 ,28 .01 EXPECTED NORMAL PLOT GOOD VERY POOR OK OK OK POOR POOR GOOD OUTLIERS NO YES YES YES YES YES YES YES CASES 16 26 24 36 36 34 48 40 N.A.:No v a r i a b i l i t y i n the d a t a . * I n d i c a t e s t - s t a t i s t i c s i g n i f i c a n t a t .05 l e v e l . 55 T a b l e IV - I n d u s t r y R e g r e s s i o n s C o n t i n u e d D9 D10 D1 1 D1 2 D1 3 D14 D1 5 INTERCEPT -.44 -.43 -.73 3.12 .69 -.14 .64 CMTA -.53 -.03 -.27 .23* -.13 N.A. -.52* ARTA -.42 .25 -.05 .42 .04 .13 -.39 INVTA -.42 -.12 .45 -.58 .42 .42 -.39 NTPTA -.62 -.06 -.23 -.44 .05 .35 -.59 SUBSEC .27 .20 .05 .35 .33 -.24 .04 SIZE -1 .74 .21 -.85 8.89* -1 .04 .07 .31 DOL -.06 .00 .05 -.25 -1.03* .14 -.25 NEWVAR 10.35 .37 -2.02 -4.54* -3.18 -.72 -.34 PFDDUM •41 .53 -.40 N.A. .15 .35* -.14 CONVDUM .04 .14 .57 .10 .21 .01 .10 YRDUM -.19 -.12 .02 .79* -.66 -.27 -.38 R-SQUARED .83 .62 .67 .92 .74 .76 .47 F-RATIO DF P(TAIL) 3.63 11,8 .04 1 .48 11,10 .27 2.17 11,12 .10 7.77 10,7 .01 3.12 11,12 .03 • 3.40 10,11 .03 1 .77 1 1 ,22 .12 EXPECTED NORMAL PLOT POOR VERY POOR OK OK POOR POOR OK OUTLIERS NO NO YES YES YES YES YES CASES 20 22 24 18 24 22 34 N.A. means no v a r i a b i l i t y i n the d a t a . * I n d i c a t e s t - s t a t i s t i c s i g n i f i c a n t a t .05 l e v e l . 56 The bottom row of the t a b l e shows t h a t most of the r e g r e s s i o n s v i o l a t e t he n o r m a l i t y a s s u m p t i o n , and have c o e f f i c i e n t s which ar e d e t e r m i n e d by a few o u t l i e r s . There were n i n e t e e n s i g n i f i c a n t c o e f f i c i e n t s , out of a p o s s i b l e t o t a l of 165. The s i g n s of the s i g n i f i c a n t c o e f f i c i e n t s a r e c o n s i s t e n t w i t h those i n T a b l e 1, w i t h the e x c e p t i o n of YRDUM i n D12, the t r u c k i n g i n d u s t r y . The c o e f f i c i e n t f o r SIZE was 8.89, and t h a t f o r NEWVAR -4.54, i n D12, and both were h i g h l y s i g n i f i c a n t . I n t h i s c a s e , the normal p r o b a b i l i t y p l o t i n d i c a t e d the p r e s e n c e of o u t l i e r s , one w i t h a v e r y l a r g e n e g a t i v e r e s i d u a l , and t h e o t h e r w i t h a v e r y l a r g e p o s i t i v e r e s i d u a l . F u r t h e r m o r e , t h e r e were o n l y e l e v e n independent v a r i a b l e s t o be de t e r m i n e d by o n l y e i g h t e e n c a s e s . I n the c o n t e x t of so few c a s e s and the i n f l u e n c e of o u t l i e r s , The r e g r e s s i o n r e s u l t s p r o v i d e l i t t l e i n f o r m a t i o n i n the case of D12. These r e s u l t s can be g e n e r a l i z e d t o a l l the i n d u s t r y r e g r e s s i o n s , t o each of which a t l e a s t one of the f o l l o w i n g c r i t i c i s m s a p p l y : the assumption of c o n s t a n t e r r o r v a r i a n c e was v i o l a t e d , the sample c o n s i s t e d of r e l a t i v e l y few o b s e r v a t i o n s , o r t h e r e were i n f l u e n t i a l p o i n t s i n the d a t a . C o n s e q u e n t l y , l i t t l e f a i t h can be a t t a c h e d t o the i n d u s t r y by i n d u s t r y r e s u l t s . When r e g r e s s i o n s were run w i t h o u t the i n d u s t r y dummies, the r e s u l t a n t e q u a t i o n was t h a t shown i n the second column of T a b l e 1. C o e f f i c i e n t s were i d e n t i c a l i n s i g n t o those of e a r l i e r r e g r e s s i o n s , and ARTA and DOL a r e b o t h s i g n i f i c a n t i n B o n f e r r o n i t e s t s a t the .05 l e v e l . I n c o n c l u s i o n , t h e r e seems t o be an i n d u s t r y e f f e c t where 57 f i r m s i n t h e same i n d u s t r y f a c e s i m i l a r c a p i t a l s t r u c t u r e s . L i q u i d i t y was found t o be n e g a t i v e l y r e l a t e d t o the degree of o p e r a t i n g l e v e r a g e , c o n t r a r y t o e x p e c t a t i o n s . O p e r a t i n g l e v e r a g e had a n e g a t i v e e f f e c t on the dependent v a r i a b l e , when measured d i r e c t l y as the e l a s t i c i t y of EBIT t o s a l e s , or through p r o x i e s such as the i n v e n t o r y t o t o t a l a s s e t s r a t i o or the net p l a n t t o t o t a l a s s e t s r a t i o . F i r m s which i s s u e d s u b o r d i n a t e d debt i s s u e d more debt r e l a t i v e t o e q u i t y . SIZE was found t o have no r e l a t i o n t o the d e b t - t o - e q u i t y r a t i o . T h i s may have been due t o t h e sa m p l i n g t e c h n i q u e , or the i n d u s t r y e f f e c t . S a l e s v a r i a n c e d i d not a f f e c t c a p i t a l s t r u c t u r e , c o n t r a t r y t o e x p e c t a t i o n s . F i r m s which i s s u e d p r e f e r r e d debt had more f i n a n c i a l l e v e r a g e , which may be due t o the f i x e d and r e s i d u a l n a t u r e of p r e f e r r e d d i v i d e n d s . C o n v e r t i b l e debt was seen t o have behaved l i k e e q u i t y . These r e s u l t s t e n d t o s u p p o r t the con c e p t of an o p t i m a l c a p i t a l s t r u c t u r e . 58 LITERATURE CITED 1. A l t m a n , Edward I . " F i n a n c i a l R a t i o s , D i s c r i m i n a n t A n a l y s i s and the P r e d i c t i o n of C o r p o r a t e B a n k r u p t c y . " J o u r n a l of F i n a n c e , September 1978. 2. B a x t e r , N e v i n s D. "Leverage, R i s k of R u i n and t h e Cost of C a p i t a l . " J o u r n a l of F i n a n c e , September 1967. 3. Beaver, W i l l i a m H. "Market P r i c e s , F i n a n c i a l R a t i o s , and t h e P r e d i c t i o n of F a i l u r e . " J o u r n a l of A c c o u n t i n g  R e s e a r c h , Autumn 1968. 4. B e l s l e y , D a v i d A.; Kuh, Edwin; and Welsh, Roy E. R e g r e s s i o n D i a g n o s t i c s . T o r o n t o : John W i l e y & Sons, 1980. 5. B r e a l e y , R i c h a r d ; and Myers, S t e w a r t . P r i n c i p l e s of  C o r p o r a t e F i n a n c e . T o r o n t o : Mc-Graw H i l l , I n c . , 1981. 6. C h a t t e r j e e , S a m p r i t ; and P r i c e , Bertram. R e g r e s s i o n  A n a l y s i s By Example. T o r o n t o : John W i l e y & Sons, 1977. 7. Chen, Andrew H.; and Kim, E. Han. " T h e o r i e s of C o r p o r a t e Debt S t r u c t u r e : A S y n t h e s i s . " J o u r n a l of F i n a n c e , May 1 979. 8. C o p e l a n d , Thomas E.; and Weston, J . F r e d . F i n a n c i a l  Theory and C o r p o r a t e P o l i c y . Don M i l l s , O n t a r i o : A d d i s o n Wesley, 1979. 9. D i x o n , W.J.; and Brown, M.B., eds., BMDP-79: B i o m e d i c a l 10. Computer Programs P - S e r i e s . B e r k e l y , C a l i f o r n i a : U n i v e r s i t y of C a l i f o r n i a , 1979. 11. D r a p e r , Norman; and S m i t h , H a r r y . A p p l i e d R e g r e s s i o n  A n a l y s i s , 2nd ed. T o r o n t o : John W i l e y & Sons, 1981. 12. F e r r i , M i c h a e l G.; and J o n e s , Wesley H. " D e t e r m i n a n t s of F i n a n c i a l S t r u c t u r e : A New M e t h o d o l o g i c a l Approach." J o u r n a l of F i n a n c e , June 1979. 13. F r a n c i s , Jack C l a r k . I n v e s t m e n t s : A n a l y s i s and  Management, 3rd ed. Toronto:McGraw H i l l Book Company, 1980. 14. Hamada, Robert S. "The E f f e c t of the F i r m ' s C a p i t a l S t r u c t u r e on the S y s t e m a t i c R i s k of Common S t o c k s . " J o u r n a l of F i n a n c e , June 1966. 15. J e n s e n , M.C.; and M e c k l i n g , W.H. "Theory of the F i r m : M a n a g e r i a l B e h a v i o r , Agency C o s t s and Ownership S t r u c t u r e . " J o u r n a l of F i n a n c i a l Economics, October 1976. 59 16. Lev, Baruch. "On The A s s o c i a t i o n Between O p e r a t i n g Leverage and R i s k . " J o u r n a l of F i n a n c i a l and Q u a n t i t a t i v e  A n a l y s i s , September 1974. 17. Marsh, P a u l . "The C h o i c e Between E q u i t y and Debt: An E m p i r i c a l Study." J o u r n a l of F i n a n c e , March 1982. 18. M i l l e r , M.H. "Debt and Taxes." J o u r n a l of F i n a n c e , May 1977. 19. M o d i g l i a n i , F r a n c o ; and M i l l e r , Merton H. " The Cost of C a p i t a l , C o r p o r a t e F i n a n c e , and the Theory of Investment." American Economic Review, June 1958. 20. Myers, Stewart C , ed. Modern Developments i n F i n a n c i a l Management. H i l l s d a l e , I l l i n o i s : H o l t , R i n e h a r t and Win s t o n , 1976. 21. N e t e r , John; and Wasserman, W i l l i a m . A p p l i e d L i n e a r  S t a t i s t i c a l M odels. 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 . , 1974. 22. Remmers, Lee; S t o n e h i l l , A r t h u r ; W r i g h t , R i c h a r d ; and Be e k h u i s e n , Theo. " I n d u s t r y and S i z e as Debt R a t i o D e t e r m i n a n t s i n M a n u f a c t u r i n g I n t e r n a t i o n a l l y . " F i n a n c i a l  Management, Summer 1974. 23. S c h w a r t z , E l i ; and Aronson, J . R i c h a r d . "Some S u r r o g a t e E v i d e n c e i n Support of t h e Concept of O p t i m a l C a p i t a l S t r u c t u r e . " J o u r n a l of F i n a n c e , March 1967. 24. S c o t t , D a v i d F., J r . "Evidence on the Importance of F i n a n c i a l S t r u c t u r e . " F i n a n c i a l Management, Summer 1972. 25. S c o t t , D a v i d F., J r . ; and M a r t i n , John D. " I n d u s t r y I n f l u e n c e on F i n a n c i a l S t r u c t u r e . " F i n a n c i a l Management, S p r i n g 1975. 26. S c o t t , James H., J r . " B a n k r u p t c y , Secured Debt, and O p t i m a l C a p i t a l S t r u c t u r e : R e p l y . " J o u r n a l of F i n a n c e , March 1979. 27. S m i t h , C l i f f o r d W., J r . ; and Warner, J e r o l d B. "On F i n a n c i a l C o n t r a c t i n g : An A n a l y s i s of Bond Covenants." J o u r n a l of F i n a n c i a l Economics, 7(1979) 117-161. 28. S t a n d a r d and Poo r ' s Compustat S e r v i c e s , I n c . I n d u s t r i a l  Compustat. New York: S t a n d a r d and Poor's Compustat S e r v i c e s , I n c . , 1982. 29. S t i g l i t z , J o s e ph E. "On t h e I r r e l e v a n c e of C o r p o r a t e F i n a n c i a l P o l i c y . " American Economic Review, December, 1974. 60 30. Van Home, James C ; Dipchand, c e c i l R.; and Hanrahan, J . R o b e r t . F i n a n c i a l Management and P o l i c y , Canadian 4 th ed. Scarborough, O n t a r i o : P r e n t i c e - H a l l of Canada L t d . , 1977. 31. Warner, J e r o l d B. "Bankruptcy C o s t s : Some E v i d e n c e . " J o u r n a l of F i n a n c e , May 1977. 61 APPENDIX A ~ LIST OF COMPANIES SAMPLED T h i s appendix l i s t s the i n d u s t r i e s and f i r m s i n c l u d e d i n the sample . Food and K i n d r e d P r o d u c t s : Anderson, C l a y t o n & Co.; CPC I n t e r n a t i o n a l I n c . ; Campbell Soup Co.; C o n s o l i d a t e d Food Corp.; K e l l o g Co.; N a b i s c o Brands I n c . ; Norton Simon I n c . ; Quaker Oats Co. T e x t i l e M i l l P r o d u c t s : B e l d i n g Heminway; B u r l i n g t o n I n d u s t r i e s I n c . ; C o l l i n s and Aikman Corp.; Cone M i l l s Corp.; Dan R i v e r I n c . ; F i e l d c r e s t M i l l s ; G r a n i t e v i l l e Co.; M. L o w e n s t e i n Corp.; Reeves B r o t h e r s I n c . ; R i e g e l T e x t i l e Corp.; S p r i n g s I n d u s t r i e s I n c . ; J.P. Stevens I n c . ; West P o i n t - P e p p e r e l l . A p p a r e l l and Other F i n i s h e d P r o d u c t s : BTK I n d u s t r i e s I n c . ; B l u e B e l l I n c . ; C l u e t t , Peabody and Co.; H a r t , S c h a f f n e i * artd Marx Co.; I n t e r c o I n c . ; Jonathan Logan I n c . ; L e v i S t r a u s s & Co.; Manhattan I n d u s t r i e s I n c . ; P h i l l i p s - V a n Heusen; U.S. I n d u s t r i e s ; VF Corp.; Warnaco I n c . Paper and A l l i e d P r o d u c t s : B o i s e Cascade Corp.; B y ^ a t e r Corp. Ltd.-ADR; Crown Z e l l e r b a c h ; Diamond I n t e r n a t i o n a l Corp.; Domtar I n c . ; F e d e r a l Paper Board Co.; F o r t Howard Pape-r; Great N o r t h e r n Nakoosa Corp.; Hammermill Paper Co.; I n t e r n a t i o n a l Paper Co.; K i m b e r l y - C l a r k Corp.; Mead Corp.; P o t l a c h Corp.; S t . R e g i s Paper Co.; S c o t t Paper Co.; Stone C o n t a i n e r Corp.; Union Camp Corp.; Westvaco Corp. C h e m i c a l s and A l l i e d P r o d u c t s : A l l i e d Corp.; American Cyanamid Co.; Diamond Shamrock Corp.; Dow C h e m i c a l ; E . I . Du Pont De Nemours; FMC Corp.; W.R. Grace & Co.; H e r c u l e s I n c . ; Monsanto Co.; Morton-Norwich P r o d u c t s ; N a t i o n a l D i s t i l l e r s and C h e m i c a l ; O l i n Corp.; PPG I n d u s t r i e s I n c . ; Pennwalt Corp.; Rohm and Haas Co.; S t a u f f e r C h e m i c a l Co.; T h i o k o l Corp.; Union C a r b i d e Corp. Drugs: A b b o t t L a b o r a t o r i e s ; American Home P r o d u c t s Corp.; B r i s t o l - M y e r s Co.; I r o q u o i s Brands L t d . ; E l i L i l l y & Co.; Merck and Co.; P f i z e r I n c . ; R i c h a r d s o n V i c k s I n c . ; R o r e r Group; S c h e r i n g - P l o u g h ; G.D. S e a r l e & Co.; S m i t h k l i n e Beckman Corp.; S q u i b b Corp.; S t e r l i n g Drug I n c . ; Syntex Corp.; Upjohn Co.; Warner-Lambert Co. P e t r o l e u m R e f i n i n g : Amerada Hess Corp.; A s h l a n d O i l I n c . ; A t l a n t i c R i c h f i e l d Co.; B r i t i s h P e t r o l e u m Co. Ltd.-ADR; C i t i e s S e r v i c e Co.; C o a s t a l Corp.; Exxon Corp.; G u l f O i l Corp.; I m p e r i a l O i l Ltd.-CL A; K e r r McGee Corp.; L o u i s i a n a Land & E x p l o r a t i o n ; M o b i l Corp.; Murphy O i l Corp.; P h i l l i p s P e t r o l e u m Co.; Quaker S t a t e O i l R e f i n i n g ; R o y a l Dutch Petroleum-NY GLDR 10; S h e l l O i l Co.; S t a n d a r d O i l Co. of C a l i f o r n i a ; S t a n d a r d O i l Co. of I n d i a n a ; Sun Co. I n c . ; Tenneco I n c . ; Texaco I n c . ; Union 62 O i l Co. of C a l i f o r n i a ; W i t c o C h e m i c a l Corp. B l a s t Furnaces-and S t e e l Works: Armco I n c . ; A t h l o n e I n d u s t r i e s ; A x i a I n c . ; Bethlehem S t e e l Corp.; C a r p e n t e r Technology; C o l t I n d u s t r i e s I n c . ; Copperweld Corp.; Crane Co.; I n l a n d S t e e l Co.; I n t e r l a k e I n c . ; K a i s e r S t e e l Corp.; Keystone C o n s t r u c t i o n I n d u s t r i e s I n c . ; LTV Corp.; Lukens I n c . ; McLouth S t e e l Corp.; N a t i o n a l - S t a n d a r d Co.; N o r t h w e s t I n d u s t r i e s ; R e p u b l i c S t e e l Corp.; U.S. S t e e l Corp.; W h e e l i n g - P i t t s b u r g S t e e l . M e t a l w o r k i n g Machinery and Equipment: Acme-Cleveland Corp.; B l a c k and Decker M a n u f a c t u r i n g Co.; Brown and Sharpe M a n u f a c t u r i n g Co.; C h i c a g o Pneumatic T o o l Co.; C i n c i n n a t i M i l l a c r o n I n c . ; E s t e r l i n e Corp.; E x - C e l l - 0 Corp.; G i d d i n g s & L e w i s I n c . ; Kennametal I n c . ; Monarch Machine T o o l Co. G e n e r a l I n d u s t r i a l M a chinery and Equipment: Cooper I n d u s t r i e s I n c . ; C u r t i s s W right Corp.; F i g g i e I n t e r n a t i o n a l I n c . ; I n g e r s o l l - R a n d Co.; M i d l a n d - R o s s Corp.; New Hampshire B a l l B e a r i n g s ; Rexnord I n c . ; S c o t t and F e t z e r Co.; S t a - R i t e I n d u s t r i e s ; S u n s t r a n d Corp; Timken Co. E l e c t r o n i c Computing Equipment: C o m p u t e r v i s i o n Corp.; C o n t r o l Data Corp.; Data G e n e r a l Corp.; D a t a p o i n t Corp.; D i g i t a l Equipment; E l e c t r o n i c A s s o c i a t e s I n c . ; E l e c t r o n i c Memories and Magnet; H a z e l t i n e Corp.; H e w l e t t - P a c k a r d Co.; Honeywell I n c . ; S t o r a g e Technology Corp.; Wang L a b o r a t o r i e s - C L B. T r u c k i n g - L o c a l and Long D i s t a n c e : C o n s o l i d a t e d F r e i g h t w a y s I n c . ; Leaseway T r a n s p o r t a t i o n Corp.; McLean T r u c k i n g Co.; N a t i o n a l C i t y L i n e s ; O v e r n i t e T r a n s p o r t a t i o n ; P u r o l a t o r I n c . ; Roadway E x p r e s s I n c . ; Transcon I n c . - C a l i f o r n i a ; Y e l l o w F r e i g h t System. A i r T r a n s p o r t a t i o n - C e r t i f i e d : American A i r l i n e s I n c . ; C o n t i n e n t a l A i r L i n e s I n c . ; D e l t a A i r L i n e s I n c . ; E a s t e r n A i r L i n e s ; Northwest A i r l i n e s I n c . ; Pan American World A i r w a y s ; T i g e r I n t e r n a t i o n a l ; Trans World Corp.; U n i t e d A i r L i n e s I n c . ; U.S. A i r I n c . ; Western A i r L i n e s I n c . ; World A i r w a y s I n c . R e t a i l - Department S t o r e s : A l l i e d S t o r e s ; A s s o c i a t e d Dry Goods Corp.; C a r t e r Hawley H a l e S t o r e s ; F e d e r a t e d Department S t o r e s I n c . ; R.H. Macy and Co.; M a r s h a l l F i e l d & Co.; May Department S t o r e s Co.; J.W. Mays I n c . ; M e r c a n t i l e S t o r e s Co.; J.C. Penny Co.; S e a r s , Roebuck & Co. R e t a i l - G r o c e r y S t o r e s : A . J . B a y l e s s M a r k e t s I n c . ; Borman's I n c . ; D i l l o n Companies; G e n e r a l Host Corp.; G r e a t A t l e n t i c and P a c i f i c Tea Co.; J e w e l Companies I n c . ; Kroger Co.; Lucky S t o r e s I n c . ; Munford I n c . ; P e t r o l a n e I n c . ; Safeway S t o r e s I n c . ; S o u t h l a n d Corp.; 'Star Supermarkets; Stop & Shop Companies; Supermarkets G e n e r a l Corp.; T h o r o f a r e M a r k e t s ; W i n n - D i x i e S t o r e s I n c . 

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