Arts, Faculty of
Vancouver School of Economics
DSpace
UBCV
Macnaughton, Alan Robert
Doctor of Philosophy - PhD
University of British Columbia
Closely-held corporations differ from widely-held corporations in that there are only a few shareholders, most or all of whom participate actively in management. This implies that the objective function is the owners' utility rather than profits, and corporate behaviour is influenced by both the corporate and personal income taxes. This dissertation builds a theoretical model of a closely-held corporation based on these features and uses this model to study empirically farmers' decisions to incorporate. The theoretical model determines the financial policy of a closely-held corporation from the static utility maximization problem of its owner. The model differs from previous work in that the set of financial instruments is extended beyond taxable dividends to include owner's salary, in-kind benefits, and the change in loans from the owner. Also, the modelling of the tax system is unusually detailed and includes the special tax provisions applying to incorporated Canadian small businesses . The Kuhn-Tucker conditions for the model show that the quantities of in-kind benefits consumed by the owner will depend on prices which are adjusted for the tax consequences of the goods' purchase. For dividends, salary, and changes in the amount of shareholder's loans, a financial optimum requires that it is not possible to decrease total personal and corporate taxes paid by increasing one financial variable and decreasing another. More specific conclusions are derived from the model in two ways. First, tax rates applying in Ontario in 1980 are substituted in the Kuhn-Tucker conditions to produce graphs showing the optimal financial policy in the more common situations'. Second, linear programming is used to provide numerical examples of optimal financial policies. This information is used to illuminate a number of tax policy issues relating to closely-held corporations. Other chapters discuss the extension of the model to multiple owners, many time periods, and the decision to incorporate. The last issue is studied empirically using a sample of 3,000 Saskatchewan farmers. Probit analysis shows that the probability that a farm will be incorporated is positively related to the farmer's education and the tax savings from incorporation.
TAXATION AND THE FINANCIAL POLICY OF CANADIAN CLOSELY-HELD CORPORATIONS by ALAN ROBERT MACNAUGHTON B.A. (Hon.), W i l f r i d L a u r i e r U n i v e r s i t y , 1976 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department o f Economics) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA March 1983 (c) A l a n Robert M a c n a u g h t o 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 E c o n o m i c s The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date M a r c h 2 5 ' 1983, DE-6 (3/81) ABSTRACT C l o s e l y - h e l d c o r p o r a t i o n s d i f f e r from w i d e l y - h e l d c o r p o r a t i o n s i n t h a t there are o n l y a few s h a r e h o l d e r s , most or a l l of whom p a r t i c i p a t e a c t i v e l y i n management. T h i s i m p l i e s t h a t the o b j e c t i v e f u n c t i o n i s the owners' u t i l i t y r a t h e r than p r o f i t s , and c o r p o r a t e behaviour i s i n f l u e n c e d by both the c o r p o r a t e and p e r s o n a l income taxes. T h i s d i s s e r t a t i o n b u i l d s a t h e o r e t i c a l model of a c l o s e l y - h e l d c o r p o r a t i o n based on these f e a t u r e s and uses t h i s model to study e m p i r i c a l l y farmers' d e c i -s i o n s to i n c o r p o r a t e . The t h e o r e t i c a l model determines the f i n a n c i a l p o l i c y o f a c l o s e l y - h e l d c o r p o r a t i o n from the s t a t i c u t i l i t y maximiza-t i o n problem o f i t s owner. The model d i f f e r s from p r e v i o u s work i n t h a t the s e t o f f i n a n c i a l instruments i s extended beyond t a x a b l e d i v i d e n d s to i n c l u d e owner's s a l a r y , i n - k i n d b e n e f i t s , and the change i n loans from the owner. A l s o , the m o d e l l i n g o f the tax system i s u n u s u a l l y d e t a i l e d and i n c l u d e s the s p e c i a l tax p r o v i s i o n s a p p l y i n g to i n c o r p o r a t e d Canadian sma l l b u s i n e s -ses . The Kuhn-Tucker c o n d i t i o n s f o r the model show t h a t the q u a n t i t i e s o f i n - k i n d b e n e f i t s consumed by the owner w i l l depend on p r i c e s which are a d j u s t e d f o r the tax consequences o f the goods' purchase. For d i v i d e n d s , s a l a r y , and changes i n the amount of shareholder's l o a n s , a f i n a n c i a l optimum r e q u i r e s t h a t i i i t i s not p o s s i b l e to decrease t o t a l p e r s o n a l and c o r p o r a t e taxes p a i d by i n c r e a s i n g one f i n a n c i a l v a r i a b l e and d e c r e a s i n g another. More s p e c i f i c c o n c l u s i o n s are d e r i v e d from the model i n two ways. F i r s t , tax r a t e s a p p l y i n g i n O n t a r i o i n 1980 are s u b s t i t u t e d i n the Kuhn-Tucker c o n d i t i o n s to produce graphs showing the o p t i m a l f i n a n c i a l p o l i c y i n the more common s i t u a -tions'. Second, l i n e a r programming i s used to p r o v i d e numerical examples of o p t i m a l f i n a n c i a l p o l i c i e s . T h i s i n f o r m a t i o n i s used to i l l u m i n a t e a number of tax p o l i c y i s s u e s r e l a t i n g t o c l o s e l y - h e l d c o r p o r a t i o n s . Other chapters d i s c u s s the e x t e n s i o n of the model to m u l t i p l e owners, many time p e r i o d s , and the d e c i s i o n to i n c o r -p o r a t e . The l a s t i s s u e i s s t u d i e d e m p i r i c a l l y u s i n g a sample of 3,000 Saskatchewan farmers. P r o b i t a n a l y s i s shows t h a t the p r o b a b i l i t y t h a t a farm w i l l be i n c o r p o r a t e d i s p o s i t i v e l y r e l a t e d t o the farmer's edu c a t i o n and the tax savings from i n -c o r p o r a t i o n . T A B L E OF CONTENTS A B S T R A C T i i T A B L E OF CONTENTS i v L I S T OF T A B L E S "v L I S T OF F I G U R E S v i ' ACKNOWLEDGEMENT v i i CH A P TER 1 : I n t r o d u c t i o n 1 1 .1 C o n t e x t 1 1 .2 P u r p o s e a n d O u t l i n e o f t h e S t u d y 8 CH A P TER 2 : T h e M o d e l a n d I t s S o l u t i o n 11 2 . 1 T h e M o d e l 11 2 . 2 N e c e s s a r y C o n d i t i o n s f o r a n O p t i m u m 29 2 . 3 A p p l i c a t i o n s o f t h e N e c e s s a r y C o n d i t i o n s 49 C H A P T E R 3 : S i m u l a t i o n R e s u l t s 7 0 3 . 1 T h e L i n e a r P r o g r a m m i n g A l g o r i t h m 7 0 3 . 2 F o u r A p p l i c a t i o n s 73 C H A P T E R 4 : R e l a x i n g t h e K e y A s s u m p t i o n s o f t h e M o d e l 96 4 . 1 M u l t i p l e O w n e r s 9 6 4 . 2 D y n a m i c D e c i s i o n - M a k i n g . . . . 101 4 . 3 S t a t i c v s . D y n a m i c M o d e l s . . 108 CH A P TER 5 : E m p i r i c a l A p p l i c a t i o n t o F a r m I n c o r p o r a t i o n D e c i s i o n s 116 5 . 1 T h e o r y 116 5 . 2 D a t a C o n s t r u c t i o n 123 5 . 3 E s t i m a t i o n a n d A n a l y s i s . . . . 138 5 . 4 C o n c l u s i o n 147 CH A P TER 6 : C o n c l u s i o n 154 6 . 1 Summary o f F i n d i n g s 154 6 . 2 P o l i c y I m p l i c a t i o n s 158 B I B L I O G R A P H Y 167 A P P E N D I X 173 i v LIST OF TABLES TABLE I' Tax-Adjusted P r i c e o f a. $10 Non-Taxable B e n e f i t 75 II Tax-Adjusted P r i c e of a $10 Taxable B e n e f i t 76 I I I Two Methods of E s t i m a t i n g the Tax Expenditures from the F e d e r a l and B.C. Small Business Rate Reductions 80 IV Tax Savings from I n c o r p o r a t i o n 83 V Percentage Decrease i n T o t a l Taxes from I n c o r p o r a t i o n 84 VI Tax Savings from I n c o r p o r a t i o n Under Pre-1978 Dividend Gross-Up and Tax C r e d i t 87 VII Tax Savings from RRSP C o n t r i b u t i o n s by Owners of Smaller C o r p o r a t i o n s 89 V I I I Optimal A l l o c a t i o n of Tax-Sheltered Savings P l a n C o n t r i b u t i o n s by Owners of Smaller C o r p o r a t i o n s 92 IX I n i t i a l P r o b i t Equation f o r O r g a n i z a t i o n a l Form 13 6 X P r o b i t Equation f o r O r g a n i z a t i o n a l Form 137 XI P r e d i c t e d P r o b a b i l i t i e s of the Corporate Form 138 XII P r e d i c t e d P r o b a b i l i t i e s of the Corporate Form w i t h A l t e r n a t i v e D i s t r i b u t i o n Assumption 139 v LIST OF FIGURES FIGURE 1 Choice of Taxable v s . Non-Taxable B e n e f i t s 35 2 F i n a n c i a l Expansion Path f o r a Large Business 54 3 F i n a n c i a l Expansion Path f o r a Medium-S i z e d Business 57 4 F i n a n c i a l Expansion Path f o r a Small Business 59 5 F i n a n c i a l Expansion Path f o r a Small Business w i t h Non-Zero RDTOH 64 v i ACKNOWLEDGEMENT I wish t o thank my t h e s i s s u p e r v i s o r , Jonathan Kesselman, f o r h i s c a r e f u l r e a d i n g o f e a r l i e r d r a f t s and h i s many h e l p f u l comments. My other committee members, Erwin Diewert and J o h n • H e l l i w e l l , have a l s o been of much a s s i s t a n c e a t c r i t i c a l p o i n t s i n the r e s e a r c h . In a d d i t i o n , a number of other f a c u l t y members and graduate students i n the Department of Economics have ai d e d me i n v a r i o u s ways. V a l u a b l e l e g a l and i n s t i t u t i o n a l i n s i g h t s have been p r o v i d e d by Mi c h a e l O'Keefe of the F a c u l t y of Law and David Lam of the F a c u l t y of Business A d m i n i s t r a t i o n . On a more p e r s o n a l l e v e l , my w i f e , Bonnie Lauber, has had a g r e a t d e a l to do with the s u c c e s s f u l completion of t h i s t h e s i s . v i i CHAPTER 1 INTRODUCTION 1. 1 CONTEXT A c l o s e l y - h e l d c o r p o r a t i o n may be d e f i n e d i n at l e a s t three ways. F i r s t , a c c o r d i n g to company law i n many j u r i s -d i c t i o n s , a c o r p o r a t i o n i s c l o s e l y - h e l d i f i t has a l i m i t on the number of s h a r e h o l d e r s , r e s t r i c t i o n s on the t r a n s f e r -a b i l i t y of i t s shares, and a p r o h i b i t i o n a g a i n s t o f f e r i n g i t s shares to the g e n e r a l p u b l i c . Second, a c o r p o r a t i o n may be c a t e g o r i z e d as c l o s e l y - h e l d on the b a s i s o f i t s economic c h a r a c t e r i s t i c s . The us u a l d e f i n i n g c h a r a c t e r i s t i c s are: a very s m a l l number of sh a r e h o l d e r s , o f t e n three or l e s s ; a l l or most of the share h o l d e r s are a c t i v e i n the b u s i n e s s , s e r v i n g as d i r e c t o r s , o f f i c e r s , o r both; and the shares are seldom traded, w i t h no e s t a b l i s h e d market f o r the corpora t e stock."*" T h i r d , a c o r p o r a t i o n i s c l o s e l y - h e l d f o r Canadian income tax purposes i f i t q u a l i f i e s as a " C a n a d i a n - c o n t r o l l e d p r i v a t e c o r p o r a t i o n " under the Income Tax A c t . A C a n a d i a n - c o n t r o l l e d p r i v a t e c o r p o r a t i o n i s a p r i v a t e c o r p o r a t i o n r e s i d e n t i n Canada which i s not c o n t r o l l e d by one or more non - r e s i d e n t s , p u b l i c c o r p o r a t i o n s , or a combination t h e r e o f . A p r i v a t e c o r p o r a t i o n i s d e f i n e d as a c o r p o r a t i o n which i s not p u b l i c and i s not c o n t r o l l e d by one or more p u b l i c c o r p o r a t i o n s . A p u b l i c cor-p o r a t i o n i s a c o r p o r a t i o n which i s l i s t e d on~a Canadian stock exchange. The income tax d e f i n i t i o n i s somewhat broader than the other two because i t i n c l u d e s c o r p o r a t i o n s whose shares 1 2 are a c t i v e l y t r aded i n the over-the-counter market through s e c u r i t i e s d e a l e r s . Since t h i s study i s concerned w i t h the income tax treatment of c l o s e l y - h e l d c o r p o r a t i o n s , the income tax d e f i n i t i o n i s the most important one f o r our purposes. C l o s e l y - h e l d c o r p o r a t i o n s tend t o be s m a l l e r than w i d e l y -h e l d c o r p o r a t i o n s , although there are notable exceptions such as the T. Eaton Co. and Olympia and York Developments L t d . I t should not be concluded t h a t c l o s e l y - h e l d c o r p o r a t i o n s are a s m a l l p a r t of the economy, however, s i n c e about 95% of a l l c o r p o r a t i o n s are C a n a d i a n - c o n t r o l l e d p r i v a t e c o r p o r a t i o n s . The Small Business S e c r e t a r i a t of the Department of Industry, Trade and Commerce has estimated t h a t i n 1974 C a n a d i a n - c o n t r o l l e d p r i v a t e c o r p o r a t i o n s comprised 42% of the s a l e s of a l l b u s i n e s -2 ses i n Canada, i n c l u d i n g u n i n c o r p o r a t e d b u s i n e s s e s . S t a t i s t i c s Canada r e p o r t s i n C o r p o r a t i o n T a x a t i o n S t a t i s t i c s t h a t i n 1976 C a n a d i a n - c o n t r o l l e d p r i v a t e c o r p o r a t i o n s c o n s t i t u t e d 35% of the t a x a b l e income of a l l c o r p o r a t i o n s . The l a t t e r p u b l i c a t i o n may a l s o be used t o estimate the d i s t r i b u t i o n by i n d u s t r y of c l o s e l y -h e l d c o r p o r a t i o n s , s i n c e the amount of t a x a b l e income which i s e l i g i b l e f o r the small b u s i n e s s deduction may be c a l c u l a t e d , and o n l y C a n a d i a n - c o n t r o l l e d p r i v a t e c o r p o r a t i o n s may c l a i m the smal l b u s i n e s s deduction. Most ta x a b l e income earned by C a n a d i a n - c o n t r o l l e d p r i v a t e c o r p o r a t i o n s was from r e t a i l t r a d e (18%), wholesale trade (17%), c o n s t r u c t i o n (16%), f i n a n c e (14%), 3 s e r v i c e s (14%) and manufacturing (13%); f i s h i n g and t r a p p i n g , a g r i c u l t u r e , f o r e s t r y , mining and t r a n s p o r t a t i o n , communica-t i o n s and u t i l i t i e s combined comprised o n l y 8%. Since indus-t r i e s vary g r e a t l y i n s i z e , the p r o p o r t i o n s of the t o t a l c o r p o r a t e t a x a b l e income of each i n d u s t r y a c c r u i n g to Canadian-c o n t r o l l e d p r i v a t e c o r p o r a t i o n s had q u i t e a d i f f e r e n t r a n k i n g : C a n a d i a n - c o n t r o l l e d p r i v a t e c o r p o r a t i o n s are most prominent i n f i s h i n g and t r a p p i n g (85%), a g r i c u l t u r e (78%), f o r e s t r y (58%), c o n s t r u c t i o n (54%) , r e t a i l t r a d e (53%) , s e r v i c e s (42%) and wholesale trade (34%), and l e a s t prominent i n manufacturing (8%) and mining ( 1 % ) . Some of those p r o p o r t i o n s may seem h i g h u n t i l i t i s remembered t h a t some i n d u s t r i e s , such as a g r i c u l t u r e , have a l a r g e non-corporate s e c t o r . I t would be i n t e r e s t i n g t o measure the income of C a n a d i a n - c o n t r o l l e d p r i v a t e c o r p o r a t i o n s r e l a t i v e to the income of a l l f i r m s , c o r p o r a t e and non-corporate, but t h i s i s not p o s s i b l e because non-corporate and c o r p o r a t e t a x a b l e income are not comparable. S a l a r i e s to business owners are d e d u c t i b l e i n computing c o r p o r a t e t a x a b l e income, but not i n computing non-corporate t a x a b l e income. The above f i g u r e s prove t h a t c l o s e l y - h e l d c o r p o r a t i o n s are an important p a r t of the economy. The q u e s t i o n then a r i s e s whether those c o r p o r a t i o n s have any d i s t i n c t i v e f e a t u r e s which are important f o r economic th e o r y . The main such f e a t u r e i s t h a t "the owners t h i n k of t h e i r c o r p o r a t e i n t e r e s t s i n a h i g h l y 4 p e r s o n a l manner; the c o r p o r a t i o n s are regarded merely as l e g a l d e v i c e s through which some p a r t of t h e i r i n d i v i d u a l p r o p e r t i e s i s managed, and the c o r p o r a t e a s s e t s i n a very r e a l sense are 3 p e r s o n a l a s s e t s one step removed." T h i s suggests t h a t i n m o d e l l i n g the behaviour of owners of c l o s e l y - h e l d c o r p o r a t i o n s , i t i s important to s t a r t w i t h the owner's u t i l i t y maximization problem(s) r a t h e r than a s s i g n i n g some o b j e c t i v e such as p r e s e n t value maximization t o the c o r p o r a t i o n . The u t i l i t y maximization method allows the p e r s o n a l tax system as w e l l as the c o r p o r a t e tax system to i n f l u e n c e the d e c i s i o n s of the owners. T h i s i s important because i t i s apparent from the l i t e r a t u r e w r i t t e n by tax p r a c t i t i o n e r s t h a t owners of c l o s e l y - h e l d c o r p o r a t i o n s c o n s i d e r both l e v e l s of t a x a t i o n i n making d e c i s i o n s about f i -n a n c i a l p o l i c y . The o t h e r reason why a separate economic theory of c l o s e l y -h e l d c o r p o r a t i o n s i s necessary i s t h a t t h e i r tax s i t u a t i o n i s q u i t e d i f f e r e n t from w i d e l y - h e l d c o r p o r a t i o n s . Mainly, t h i s i s a r e s u l t of the d i f f e r e n c e i n economic c h a r a c t e r i s t i c s . One example i s t h a t owners o f c l o s e l y - h e l d c o r p o r a t i o n s have a c h o i c e between remunerating themselves i n d i v i d e n d s or i n s a l a r y , w h i l e owners of w i d e l y - h e l d c o r p o r a t i o n s cannot pay themselves a s a l a r y because they do not work f o r the c o r p o r a t i o n . Another example i s t h a t owners of c l o s e l y - h e l d c o r p o r a t i o n s can convert t a x a b l e d i v i d e n d s i n t o c a p i t a l gains through the use of a 5 complicated type o f co r p o r a t e r e o r g a n i z a t i o n . I t i s the smal l number of shareholders i n a c l o s e l y - h e l d c o r p o r a t i o n t h a t makes t h i s manoeuver, known as "s u r p l u s s t r i p p i n g , " p o s s i b l e . Yet another example i s t h a t a c l o s e l y - h e l d b u s i n e s s i s i n a p o s i t i o n to choose, mainly on the b a s i s of tax f a c t o r s , between o p e r a t i n g the b u s i n e s s as a p a r t n e r s h i p and as a c o r p o r a t i o n , while f o r a p u b l i c l y - h e l d b u s i n e s s t h i s i s seldom a v i a b l e q u e s t i o n due to the non-tax f a c t o r s . There i s another reason why the tax s i t u a t i o n of c l o s e l y -h e l d c o r p o r a t i o n s i s so d i f f e r e n t from w i d e l y - h e l d c o r p o r a t i o n s : governments may l e g i s l a t e tax p r o v i s i o n s which apply only to c l o s e l y - h e l d c o r p o r a t i o n s . In p a r t t h i s i s a response to the g r e a t e r o p p o r t u n i t y f o r tax avoidance and. tax-based d e c i s i o n -making i n c l o s e l y - h e l d c o r p o r a t i o n s , as d i s c u s s e d above. Examples of t h i s type are p r o v i s i o n s which are intended to det e r the accumulation of u n d i s t r i b u t e d c o r p o r a t e income which i s i n v e s t e d i n non-business a s s e t s , such as the p e r s o n a l h o l d i n g company tax i n the U.S. and the P a r t IV tax i n Canada.^ Another s e t of tax p r o v i s i o n s a p p l y i n g o n l y to c l o s e l y - h e l d c o r p o r a t i o n s are those intended t o p r o v i d e r e l i e f f o r smal l b u s i n e s s , such as Subchapter S i n the U.S. and the s m a l l business deduction i n Canada. T h i s o b j e c t i v e o f t e n c l a s h e s w i t h the p r e v i o u s one because tax r e l i e f f o r s m a l l b u s i n e s s may c r e a t e o p p o r t u n i t i e s f o r tax avoidance. 6 The t h e o r e t i c a l l i t e r a t u r e i n economics r e l a t i n g to c l o s e l y - h e l d c o r p o r a t i o n s has been of two types. One type of l i t e r a t u r e c o n s i s t s of s t a t i c models of the consumption, labour supply and p r o d u c t i o n d e c i s i o n s of b u s i n e s s p r o p r i e t o r s . These models have been developed and a p p l i e d e m p i r i c a l l y to f a m i l y farms by Barnum and S q u i r e (1979), Lau, L i n and Yotopoulos (1978), and Lopez (1980). T h i s l i t e r a t u r e i s not of much re l e v a n c e to t h i s study as i t does not d e a l w i t h the f i n a n c i a l d e c i s i o n s of c o r p o r a t i o n owners, but i t may have much to c o n t r i b u t e to a f u t u r e u n i f i e d theory of the r e a l and f i n a n -c i a l d e c i s i o n s of a l l types of c l o s e l y - h e l d b u s i n e s s e s . The second type of l i t e r a t u r e c o n s i s t s of dynamic models of c o r p o r a t e investment and f i n a n c i a l p o l i c y . The two models of t h i s type, S t i g l i t z (1973) and Boadway and Bruce (19 79) , use the assumption of u t i l i t y maximization on the p a r t of the owner to determine, i n each p e r i o d , the amount of borrowing and l e n d -i n g by the owner i n h i s p e r s o n a l c a p a c i t y , the amount of borrow-i n g and l e n d i n g by the c o r p o r a t i o n and the amount of r e a l investment by the c o r p o r a t i o n . The l a s t two d e c i s i o n s determine the amount of the owner's remuneration, with the form of the remuneration being e i t h e r a l l d i v i d e n d s (Boadway and Bruce), or repayment of loans from the owner to h i s c o r p o r a t i o n , f o l l o w e d by d i v i d e n d s ( S t i g l i t z ) . As models of the behavior of c l o s e l y -h e l d c o r p o r a t i o n s , which n e i t h e r of them s p e c i f i c a l l y c l aims to 7 be, they are d e f i c i e n t i n t h a t they do not take account o f the s p e c i a l tax s i t u a t i o n o f c l o s e l y - h e l d c o r p o r a t i o n s . 5 The owner's c h o i c e between d i v i d e n d s and s a l a r y as forms of remu-n e r a t i o n i s not c o n s i d e r e d , and none of the s p e c i a l tax p r o v i s i o n s f o r c l o s e l y - h e l d c o r p o r a t i o n s are modelled. The s p e c i a l p r o v i s i o n s t h a t should be modelled vary from country t o country. In the U.S., the most important are Subchapter the accumulated earnings tax and the p e r s o n a l h o l d i n g company tax; i n Canada, the s m a l l business d e d u c t i o n i s the key p r o v i -s i o n . A completely d i f f e r e n t l i t e r a t u r e on c l o s e l y - h e l d corpor-a t i o n s i s t h a t produced by lawyers and accountants t o help other tax p r a c t i t i o n e r s a dvise t h e i r c l i e n t s . The tax p r a c t i -t i o n e r l i t e r a t u r e does take i n t o account the s p e c i a l tax s i t u a t i o n o f c l o s e l y - h e l d c o r p o r a t i o n s , as i t must i n view of i t s purpose, and so i t i s a f r u i t f u l source o f i n f o r m a t i o n and i n s i g h t s . On the ch o i c e between d i v i d e n d s and s a l a r y by Canadian c l o s e l y - h e l d c o r p o r a t i o n s , f o r example, the work of Reid (1979), McNair (1978), Cadesky and Kwan (1981), and Kwan and Murray (19 81), i s very u s e f u l . T h i s work c o u l d be improved by the a p p l i c a t i o n o f mathematical and q u a n t i t a t i v e methods, however. The s t a t e o f the a r t on the q u a n t i t a t i v e s i d e appears to be the computer-based g r i d - s e a r c h approach of t r y i n g out a l a r g e number of p o s s i b l e combinations o f d i v i d e n d s and s a l a r y , as e x e m p l i f i e d by Novis and Lazarus (1980). In a d i f f e r e n t 8 context, an example of how t h i s c o u l d be done has been p r o v i d e d i n the a p p l i c a t i o n by Reinders, Boehlje and H a r l (1980) of l i n e a r programming t o a U.S. e s t a t e p l a n n i n g problem. 1.2 PURPOSE AND OUTLINE OF THE STUDY The t h e o r e t i c a l p a r t of t h i s t h e s i s aims to c o n s t r u c t and s o l v e a model of the f i n a n c i a l p o l i c y of Canadian c l o s e l y -h e l d c o r p o r a t i o n s . I t w i l l combine the mathematical and q u a n t i t a t i v e approach of the economic l i t e r a t u r e w i t h the i n s t i t u t i o n a l tax i n f o r m a t i o n on c l o s e l y - h e l d c o r p o r a t i o n s d e r i v e d from the w r i t i n g s of tax p r a c t i t i o n e r s . Chapter 2 se t s out t h i s t h e o r e t i c a l model, d e l i n e a t i n g the choice v a r i a b l e s and c o n s t r a i n t s f a c i n g the owner of a c l o s e l y - h e l d c o r p o r a t i o n who wishes to choose the f i n a n c i a l p o l i c y of h i s c o r p o r a t i o n so as to maximize h i s u t i l i t y . The model i s s o l v e d by the Kuhn-Tucker method, the c o n d i t i o n s f o r an optimum are s p e c i f i e d and ex p l a i n e d , and a s e r i e s of diagrams showing common optimal f i n a n c i a l p o l i c i e s i s presented. Chapter 3 shows how the model can be m o d i f i e d to compute a c t u a l optimal f i n a n c i a l p o l i c i e s by l i n e a r programming. T h i s method i s used t o perform s i m u l a t i o n s which examine the c a l c u l a t i o n of tax expenditures, i n t e g r a t i o n of c o r p o r a t e and p e r s o n a l income taxes, the choice between r e g i s t e r e d r e t i r e m e n t savings plans and d e f e r r e d p r o f i t - s h a r i n g p l a n s , and the e f f e c t i v e p r i c e s o f tax a b l e and non-taxable b e n e f i t s . Chapter 4 d i s c u s s e s how c e r t a i n assumptions of the t h e o r e t i c a l model might be r e l a x e d and how t h a t would a f f e c t the 9 a n a l y s i s . These assumptions are s t a t i c u t i l i t y maximization and the ownership of the c o r p o r a t i o n by one i n d i v i d u a l . Chapters 2, 3 and 4 are based on the tax r u l e s p r e v a i l i n g p r i o r to the November 12, 1981 f e d e r a l budget p r o p o s a l s . The e m p i r i c a l p a r t of the t h e s i s a p p l i e s an amended v e r s i o n of the t h e o r e t i c a l model t o a sample of Saskatchewan farmers i n 1978, c a l c u l a t i n g f o r each farmer the estimated d i f f e r e n c e i n the t o t a l tax burden f o r 1977 between o p e r a t i n g i n i n c o r p o r a t e d and u n i n c o r p o r a t e d forms. T h i s d i f f e r e n c e , along w i t h other v a r i a b l e s , i s used to e x p l a i n the observed p a t t e r n of forms of business o r g a n i z a t i o n used by Saskatchewan farmers and to p r e d i c t the e f f e c t s of two r e c e n t tax changes on t h i s p a t t e r n . T h i s work, r e p o r t e d i n Chapter 5, i s an e x t e n s i o n of the theory to cover the choice of o r g a n i z a t i o n a l form, and a l s o a t e s t o f the assumption t h a t the owners of c l o s e l y - h e l d c o r p o r a t i o n s w i l l adopt the optimal tax p l a n n i n g s t r a t e g i e s . Chapter 6, which concludes the t h e s i s , summarizes the f i n d i n g s and d i s c u s s e s the i m p l i c a t i o n s f o r tax p o l i c y . 10 N O T E S 1. See O'Neal (1971) and I a c o b u c c i and Johnston (1973) . 2. M i n i s t r y of S t a t e f o r Small Business (1978) . 3. Smith (1952), p. 1. 4. P a r t IV tax a l s o a p p l i e s to p r i v a t e c o r p o r a t i o n s which are not C a n a d i a n - c o n t r o l l e d . See H a r r i s (1981). 5. Boadway and Bruce (1979) a l s o i n c l u d e i n t h e i r model a cor p o r a t e borrowing c o n s t r a i n t based on l i m i t e d l i a b i l i t y . T h i s i s not a p p r o p r i a t e f o r c l o s e l y - h e l d c o r p o r a t i o n s s i n c e banks, o f t e n r e q u i r e the owners to p r o v i d e p e r s o n a l guarantees f o r c o r p o r a t e l o a n s . See B a r c l a y (1979) and B i r d (1974). CHAPTER 2 THE MODEL AND ITS SOLUTION 2 . 1 THE MODEL Consider the s i m p l e s t p o s s i b l e owner-manager s i t u a t i o n : one i n d i v i d u a l owns 1 0 0 % of the shares o f a c o r p o r a t i o n ; t h a t i n d i v i d u a l , the owner, i s a l s o an employee of the c o r p o r a t i o n — u s u a l l y i t s p r e s i d e n t ; and a l l o f the other employees are a t arm's l e n g t h to the owner, so the r e i s no reason to pay them i n f l a t e d s a l a r i e s . The owner's o b j e c t i v e i n t h i s s t a t i c model i s t o maximize h i s u t i l i t y U (Z f + Z p, X f + X p, I) ( 1 ) where U i s a s t r i c t l y i n c r e a s i n g f u n c t i o n of non-taxable b e n e f i t goods ( Z f + Z p), t a x a b l e b e n e f i t goods (X f + X P ) V and a H i c k s i a n composite o f a l l other goods ( I ) . Non-taxable and t a x a b l e b e n e f i t goods are the types of goods which a c o r -p o r a t i o n might p r o v i d e as f r i n g e b e n e f i t s t o i t s owner, although the owner c o u l d purchase them p e r s o n a l l y . 1 Expenditures by the c o r p o r a t i o n on e i t h e r type o f goods are a d e d u c t i b l e expense to i t , but expenditures on these goods by the owner p e r s o n a l l y are not d e d u c t i b l e t o him. Non-taxable b e n e f i t goods purchased by the f i r m (Z f) do not a f f e c t the p e r s o n a l income tax p o s i t i o n of the owner, and are co n s i d e r e d by him to be a p e r f e c t s u b s t i -t u t e f o r non-taxable b e n e f i t goods purchased p e r s o n a l l y ( Z p ) . Taxable b e n e f i t goods purchased by the f i r m (X f) are p a r t i a l l y i n c l u d e d i n computing the ta x a b l e income of i t s owner, and are 1 1 12 a perfect substitute for taxable benefit goods purchased personally ( X p). Purchases by the firm of these two types of goods are also known as in-kind benefits, and the two categories of in-kind benefits are commonly known as non-taxable benefits and taxable benefits. Non-taxable benefits include: restaurant meals and entertainment expenses, prov-ided that there i s some business purpose; f i r s t - c l a s s t r a v e l , as opposed to economy class; l a v i s h o f f i c e furniture and decorations; and company-sponsored health care and dental plans. Taxable benefits include company cars, company a i r c r a f t and holiday t r i p s . The exact contents of the two categories of benefits change from time to time with the current assessing p o l i c y of the Department of National Revenue. Taxable benefits, e s p e c i a l l y company cars, have become very popular among a l l types of highly-paid employees, not only owners of closely-held corporations. One reason i s that the corporation may be able to get a discount that an in d i v i d u a l purchaser could not. Besides reducing the corporation's cost t h i s reduces the amount of the benefit which has to be included i n the employee's income, since the Department of National Revenue values the benefit at the lower of cost and f a i r market value. Another reason for the popularity of taxable benefits i s that often only a small proportion of the company's expendi-ture has to be included i n the employee's income. The c l a s s i c 13 example of t h i s i s l e a s e d company c a r s , one of the most popular t a x a b l e b e n e f i t s , f o r which on l y o n e - t h i r d of the r e n t a l c o s t has to be i n c l u d e d i n the employee's income. A c c o r d i n g to the l e t t e r of the law, i t appears t h a t t h i s f r a c t i o n should a c t u a l l y be the p r o p o r t i o n o f the car ' s use which i s p e r s o n a l , i f t h i s i s high e r than one-t h i r d , but t h i s i s not u s u a l l y e n f o r c e d . Both t a x a b l e and non-taxable b e n e f i t s must have some business purpose i n order to be a d e d u c t i b l e expense to the f i r m . The a p p r o p r i a t e way to r e c o g n i z e t h i s f a c t i n an economic model i s to i n c l u d e the amount of these goods i n the p r o d u c t i o n f u n c t i o n , as i s done by C l o t f e l t e r (1979). T h i s i s not done i n the presen t model i n order to concentrate s o l e -l y on f i n a n c i a l p o l i c y , so the e f f e c t i v e p r i c e of these goods w i l l be o v e r s t a t e d t o some e x t e n t . The presence of "perks" such as t a x a b l e and non-taxable b e n e f i t s i n the owner-manager's u t i l i t y f u n c t i o n i m p l i e s t h a t p r o f i t maximization cannot be an o b j e c t i v e of the c l o s e l y - h e l d c o r p o r a t i o n . Both perks and the owner's s a l a r y are expenses to the c o r p o r a t i o n , so i t c o u l d have no p r o f i t a t a l l even though i t was very h e a l t h y f i n a n c i a l l y , i f perks and s a l a r y were the owner's p r e f e r r e d methods of compensation. The same r e s u l t occurs i n Williamson's (1964) model of a manager-c o n t r o l l e d c o r p o r a t i o n , i n which there e x i s t s a c l a s s of expenses 14 managers c o n t r o l f o r t h e i r own b e n e f i t . The model of Lopez (1980) a l s o y i e l d s a s i m i l a r r e s u l t , but i n h i s model the c o n c l u s i o n t h a t c l o s e l y - h e l d f i r m s w i l l not maximize p r o f i t s i s reached by examining the labour supply d e c i s i o n of the owner. Taxable b e n e f i t s , non-taxable b e n e f i t s and s a l a r y are t h r e e o f the s i x compensation c h o i c e s f o r the owner, the o t h e r three being t a x a b l e d i v i d e n d s , c a p i t a l d i v i d e n d s , and repayment of loans from the owner. S a l a r y i s a c h o i c e v a r i a b l e because the owner i s assumed to be an employee of h i s c o r p o r a -t i o n , which i s t y p i c a l f o r c l o s e l y - h e l d c o r p o r a t i o n s . Taxable d i v i d e n d s are the o r d i n a r y s o r t of d i v i d e n d s t h a t c o r p o r a t i o n s of a l l types pay. C a p i t a l d i v i d e n d s are a s p e c i a l type of d i v i d e n d which can be p a i d o n l y by p r i v a t e c o r p o r a t i o n s , and which have the advantage of being non-taxable. The repayment o f loans from the owner i s not u s u a l l y c o n s i d e r e d a form of compensation, but i t can be c o n s i d e r e d as such because i t i s a way of t r a n s f e r r i n g money from the c o r p o r a t i o n to i t s owner, j u s t l i k e d i v i d e n d s or s a l a r y . Loan repayments have no tax consequences i n t h i s model, e i t h e r to the c o r p o r a t i o n or to i t s owner. The v a r i a b l e f o r l o a n repayments i n the model i s allowed to be n e g a t i v e , i n d i c a t i n g t h a t loans from the owner are being i n c r e a s e d r a t h e r than r e p a i d . T h i s i s not s t r i c t l y a compensation c h o i c e , but i t allows other forms of compen-s a t i o n to be l a r g e r than would otherwise be p o s s i b l e w i t h a 15 given amount of money a v a i l a b l e f o r compensation. Some of the compensation c h o i c e s which are not i n c l u d e d i n the model are the r e d u c t i o n of paid-up c a p i t a l , loans to the owner, s u r p l u s s t r i p p i n g , and the repurchase by the c o r -p o r a t i o n of i t s own shares. Reduction of paid-up c a p i t a l i s a s t r a t e g y t h a t may be employed i f more than a nominal amount of the owner's e q u i t y investment has been made i n the form of share c a p i t a l . T h i s i s r a r e f o r c l o s e l y - h e l d c o r p o r a t i o n s , as most investment u s u a l l y comes i n the form o f loans from the s h a r e h o l d e r s , but i f i t occurs the investment can be r e t u r n e d i n t h i s way. Such payments are non-taxable, so f o r the purpose of t h i s model, t h i s compensation method i s i d e n t i c a l t o repay-ment of loans from the owner. Loans to the owner are,a q u i t e d i f f e r e n t matter. Except i n very l i m i t e d circumstances, such loans are viewed as d i s g u i s e d d i v i d e n d s and are t h e r e f o r e s u b j e c t t o very s e r i o u s tax consequences, so t h i s i s not an a t t r a c t i v e compensation c h o i c e . Another compensation c h o i c e i s the d i s t r i b u t i o n of c o r p o r a t e s u r p l u s i n the form o f c a p i t a l gains through a complicated c o r p o r a t e r e o r g a n i z a t i o n . Known as " s u r p l u s s t r i p p i n g " or " d i v i d e n d s t r i p p i n g , " t h i s method of remuneration appears to have been exterminated by a combina-t i o n of the a d d i t i o n of a s p e c i a l a n t i - s t r i p p i n g s e c t i o n of the Income Tax Act and the r e d u c t i o n of the tax burden on.dividends r e l a t i v e to c a p i t a l gains i n 1978. Another p o t e n t i a l method 16 of removing money from the c o r p o r a t i o n i s the repurchase of some of the owner's shares by the c o r p o r a t i o n a t an amount g r e a t e r than t h e i r paid-up c a p i t a l . T h i s method has been blocked by a p r o v i s i o n i n the Income Tax Act which deems the excess over paid-up c a p i t a l to be a t a x a b l e d i v i d e n d r a t h e r than a c a p i t a l g a i n . The f i r s t c o n s t r a i n t on the maximization of the owner's u t i l i t y i s a p e r s o n a l budget c o n s t r a i n t , which s t a t e s t h a t a l l o f the owner's d i s p o s a b l e income i s spent on p e r s o n a l purchases of t a x a b l e b e n e f i t goods, non-taxable b e n e f i t goods, X f x p and the composite of a l l other goods, a t p r i c e s p . p a n d I. S + L + D r + D n r 4 D K A T yP 7P n - { ( 1 + p) | B ± " B ! ~ 0.09-B3} = p i + p X P + p Z p (2) 1=1 The owner's gross income i s the sum of cash compensation r e c e i v e d as s a l a r y (S), repayment of loans to the c o r p o r a t i o n K r nr 3 ( L ) , c a p i t a l d i v i d e n d s (D ), and t a x a b l e d i v i d e n d s (D + D ). (The d i f f e r e n c e between the two types of t a x a b l e d i v i d e n d s i s e x p l a i n e d l a t e r i n the chapter.) The e x p r e s s i o n i n c u r l y b r a c k e t s i s p e r s o n a l income tax, which i s b a s i c f e d e r a l tax 4 4 (•£ B. ) p l u s p r o v i n c i a l tax (p j B.), l e s s the f e d e r a l tax i = l 1 i = l 1 4 r e d u c t i o n (B^ + 0.09 B^). P r o v i n c i a l tax i s t r e a t e d as a f i x e d p r o p o r t i o n (p) of b a s i c f e d e r a l tax, which i s not too g r e a t a s i m p l i f i c a t i o n i n p r o v i n c e s other than Quebec. 5 17 B a s i c f e d e r a l tax i s w r i t t e n as the sum of f o u r amounts to make i t p o s s i b l e t o express the f e d e r a l tax r e d u c t i o n simply. The f e d e r a l tax r e d u c t i o n i s a piecewise l i n e a r f u n c t i o n o f b a s i c f e d e r a l tax wi t h f o u r l i n e a r segments, so b a s i c f e d e r a l tax i s d i v i d e d i n t o f o u r b r a c k e t s . The f i r s t b r a c k e t covers the f i r s t $200 of b a s i c f e d e r a l tax, and i n t h i s range the f e d e r a l tax r e d u c t i o n i s equal to b a s i c f e d e r a l tax. The $200 l i m i t i s imposed by: B± £ 200 (3) The second b r a c k e t covers the next $2,022 of b a s i c f e d e r a l tax: B 2 I 2,022 (4) In t h i s range the f e d e r a l tax r e d u c t i o n i s constant. The b r a c k e t ends when 9% of b a s i c f e d e r a l tax i s equal to $200, which occurs when b a s i c f e d e r a l tax equals $2,022 p l u s $200. or $2,222. In the next b r a c k e t the f e d e r a l tax r e d u c t i o n i s $200 p l u s 9% of b a s i c f e d e r a l tax over $2,222, and i t ends when t h i s t o t a l reaches the f e d e r a l tax r e d u c t i o n maximum of $500. T h i s occurs when b a s i c f e d e r a l tax reaches $5,556, so the l i m i t on the t h i r d b r a c k e t i s $5,556 l e s s $2,222, or $3,334: B'3 Z 3,334 (5) The f e d e r a l tax r e d u c t i o n i s constant once the maximum has been reached, so the f o u r t h b r a c k e t has no c e i l i n g . There i s 18 one problem w i t h the d i v i s i o n o f b a s i c f e d e r a l tax i n t o f o u r b r a c k e t s : there i s nothing to ensure t h a t the b r a c k e t s are f i l l e d i n the r i g h t order, which i s necessary f o r the c a l c u -l a t i o n of the f e d e r a l tax r e d u c t i o n to be c o r r e c t . U t i l i t y maximization i m p l i e s t h a t the b r a c k e t s w i l l be f i l l e d i n de-c r e a s i n g order of the r a t e s of the f e d e r a l tax r e d u c t i o n , which causes a problem because the t h i r d b r a c k e t , w i t h i t s 0.09 r a t e , w i l l be f i l l e d b e f o r e the second. The s o l u t i o n i s to add a c o n s t r a i n t t h a t the second b r a c k e t must be f i l l e d b e f o r e the t h i r d : B 3 (2,022 - B 2) = 0 (6) B a s i c f e d e r a l tax i s d e f i n e d as f e d e r a l income tax on t a x a b l e income ( i ^ t . Y?) l e s s the d i v i d e n d tax c r e d i t : i = l 4 13 Z B. > E t . Y? - (3/8) (D r + D n r) (7) i = l 1 i = l 1 1 The d i v i d e n d tax c r e d i t i s g e n e r a l l y t h r e e - e i g h t h s of t a x a b l e d i v i d e n d s , but i t cannot exceed f e d e r a l income tax on t a x a b l e income. 6 The i n e q u a l i t y s i g n handles t h i s problem by a l l o w i n g the c o n s t r a i n t to become non-binding i f the r i g h t - h a n d s i d e i s n e g a t i v e , as each i s r e s t r i c t e d t o be non-negative. On the o t h e r hand, u t i l i t y maximization i m p l i e s t h a t the c o n s t r a i n t w i l l be b i n d i n g i f the r i g h t - h a n d s i d e i s non-negative. F e d e r a l income tax on t a x a b l e income i s a piecewise l i n e a r f u n c t i o n of t a x a b l e income, j u s t as the f e d e r a l tax r e d u c t i o n i s a piecewise l i n e a r f u n c t i o n of b a s i c f e d e r a l tax, so i t i s 19 convenient to use the same t r i c k of d i v i d i n g the independent v a r i a b l e i n t o b r a c k e t s . T h i s allows f e d e r a l income tax on t a x a b l e income to be w r i t t e n as the sum over b r a c k e t s of the amount of t a x a b l e income f a l l i n g i n t o each b r a c k e t (Y?) mul-t i p l i e d by the a p p r o p r i a t e f e d e r a l m a r g i n a l tax r a t e ( t ^ ) . There are t h i r t e e n b r a c k e t s , and each but the h i g h e s t b r a c k e t has a l i m i t on the amount of t a x a b l e income which i t can c o n t a i n : Y? £. Y? i = 1.2 ... 12 (8) i i ' U t i l i t y maximization i m p l i e s t h a t the t a x a b l e income brack e t s w i l l be f i l l e d i n i n c r e a s i n g order o f f e d e r a l marginal tax r a t e s . T h i s i s the c o r r e c t order i n t h i s case, so i t i s not necessary to impose a c o n s t r a i n t l i k e (6). The p e r s o n a l s i d e of the model i s completed by the d e f i n i -t i o n of p e r s o n a l t a x a b l e income: 13 f E Y? > S + (3/2) (D r + D n r) + r p X X f - A (9) 1=1 i The r i g h t - h a n d s i d e i s computed as s a l a r y p l u s grossed-up tax-able d i v i d e n d s , p l u s the f r a c t i o n (r) of the f i r m ' s expenditure on t a x a b l e b e n e f i t s (p X ) which the owner must i n c l u d e i n h i s t a x a b l e income, l e s s p e r s o n a l exemptions and deductions (A). P e r s o n a l exemptions 5 and deductions are t r e a t e d as exogenous, i g n o r i n g the dependence of the employment expense deduction on 20 s a l a r y . The amount of t a x a b l e d i v i d e n d s p a i d by the c o r p o r a t i o n does not a f f e c t the i n t e r e s t , d i v i d e n d s , and c a p i t a l gains deduction of the owner s i n c e d i v i d e n d s from a c o r p o r a t i o n which i s not a t arm's l e n g t h do not q u a l i f y f o r t h i s d e d u c t i o n . U t i l i t y maximization i m p l i e s t h a t the p e r s o n a l t a x a b l e income c o n s t r a i n t w i l l be b i n d i n g i n most circumstances. I t w i l l not be b i n d i n g i f the r i g h t - h a n d s i d e i s n e g a t i v e , s i n c e each Y? i s c o n s t r a i n e d to be non-negative, or i f b a s i c f e d e r a l tax i s reduced to zero by the d i v i d e n d tax c r e d i t . On the c o r p o r a t e s i d e of the model there i s a l s o a budget c o n s t r a i n t : M = S+L + D K + D r+ D n r + X f+ p 7' f Z r + u SY S t u ¥ - (D r / 4 ) (10) I t s t a t e s t h a t as a r e s u l t of the c o r p o r a t i o n ' s p r o d u c t i o n , r e a l investment, borrowing and l e n d i n g d e c i s i o n s , which are a l l exogenous to the model, the c o r p o r a t i o n has some f i x e d amount of money a v a i l a b l e to pay c o r p o r a t e income tax and compensation to the owner. Out of t h i s amount, P a r t IV tax income from p o r t f o l i o d i v i d e n d s and P a r t I tax on Canadian investment income are p a i d , and then the amount of money t h a t remains i s the amount M i n the budget c o n s t r a i n t . 7 T h i s amount i s d i v i d e d among the s i x d i f f e r e n t types of owner's compensation and the remaining c o r p o r a t e income tax l i a b i l i t y , which i s c o r p o r a t e income tax on a c t i v e business income and 21 n o n - q u a l i f y i n g business income ( u V + u^Y^) l e s s the d i v i d e n d refund ( D r / 4 ) . 8 Although t h i s account i m p l i e s t h a t the v a r i o u s f i n a n c i a l d e c i s i o n s are made s e q u e n t i a l l y and a l l a t one time, i t i s more c o r r e c t to t h i n k o f these d e c i s i o n s as the f i n a l outcome of a s e r i e s o f c h o i c e s made a t v a r i o u s times i n the year. In the c o r p o r a t e budget c o n s t r a i n t i t i s important to d i s t i n g u i s h between Canadian investment income and a c t i v e g b u s i n e s s income. Canadian investment income g e n e r a l l y i n c l u d e s i n t e r e s t , r e n t a l s , and the t a x a b l e h a l f o f c a p i t a l g a i n s , but these types o f income may be c o n s i d e r e d to be a c t i v e b u s i n e s s income i f the income i s i n c i d e n t a l to an a c t i v e b u s i n e s s , such as i n t e r e s t on accounts r e c e i v a b l e , or i f the number of employees who are not a l s o s i g n i f i c a n t shareholders i n the busi n e s s exceeds f i v e . A c t i v e b u s i n e s s income, which i s the type of income t h a t most businesses earn, may a l s o q u a l i f y as manufac-t u r i n g and p r o c e s s i n g p r o f i t s . One type o f business income t h a t i s excluded from a c t i v e b u s i n e s s income i s n o n - q u a l i f y i n g business income, which i s a category o f income c r e a t e d i n 1979 to c a t c h the incomes of i n c o r p o r a t e d p r o f e s s i o n a l s , management c o r p o r a t i o n s f o r p r o f e s s i o n a l s , and p e r s o n a l s e r v i c e c o r p o r a -t i o n s . T h e r e f o r e , the f i v e types o f taxed c o r p o r a t e income t h a t are d i s t i n g u i s h e d i n the model are income from p o r t f o l i o dividends,. Canadian investment income, a c t i v e business income 22 from manufacturing and p r o c e s s i n g , other a c t i v e business income, and n o n - q u a l i f y i n g business i n c o m e . 1 0 For s i m p l i c i t y i t i s assumed t h a t the c o r p o r a t i o n earns o n l y one of the l a s t three types of income. The tax r a t e s a p p l y i n g to the v a r i o u s types of c o r p o r a t e income vary from p r o v i n c e to p r o v i n c e , except f o r P a r t IV tax, which i s a s o l e l y f e d e r a l tax imposed a t a 25% r a t e . In B.C. i n 19 80, the combined f e d e r a l and p r o v i n c i a l r a t e s on the o t h e r f o u r types of taxed c o r p o r a t e income were: Canadian investment income, 52.8%; n o n - q u a l i f y i n g business income, 39.5% and 52.8%; a c t i v e business income from manufacturing and pro-c e s s i n g , 20.5% and 46.5%; and other a c t i v e business income, 25.75% and 52.8%. N o n - q u a l i f y i n g business income and the two c a t e g o r i e s of a c t i v e business income each have two r a t e s l i s t e d because p a r t o f these types of income i s e l i g i b l e f o r the s m a l l business deduction and p a r t i s not. The p a r t which i s e l i g i b l e i s i n e f f e c t taxed a t a lower "small b u s i n e s s r a t e , " i£ , and the other p a r t i s taxed a t a " l a r g e business r a t e , " u L . In c o n s t r a i n t (10), the amounts of the c o r p o r a t i o n ' s income which S L are taxed a t the two r a t e s are d e s i g n a t e d as Y and Y r e s p e c -S S L L t i v e l y , so the t o t a l tax of t h i s type i s u Y + u Y . The o n l y aspect of c o n s t r a i n t (10) remaining to be e x p l a i n e d i s the d i v i d e n d refund (D r/4). T h i s i s a r e f u n d a b l e tax c r e d i t o f one-quarter of the amount of t a x a b l e d i v i d e n d s p a i d , up to 23 the balance i n the refu n d a b l e d i v i d e n d tax on hand account. The RDTOH balance i s i n c r e a s e d by the amount of P a r t IV tax p a i d and the amount of refundable P a r t I tax, where the l a t t e r amount i s o n e - s i x t h of the c o r p o r a t i o n ' s Canadian investment income. The purposes of t h i s system are to i n t e g r a t e corpo-r a t e and p e r s o n a l taxes on Canadian investment income and income from p o r t f o l i o d i v i d e n d s , and to encourage p r i v a t e c o r p o r a t i o n s to pay t a x a b l e d i v i d e n d s from these types o f income t o sh a r e h o l d e r s . The system i s modelled by d i v i d i n g t a x a b l e d i v i d e n d s i n t o two types, one t h a t q u a l i f i e s f o r a • r nr d i v i d e n d refund, D , and one t h a t does not, D . T h i s makes the d i v i d e n d refund Dr/4 and the maximum amount of tax a b l e — d i v i d e n d s which q u a l i f y f o r a d i v i d e n d refund D ; D r -1 D r (11) where D i s f o u r times the RDTOH balance. Taxable d i v i d e n d s which do not q u a l i f y f o r a d i v i d e n d refund may not be p a i d u n t i l the RDTOH balance has been reduced to zero. D n r (D r - D r) = 0 (12) For a reason to be d i s c u s s e d below, u t i l i t y maximization by the owner without t h i s c o n s t r a i n t might not l e a d to the c o r -r e c t order o f t a x a b l e d i v i d e n d payments. The amount of a c t i v e business income or n o n - q u a l i f y i n g business income which i s taxed a t the sm a l l b u s i n e s s r a t e u 24 i s l i m i t e d t o a maximum amount Y by the terms of the s m a l l business deduction: Y S i Y S (13) One of the l i m i t s i s the business l i m i t , which r e s t r i c t s the amount o f a c t i v e business income or n o n - q u a l i f y i n g business income which i s e l i g i b l e f o r the reduced r a t e to $150,000 i n any year. The other l i m i t i s the t o t a l b usiness l i m i t , which r e s t r i c t s the amount of reduced-rate income to $750,000 l e s s the balance i n the c o r p o r a t i o n ' s cumulative d e d u c t i o n account at the end of the pre v i o u s t a x a t i o n y e a r . 1 1 I f the pr e v i o u s year's balance i s over $750,000, a l l o f the c o r p o r a t i o n ' s a c t i v e b u s i n e s s income or n o n - q u a l i f y i n g business income i s taxed a t the l a r g e business r a t e . Both of these l i m i t s are independent of the f i r m ' s a c t i o n s i n the c u r r e n t year, so the amount Y i s exogenously determined as the l e s s e r o f the two l i m i t s . The t o t a l business l i m i t f o r f u t u r e years i s a f f e c t e d by c u r r e n t d e c i s i o n s , however,, so the owner may c o n s t r a i n h i s compensation c h o i c e by s p e c i f y i n g t h a t the cumulative deduction account may not i n c r e a s e by more than some s p e c i f i e d amount i n the c u r r e n t year. Since t h i s i s a s t a t i c model, the maximum i n c r e a s e must be s p e c i f i e d exogenously, say as some amount n: Y S +, Y L - (4/3) D n r < n (14) 25 The i n c r e a s e i n the c u r r e n t year i s the c o r p o r a t i o n ' s a c t i v e business income or n o n - q u a l i f y i n g business income f o r the S L year (Y + Y ) l e s s a s p e c i f i e d f r a c t i o n of the amount of t a x a b l e d i v i d e n d s p a i d which do not q u a l i f y f o r a d i v i d e n d refund. The s p e c i f i e d f r a c t i o n i s 4/3 f o r an a c t i v e business ( i n (14) an a c t i v e business i s assumed) and 3/2 f o r a non-q u a l i f y i n g b u s i n e s s . C o n s t r a i n t (14) p r o v i d e s the reason why c o n s t r a i n t (12) i s necessary. I f (14) i s b i n d i n g , there i s an i n c e n t i v e t o v i o l a t e the c o r r e c t order of t a x a b l e d i v i d e n d payments. C o n s t r a i n t (14) a l s o shows how Canadian investment income can c r e a t e a "blockage" i n the cumulative deduction account, s i n c e paying t a x a b l e d i v i d e n d s does not reduce the cumulative deduction account balance u n t i l enough t a x a b l e d i v i d e n d s have been p a i d t o reduce the RDTOH balance to zero. One s o l u t i o n t o t h i s problem t h a t has been recommended i s to move the a s s e t s c r e a t i n g the Canadian investment income i n t o a second c o r p o r a t i o n , but i t i s assumed i n t h i s model t h a t the owner has on l y one c o r p o r a t i o n . The c o r p o r a t i o n ' s a c t i v e business income or n o n - q u a l i f y -i n g b u s i n e s s income i s d e f i n e d as an exogenous gross amount Y*3 l e s s deductions f o r s a l a r y and expenditure on t a x a b l e 12 13 1A b e n e f i t s and non-taxable b e n e f i t s : ' ' Y S + Y L = Y b - S - p x f X f - p z f Z f (15) 26 T h i s assumes t h a t these expenses are f u l l y d e d u c t i b l e , which i s t r u e p r o v i d e d t h a t each expense i s "reasonable" i n amount. The reasonableness c r i t e r i o n has been used i n the c o u r t s to c h a l l e n g e the deduction of some amounts of t a x a b l e and non-ta x a b l e b e n e f i t s , so i t i s assumed t h a t the owner knows the l i m i t s to d e d u c t i b i l i t y and does not exceed them: 1 5 X f 1 X f (16) Zf 1 Z f (17) S t r a n g e l y , the reasonableness c r i t e r i o n i s not used to l i m i t s a l a r i e s p a i d by owner-managers, which i s i n s t r o n g c o n t r a s t 16 to U.S. p o l i c y . The f e a r t h a t t h i s t e s t of d e d u c t i b i l i t y might be a p p l i e d may prevent c l o s e l y - h e l d c o r p o r a t i o n s from paying very l a r g e owners' s a l a r i e s , such as h a l f a m i l l i o n d o l l a r s , but t h i s i s o n l y c o n j e c t u r e . T h i s t e s t probably does prevent l a r g e amounts of s a l a r y and i n - k i n d b e n e f i t s from being charged a g a i n s t Canadian investment income, so these expenses are not d e c i s i o n v a r i a b l e s i n the model. Another compensation c h o i c e f o r the owner, paying c a p i t a l d i v i d e n d s , i s s u b j e c t to a d i f f e r e n t k i n d of l i m i t . The c o r -p o r a t i o n can o n l y pay out c a p i t a l d i v i d e n d s to the extent of the balance i n i t s c a p i t a l d i v i d e n d account: D K i D K (18) 27 The c a p i t a l d i v i d e n d account i s i n c r e a s e d by s e v e r a l types of r e c e i p t s , n o t a b l y the untaxed h a l f of post-1971 net c a p i t a l gains and the untaxed p o r t i o n of the net proceeds from the d i s p o s i t i o n of e l i g i b l e c a p i t a l p r o p e r t y such as trademarks, government l i c e n c e s , and government quotas. The i n t e n t of t h i s p r o v i s i o n i s to i n t e g r a t e c o r p o r a t e and p e r s o n a l income taxes f o r t h i s type of income. The l i m i t t o the repayment of loans from the owner i s the t o t a l amount of loans o u t s t a n d i n g , but there may be a lower l i m i t i f a "postponement of c l a i m " has been signed. T h i s i s an agreement, o f t e n r e q u i r e d as a c o n d i t i o n f o r a bank loan, which p r o v i d e s t h a t loans from the owner are to be t r e a t e d as e q u i t y f o r the purpose of determining the bank's c l a i m on the f i r m ' s a s s e t s i n bankruptcy proceedings, and t h a t such loans are not to be reduced without the bank's c o n s e n t . 1 7 In any event, there w i l l be a l i m i t t o the amount of repayment of loans from the owner: L l L (19) In some circumstances i t may be o p t i m a l to i n c r e a s e the amount of loans from the owner. T h i s i s accommodated i n the model by a l l o w i n g L to p o s s i b l y take on.negative v a l u e s . A problem a r i s e s i f i n c r e a s e s i n loans from the owner - are used to f i n a n c e payment of d i v i d e n d s i n excess, of r e t a i n e d earnings p l u s c u r r e n t - y e a r p r o f i t : the payments above t h i s l e v e l may 2 8 be a t t a c k e d by the Department of N a t i o n a l Revenue as not being d i v i d e n d s a c c o r d i n g t o company law, because they are 18 not d i s t r i b u t i o n s of c o r p o r a t e s u r p l u s . Instead, they may be c o n s i d e r e d to be shareholder b e n e f i t s , which are f u l l y t a x a b l e t o the owner. To a v o i d t h i s problem, the c o r p o r a t i o n w i l l not pay out d i v i d e n d s i n excess of i t s c o r p o r a t e s u r p l u s , One way to do t h i s i s to c o n s t r a i n r e t a i n e d earnings a t the end of the year to be non-negative, which i s d e s i r a b l e i n order to p r o t e c t the c o r p o r a t i o n ' s c r e d i t s t a n d i n g : R + Y S + Y L - u S Y S - u L Y L + (D r /4 ) - D R - D H R - D K > 0 On the l e f t - h a n d s i d e , R i s r e t a i n e d earnings a t the beginning of the year and the r e s t o f the e x p r e s s i o n i s p r o f i t s f o r the year l e s s d i v i d e n d payments, assuming t h a t c o r p o r a t e t a x a b l e income l e s s c o r p o r a t e income tax i s approximately equal to p r o f i t s (as measured by g e n e r a l l y - a c c e p t e d accounting p r i n c i -p l e s ) . Using (10) and (15), t h i s can be w r i t t e n as L 1 L m i n (20). where L m i n = - R - Y*3 + M i s exogenous. In most cases Lm"""n w i l l be n e g a t i v e , i n which case the c o n s t r a i n t says t h a t loans from the owner may not be i n c r e a s e d beyond a c e r t a i n c e i l i n g . The l a s t c o n s t r a i n t i n the model s p e c i f i e s a minimum l e v e l f o r the owner's employment income, which i s the sum of the owner's s a l a r y and the amount of t a x a b l e b e n e f i t s i n c l u d e d i n the owner's t a x a b l e income: S + r p " X" •* S1""11 (21) X „f > „min There are s e v e r a l j u s t i f i c a t i o n s f o r t h i s . One i s t h a t the owner may wish t o make the maximum Canada Pension P l a n c o n t r i b u t i o n so as to be e n t i t l e d to the maximum amount of CPP b e n e f i t s , and the c o n t r i b u t i o n i s l i n k e d to the owner's employment income. Another j u s t i f i c a t i o n i s t h a t the maximum reasonable r e t i r i n g allowance has been l i n k e d by the Depart-ment of N a t i o n a l Revenue to the owner's average employment income f o r the f i v e years p r e c e d i n g r e t i r e m e n t . The advantage of a r e t i r i n g allowance i s t h a t i t can be t r a n s f e r r e d to a r e g i s t e r e d r e t i r e m e n t savings p l a n , so t h a t the tax payable i s d e f e r r e d and i n t e r e s t income earned w i t h i n the p l a n i s t a x - s h e l t e r e d . The sums i n v o l v e d may be very l a r g e : a $240,000 r e t i r i n g allowance was approved as reasonable i n one case. The t h i r d j u s t i f i c a t i o n f o r the employment income c o n s t r a i n t , and probably the most important one, i s t h a t the l i m i t s to r e g i s t e r e d r e t i r e m e n t savings p l a n c o n t r i b u t i o n s and cor p o r a t e d e f e r r e d p r o f i t - s h a r i n g p l a n c o n t r i b u t i o n s are l i n k e d to employ-ment income. T h i s j u s t i f i c a t i o n i s examined i n Chapter 3 below. 2.2 NECESSARY CONDITIONS FOR AN OPTIMUM The above n o n - l i n e a r programming problem may be s o l v e d using the Kuhn-Tucker method to y i e l d the necessary c o n d i t i o n s f o r an optimum. 1 9 The d e r i v a t i o n of these c o n d i t i o n s i s con-t a i n e d i n the appendix. The f i r s t s e t of these c o n d i t i o n s s t a t e s t h a t any f e a s i b l e p e r t u r b a t i o n i n v o l v i n g any two of 30 s a l a r y , t a x a b l e d i v i d e n d s , c a p i t a l d i v i d e n d s and repayment of loans from the owner must not decrease the t o t a l taxes p a i d by the c o r p o r a t i o n and i t s owner. T h i s makes sense, s i n c e otherwise i t would be p o s s i b l e to i n c r e a s e the owner's d i s p o s a b l e income, which would enable him to purchase more goods and i n c r e a s e h i s u t i l i t y . F e a s i b l e p e r t u r b a t i o n s i n v o l v e i n c r e a s i n g one form o f compensation and d e c r e a s i n g another s i m u l t a n e o u s l y s i n c e the cor p o r a t e budget c o n s t r a i n t , (10), r e q u i r e s t h a t the amount of funds d i s t r i b u t e d by the c o r p o r a t i o n must stay constant. F e a s i b l e p e r t u r b a t i o n s a l s o must not v i o l a t e any o f the c o n s t r a i n t s on the v a r i a b l e s . These c o n s t r a i n t s i n c l u d e minimum c o n s t r a i n t s , maximum cons-t r a i n t s , and the c o n s t r a i n t on the change i n the cumulative deduction account. In summary, each of the f i r s t s e t of c o n d i t i o n s s t a t e s t h a t a t the op t i m a l p o i n t , i f v a r i a b l e i i s i n c r e a s e d and v a r i a b l e j i s decreased w i t h the corporat e budget c o n s t r a i n t s t i l l s a t i s f i e d , c o r p o r a t e income tax p l u s the owner's p e r s o n a l income tax must not decrease, u n l e s s : v a r i a b l e i i s a t a maximum, so i t cannot be i n c r e a s e d ; v a r i a b l e j i s a t a minimum, so i t cannot be decreased; or the c u r r e n t - y e a r change i n the cumulative deduction account i s a t the maximum allowed, and the proposed p e r t u r b a t i o n would i n -crease i t f u r t h e r . The s i x c o n d i t i o n s of t h i s type are 31 T S D >. 0 unless Y S + Y L = 0 or D r + D n r = 0 (22a) or ( N S D > 0 and Y S + Y L - (4/3) D n r = n) T D S > 0 unless S = 0 or S + r p ^ X f = S m ± n (22b) or ( N D S > 0 and Y S + Y L - (4/3)D n r = n) T L D > 0 unless L + D K = D K + L or D r + D n r = 0 (22c) or ( N L D > 0 and Y S + Y L - (4/3) D n r = n) T D L > 0 unless L + D K = L m i n (22d) T O V —V — T > 0 unless L + D = D + L or S = 0 . or S + rp X = S (22e) or Y S V+ Y L - (4/3) D n r = n T S L > 0 unless Y S + Y L = 0 or L + D K = L m l n (22f) where T1-1 and N 1^ are the r a t e s of change at the optimum of t o t a l taxes and the cumulative deduction account r e s p e c t i v e l y w i t h v a r i a b l e i i n c r e a s i n g and v a r i a b l e j d e c r e a s i n g so as to continue to s a t i s f y the c o r p o r a t e budget c o n s t r a i n t . The s u p e r s c r i p t s are S f o r s a l a r y , D f o r t a x a b l e d i v i d e n d s , and L f o r c a p i t a l d i v i d e n d s and repayment of loans from the owner. The l a s t two v a r i a b l e s are combined i n t o one because they are p e r f e c t s u b s t i t u t e s i n terms of the model, as both are tax-f r e e ways of t r a n s f e r r i n g money from the c o r p o r a t i o n to i t s 32 owner. Consequently, c o n s t r a i n t s (18) and (19) can be combined i n t o L + D K < D -K + L and L + D' K > LJ m m which are used i n the c o n d i t i o n s above. Three of the s i x c o n d i t i o n s do not i n v o l v e an e x p r e s s i o n f o r the r a t e of change of the cumulative deduction account, because t h i s i s needed o n l y i f the p e r t u r b a t i o n i n c r e a s e s the cumulative deduction account inxsome circumstances and not i n o t h e r s . I n c r e a s i n g t a x a b l e d i v i d e n d s or s a l a r y and d e c r e a s i n g repayment of loans from the owner cannot i n c r e a s e the cumula-t i v e d eduction account i n any circumstances, so (22d) and (22f) have no q u a l i f i c a t i o n r e l a t i n g to i t . On the other hand, i n c r e a s i n g repayment o f loans from the owner and d e c r e a s i n g s a l a r y always i n c r e a s e s the cumulative deduction account, so the o n l y q u a l i f i c a t i o n i n (22e) i s t h a t the cumulative deduc-t i o n account must not be a t the maximum, or e l s e the p e r t u r -b a t i o n i s not f e a s i b l e . A second s e t of necessary c o n d i t i o n s governs the p e r s o n a l purchase of goods by the owner. These c o n d i t i o n s , which cover p e r s o n a l purchases of t a x a b l e b e n e f i t goods, non-taxable bene-f i t goods and a l l o t h e r goods, are the standard c o n d i t i o n s of consumer theory. Assuming t h a t a p o s i t i v e amount of a l l other 33 goods i s purchased, which i s a l s o assumed i n the r e s t o f the necessary c o n d i t i o n s , the c o n d i t i o n s are (23a) m y * (I! • as z p i . ^ 0 (23b) u z x p 2 — 'Z > 0 and X P =1 0 Z p = 0 and X P > 0 Z p > 0 and X p > 0 — as X? < p p \ (23c) where U , U and U T are the marginal u t i l i t i e s of t a x a b l e b e n e f i t goods, non-taxable b e n e f i t goods, and a l l other goods r e s p e c t i v e l y . A t h i r d s e t of necessary c o n d i t i o n s d e a l w i t h the c h o i c e i n c o r p o r a t e purchases of goods between t a x a b l e b e n e f i t goods and non-taxable b e n e f i t goods. The marginal r a t e of s u b s t i t u -t i o n between these two types of goods i s bounded by two tax-a d j u s t e d p r i c e r a t i o s : u x f i V-rr (1 + T X Z ) unless X f = X f or Z f - -,0' (24a) Z Z P U X^ z £ 1 B-F- (1 - T Z X) unless X f = 0 or Z f = Z f (24b) P or S + r p X x f = s m i n 34 C o n d i t i o n (24a) s t a t e s t h a t t h i s marginal r a t e of s u b s t i t u -t i o n i s bounded from above by the p r i c e r a t i o f aced by the f i r m , as a d j u s t e d f o r the change i n t o t a l taxes caused by an i n c r e a s e i n t a x a b l e b e n e f i t s and a decrease i n non-taxable b e n e f i t s , u n l e s s t h i s p e r t u r b a t i o n i s not f e a s i b l e because of minimum and maximum c o n s t r a i n t s on the q u a n t i t i e s of the two goods. C o n d i t i o n (2 4b) s t a t e s t h a t the marginal r a t e of sub-s t i t u t i o n i s bounded from below by another t a x - a d j u s t e d p r i c e , p r o v i d e d t h a t a p e r t u r b a t i o n i n the r e v e r s e d i r e c t i o n i s f e a s i b l e . The i n t u i t i o n behind these c o n d i t i o n s can be ex-p l a i n e d by r e f e r e n c e to F i g u r e 1, assuming an i n t e r i o r s o l u t i o n f o r the c h o i c e v a r i a b l e s . The owner i s choosing the q u a n t i t i e s of t a x a b l e b e n e f i t s and non-taxable b e n e f i t s so as t o maximize h i s u t i l i t y s u b j e c t to a budget c o n s t r a i n t , where the t o t a l budget i s the expenditure on non-taxable b e n e f i t s which i s p o s s i b l e i f t a x a b l e b e n e f i t s equal zero and a l l other v a r i a b l e s are a t f i x e d l e v e l s . In the f i g u r e , the budget c o n s t r a i n t appears as a piecewise l i n e a r f r o n t i e r i n s t e a d of the conven-t i o n a l s t r a i g h t l i n e . The reason i s t h a t i n moving along the budget f r o n t i e r from p o i n t Q, the owner i s i n c r e a s i n g t a x a b l e b e n e f i t s and d e c r e a s i n g non-taxable b e n e f i t s , which i n c r e a s e s h i s t a x a b l e income and e v e n t u a l l y pushes him i n t o a h i g h e r t a x a b l e income b r a c k e t . T h i s causes an i n c r e a s i n g e f f e c t i v e (tax-adjusted) p r i c e of t a x a b l e b e n e f i t s as the amount of t a x a b l e b e n e f i t s purchased i n c r e a s e s , r e s u l t i n g i n the shape 35 X (Taxable B e n e f i t s ) FIGURE 1: Choice of Taxable vs. Non-Taxable B e n e f i t s 36 shown f o r the budget f r o n t i e r . I f the h i g h e s t f e a s i b l e i n d i f f e r e n c e curve touches the budget f r o n t i e r a t one of i t s k i n k s , then the slope of the i n d i f f e r e n c e curve a t t h i s p o i n t w i l l be no l a r g e r i n a b s o l u t e v a l u e than the slope of the budget f r o n t i e r approached from the r i g h t , and no s m a l l e r i n a b s o l u t e value than the slope o f the budget f r o n t i e r approached from the l e f t . C o n d i t i o n s (24) s t a t e e x a c t l y t h i s . I f the h i g h e s t f e a s i b l e i n d i f f e r e n c e curve touches the budget f r o n t i e r on one of i t s s t r a i g h t segments, so there i s a tangency s o l u -XZ ZX t i o n , T w i l l equal -T and the f a m i l i a r e q u a l i t y of a mar-g i n a l r a t e o f s u b s t i t u t i o n to a p r i c e r a t i o w i l l be observed. The f o u r t h and l a r g e s t s e t of necessary c o n d i t i o n s concerns the purchase o f t a x a b l e b e n e f i t goods and non-taxable b e n e f i t goods by the c o r p o r a t i o n i n c o n j u n c t i o n w i t h the purchase of a l l o ther goods by the owner. The p e r t u r b a t i o n s t h a t are i m p l i c i t i n these c o n d i t i o n s are more complicated because the t o t a l c o r p o r a t e expenditure on goods i s changing, as i s the t o t a l p e r s o n a l expenditure on goods. The p e r s o n a l and c o r p o r a t e budget c o n s t r a i n t s must s t i l l be s a t i s f i e d a f t e r any p e r t u r b -a t i o n , so one of the amounts of cash compensation must change. I f s a l a r y i s chosen as the one to vary, then the c h o i c e between ta x a b l e b e n e f i t goods purchased by the c o r p o r a t i o n and purchases o f a l l other goods by the owner y i e l d s the f o l l o w i n g c o n d i t i o n s f o r an optimum: 37 U x < n X y q f - f - I ( 1 + T ) unless X r = X 1 or S = 0 (25a) or S + rp X = S ux > o x f SX f ^ - 2j- (1 - T b A ) unless X = 0 (25b) 1 P These c o n d i t i o n s are analogous t o c o n d i t i o n s (24) and have the same i n t e r p r e t a t i o n . The c o m p l i c a t i o n i s t h a t s a l a r y i s not the o n l y method of cash compensation t h a t can be v a r i e d . Tax-able d i v i d e n d s and repayment of loans from the owner are the other p o s s i b i l i t i e s , and each of these has i t s own s i m i l a r c o n d i t i o n s : u x^ — < r £ — (1 + T X D ) unless X f = X f or Y S + Y L = 0 (26a) UT - I I P or D r + D n r = 0 or (N™ •> 0 and Y S + Y L - (4/3)D n r = n) I P (1 - T" A) unless X = 0 or S + r p " X 1 = S U i i"(26b) or ( N D X > 0 and Y S + Y L - (4/3)D n r = n) U < x f - \ - '(1 + T X L ) unless X f = X f or Y S + Y L = 0 (27a) I p „ or L + D = L U > X^ - (1 - T L X ) unless L + D K = L + D K or X f = 0 (27b) I f o r S + r p X = S or Y + Y - (4/3)D = n 38 The i n t u i t i o n behind these s i x c o n d i t i o n s i s t h a t there are three budget f r o n t i e r s f o r t h i s sub-problem, one f o r each of the forms of cash compensation, and each of these f r o n t i e r s i s k inky. The budget f r o n t i e r t h a t i s r e l e v a n t f o r u t i l i t y maximization i s the o u t e r envelope of the t h r e e . Corresponding t o these s i x c o n d i t i o n s f o r t a x a b l e bene-f i t s are another s i x f o r non-taxable b e n e f i t s , which are omitted to save space. The o n l y changes are the replacement of X f by Z f and X by Z and m o d i f i c a t i o n of two of the f e a s i -b i l i t y c o n d i t i o n s . The words "or S + r p X = s™^" should be dropped from (26b) and (27b) because i n c r e a s i n g t a x a b l e d i v i d e n d s and d e c r e a s i n g non-taxable b e n e f i t s does not a f f e c t employment income. T h i s completes the necessary c o n d i t i o n s f o r an optimum, apart from the d e f i n i t i o n s of N1-* and T1-', which are the r a t e s of change of the cumulative deduction account and t o t a l taxes r e s p e c t i v e l y . To d e f i n e N1-', c o n s i d e r the f u n c t i o n which r e l a t e s c o r p o r a t e income tax on a c t i v e business income or n o n - q u a l i f y i n g business income tQ; i t s argument, a c t i v e b u s i -ness income or n o n - q u a l i f y i n g business income. T h i s f u n c t i o n has a kink, due to the s m a l l business deduction, so the d e r i v a t i v e s of t h i s f u n c t i o n from the l e f t and the r i g h t w i l l not always be e q u a l . The d e r i v a t i v e from the l e f t i s 39 u = u S i f Y S + Y L < Y S u L i f Y S + Y L > Y S and the d e r i v a t i v e from the r i g h t i s : u + = u S i f Y S + Y 1 1 Y S { u L i f Y S + Y L > Y S S —S L The kink occurs when Y = Y and Y = 0 , which w i l l most o f t e n occur when the f i r m ' s a c t i v e business income or n o n - q u a l i f y i n g business income i s e x a c t l y $150,000. At t h i s p o i n t i n c r e a s e s i n income do not i n c r e a s e the s m a l l business deduction, so u = u^, and decreases i n income reduce the s m a l l business + S deduction, so u = u . At higher l e v e l s of income than $150,000, Y S = Y S and Y L > 0, so u~ = u + = u L and any s m a l l change i n income does not a f f e c t the smal l business deduction. At lower l e v e l s of income than $150,000, Y S < Y S and Y L = 0, — + S so u = u = u and s m a l l changes i n income do change the s i z e of the smal l business deduction. Another f u n c t i o n which i s needed to d e f i n e N1-* i s the f u n c t i o n which determines the amount of tax a b l e d i v i d e n d s p a i d from the amount of the c o r p o r a t i o n ' s own money used f o r t h i s purpose. The d e r i v a t i v e of t h i s f u n c t i o n would always be one i f not f o r the d i v i d e n d refund. I f an i n c r e a s e i n d i v i d e n d s i n c r e a s e s the d i v i d e n d r e f u n d , then the c o r p o r a t i o n ' s own funds are supplemented by a refund o f tax money from the 40 government of one-quarter of the d i v i d e n d s p a i d . T h i s allows $1 1/3 to be p a i d out i n t a x a b l e d i v i d e n d s f o r every $1 of the c o r p o r a t i o n ' s own money. The d e r i v a t i v e of t h i s f u n c t i o n from the l e f t , which r e l a t e s to d i v i d e n d i n c r e a s e s , i s t h e r e -f o r e • d " = | i f D r + D n r < D r { 1 i f D r + D n r > D r For d i v i d e n d decreases the r e l e v a n t d e r i v a t i v e i s the d e r i v a -t i v e from the r i g h t , which i s d + = f • i f D r + D n r < D r ^ 1 i f D r + D n r > D r r — r The two one-sided d e r i v a t i v e s are unequal where D = D and nr D = 0 , s i n c e a t t h i s p o i n t the f u n c t i o n has a k i n k . The t h i r d f u n c t i o n r e q u i r e d to d e f i n e the r a t e s of change o f the cumulative deduction account i s the f u n c t i o n which determines the change i n the cumulative deduction account i n the c u r r e n t year from the amount of t a x a b l e d i v i d e n d s p a i d . Taxable d i v i d e n d s which q u a l i f y f o r the d i v i d e n d refund have no e f f e c t on the cumulative deduction account, w h i l e o t h e r t a x a b l e d i v i d e n d s reduce i t by $1 1/3 per d o l l a r of t a x a b l e d i v i d e n d s p a i d (assuming the business i s an a c t i v e b u s i n e s s ) . Thus the one-sided d e r i v a t i v e s of t h i s f u n c t i o n are 41 0 if Dr + D n r * Dr ^ 4 r nr ^ — r - ~ if D + D - D and 0 i f Dr + Dnr•< Dr c + = { - f if Dr + D n r > Dr The above d e f i n i t i o n s allow the rates of change of the cumulative deduction account for the various perturbations to be written as: „SD ATXD ,,ZD . (- -K + ,+ N = N = N =-1 - ( l - u ) c d MDS .TDX .TDZ . , - ,-N = N = N = l + ( l - u ) c d N = -c d The simplest of these i s N L D, the rate of change of the cumulative deduction account when the amount of loans from the owner repaid increases by a small amount and taxable dividends are decreased just enough to s a t i s f y the corporate budget contraint. I f the increase i n loan repayment i s $1, then the corporation has $1 less with which to pay taxable dividends, and thus the change i n the amount of taxable dividends paid i s -d +. For every d o l l a r change i n taxable dividends paid, there i s a change of c + i n the cumulative deduction account, and so the t o t a l change i n the cumulative deduction account i s - c + d + . 42 A more complicated e x p r e s s i o n i s t h a t f o r N D U, which may be i n t e r p r e t e d as the change i n the cumulative deduc-t i o n account caused by a $1 i n c r e a s e i n s a l a r y and a reduc-t i o n i n t a x a b l e d i v i d e n d s i n the amount r e q u i r e d by the c o r p o r a t e budget c o n s t r a i n t . The i n c r e a s e i n s a l a r y of $1 r e q u i r e s o n l y 1 - u + i n c o r p o r a t e funds, s i n c e s a l a r y i s a d e d u c t i b l e expense, and the r e s u l t i n g change i n t a x a b l e d i v i d e n d s i s -(1 - u + ) d + . The change i n the cumulative d e d u c t i o n account i s thus -(1 - u + ) d + c + - 1, where the -1 a t the end i s from the $1 decrease i n a c t i v e business income caused by the s a l a r y i n c r e a s e . The r e v e r s e p e r t u r b a t i o n of i n c r e a s i n g t a x a b l e d i v i d e n d s and d e c r e a s i n g s a l a r y y i e l d s a c o r r e s p o n d i n g e x p r e s s i o n , the d i f f e r e n c e s being i n s i g n and i n the replacement of d e r i v a t i v e s from the r i g h t by d e r i v a -t i v e s from the l e f t . The e x p r e s s i o n s f o r p e r t u r b a t i o n s i n v o l v i n g t a x a b l e b e n e f i t s and non-taxable b e n e f i t s are i d e n -t i c a l t o the c o r r e s p o n d i n g e x p r e s s i o n s i n v o l v i n g s a l a r y , s i n c e expenditures on i n - k i n d b e n e f i t s reduce a c t i v e business income or n o n - q u a l i f y i n g business income d o l l a r f o r d o l l a r , j u s t as s a l a r y does. A p r e r e q u i s i t e f o r proceeding to the d e f i n i t i o n of the r a t e s of change of t o t a l taxes i s the d e f i n i t i o n of two func-t i o n s i n v o l v i n g the p e r s o n a l tax system. The f i r s t i s a f u n c t i o n which determines t o t a l p e r s o n a l income tax from 43 "extended b a s i c f e d e r a l tax," which i s d e f i n e d t o be f e d e r a l income tax on t a x a b l e income l e s s t h r e e - e i g h t h s o f ta x a b l e d i v i d e n d s . R e c a l l i n g the d i s c u s s i o n of c o n s t r a i n t (7), exten-ded b a s i c f e d e r a l tax (B e) i s j u s t b a s i c f e d e r a l tax extended to allow negative v a l u e s . The one-sided d e r i v a t i v e s of t h i s f u n c t i o n are b = < < B c < 200 1 + p . i f 200 < B < 2,222 1 + p - 0.09 i f 2,222 < B e < 5,556 ^1 + p i f B e > 5,556 and < 2,222 1 + p - 0.09 i f 2,222 < B e < 5,556 L l + p i f B e > 5,556 The purpose of t h i s f u n c t i o n i s to show how a change i n b a s i c f e d e r a l tax a f f e c t s t o t a l p e r s o n a l income tax,, accounting f o r changes i n the f e d e r a l tax r e d u c t i o n and i n p r o v i n c i a l income tax. The second function;-shows how f e d e r a l income tax on taxable income i s dependent on "extended ta x a b l e income" (Y ), where t h i s i s net income f o r tax purposes l e s s exemptions and dedu c t i o n s , i . e . , the r i g h t - h a n d s i d e o f (9). The d e r i v a t i v e s of t h i s f u n c t i o n from the l e f t and the r i g h t are and "0 i f Y c < 0 0 . 0 6 i f 0 < Y < 9 0 3 t = < 0 . 1 6 i f 9 0 3 < Y < 1 8 0 6 0 . 4 3 i f Y e > 1 0 8 , 3 6 0 '0 i f Y c 0 t + = 0 . 0 6 i f 0 < Y < 9 0 3 0 . 4 3 i f Y > 1 0 8 , 3 6 0 1 9 8 0 t a x a b l e income b r a c k e t s are used i n the d e f i n i t i o n of the d e r i v a t i v e s f o r i l l u s t r a t i o n o n l y . The f u l l d e t a i l o f the t a x a b l e income b r a c k e t s and r a t e s can be found i n S e c t i o n 1 1 7 . 1 of the Income Tax A c t and many other sources. LX The f i r s t r a t e of change of t o t a l taxes i s T , which r e l a t e s t o a decrease of $ 1 i n the c o r p o r a t i o n ' s expenditure on t a x a b l e b e n e f i t s and an i n c r e a s e i n the repayment of loans from the owner i n the amount allowed by the c o r p o r a t e budget c o n s t r a i n t . The $ 1 decrease i n expenditure on t a x a b l e b e n e f i t s i n c r e a s e s c o r p o r a t e income tax by u and decreases p e r s o n a l income tax by r b + t + , so the change i n t o t a l taxes i s : m L X - 4_+v + T = u - r t b The p e r s o n a l income tax decrease i s r t + b + because the decrease i n t a x a b l e income of r i m p l i e s t h a t f e d e r a l income tax on 45 t a x a b l e income decreases by r t + , and t h i s must be m u l t i p l i e d by b + to get the o v e r a l l p e r s o n a l tax decrease. The r e v e r s e p e r t u r b a t i o n , i n which expenditure on t a x a b l e b e n e f i t s i s i n c r e a s e d and repayment of loans from the owner i s decreased, t h e r e f o r e r e s u l t s i n a change of t o t a l taxes o f : T X L = r t " b " - u + The p e r t u r b a t i o n f o r T L D i s a $1 i n c r e a s e i n the repay-ment of loans from the owner and a decrease i n t a x a b l e d i v i d e n d s i n the amount r e q u i r e d by the c o r p o r a t e budget c o n s t r a i n t . As d i s c u s s e d i n . t h e e x p l a n a t i o n of N L D , the decrease i n t a x a b l e d i v i d e n d s i s d + . T h i s causes t a x a b l e income to f a l l by ( 3 / 2 ) d + , due to the gross-up. F e d e r a l income tax on ta x a b l e income decreases by ( 3 / 2 ) t + d + , l e a d i n g to a change i n extended b a s i c f e d e r a l tax of - d + ( ( 3 / 2 ) t + - (3/8) ). T h i s may be of e i t h e r s i g n , so by d e f i n i n g b~ i f - d + ( ( 3 / 2 ) t + - (3/8) ) > 0 b L D = ( . + b otherwise the change i n t o t a l taxes can be expressed as: TL D = _ d + ( ( 3 / 2 ) t + - (3/8) ) b L D + d + -1 The l a s t term i s the decrease i n the d i v i d e n d refund, which i s the o n l y change i n co r p o r a t e income tax. A s i m i l a r e x p l a n a t i o n would show why the r e v e r s e p e r t u r b a t i o n , which i n v o l v e s i n c r e a -s i n g t a x a b l e d i v i d e n d s and d e c r e a s i n g repayment of loans t o the 46 owner, can be w r i t t e n as T D L = d" ( ( 3 / 2 ) t " - 3 / 8 ) b D L - ( d " -1) where b D L = b~ i f d" ( (3/2) t " - (3/8) ) _> 0 b + otherwise XD Some new c o m p l i c a t i o n s are i n v o l v e d i n T , the change i n t o t a l taxes when expenditure on t a x a b l e b e n e f i t s i s i n -creased by $1 and t a x a b l e d i v i d e n d s are decreased i n the amount r e q u i r e d by the co r p o r a t e budget c o n s t r a i n t . J u s t as i n the SD p e r t u r b a t i o n f o r N , the change i n t a x a b l e d i v i d e n d s i s - ( l - u + ) d + , which may be of e i t h e r s i g n . By d e f i n i n g t " i f r - (3/2) (1 - u +) d + _> 0 t X D =( + t otherwise the change i n extended b a s i c f e d e r a l tax may be expressed as r t X D - ( ( 3 / 2 ) t X D - (3/8) ) (1 - u + ) d + which a l s o may be of e i t h e r s i g n . Using the d e f i n i t i o n b~ i f r t X D - ( ( 3 / 2 ) t X D - (3/8) )(1 - u + ) d + > 0 bXD = { + b otherwise the change i n t o t a l taxes i s : T X D = r t X D b X D - ( ( 3 / 2 ) t X D - (3/8) ) b X D (1 - u + ) d + + ( d + - 1) (1 - u +) - u + 47 The two terms at the end are the decrease i n the dividend refund and the change i n corporate income tax on active business income or non-qualifying business income. For similar reasons, the change i n t o t a l taxes for a $1 decrease in expenditure on taxable benefits and an appropriate increase in taxable dividends i s T D X = ( ( 3 / 2 ) t D X - (3/8) ) b D X (l-u~)d~ - r t D X b D X - (d" - 1) (1 - u") + u" where n v t " i f (3/2) (l-u~)d~ - r > 0 t ° X ={ + t otherwise and D X b" i f ( ( 3 / 2 ) t D X - (3/8) ) (l-u")d~ - r t D X > 0 b =;{ + b otherwise Since non-taxable benefits are i n a sense an extreme ZD DZ ZL form of taxable benefits, expressions for T , T , T and LZ T can be found by setting r = 0 i n the expressions given for T X D , T D X , T X L and T L X respectively. Salary i s an extreme form of taxable benefits of the opposite type, so setting r = 1 • ' ~i J3 mSD mDS mSL , mLS in these expressions y i e l d s T , T , T and T The remaining rates of change of t o t a l tax are those involving any two of salary, taxable benefits and non-taxable benefits: 48 T S X = t " b" (1-r) T X S = - t + b + (1 - r) T S Z = t ~ b~ T Z S = - t + b + T X Z = r t " b" U z P 1 U I z f P m z x . + , + T = - r t b Un, I Z p U I Z f P The l a s t two e x p r e s s i o n s are unusual and i t i s necessary to e x p l a i n why these can be i n t e r p r e t e d as changes i n t o t a l tax. XZ Consider T , which i s the change i n t o t a l taxes r e s u l t i n g from an i n c r e a s e of $1 i n expenditure on t a x a b l e b e n e f i t s and an a p p r o p r i a t e r e d u c t i o n i n expenditure on non-taxable b e n e f i t s . T h i s p e r t u r b a t i o n i n c r e a s e s p e r s o n a l income tax, so i n order to continue to s a t i s f y the p e r s o n a l budget c o n s t r a i n t , there must be an i n c r e a s e i n s a l a r y , d i v i d e n d s or repayment of shareholder's l o a n s . The compensating change i n order to meet the c o r p o r a t e budget c o n s t r a i n t i s a f u r t h e r r e d u c t i o n i n non-t a x a b l e b e n e f i t s . Thus non-taxable b e n e f i t s must be reduced by more than the $1 r e q u i r e d f o r the i n c r e a s e i n expenditure on t a x a b l e b e n e f i t s , and t h i s e x t r a amount i s the change i n XZ t o t a l taxes (T ). The e x t r a amount i s determined by d i v i d i n g the i n c r e a s e i n p e r s o n a l income tax from the i n c r e a s e i n 4 9 t a x a b l e b e n e f i t s , r t b , by the amount of p e r s o n a l a f t e r - t a x income a v a i l a b l e per d o l l a r of funds withdrawn from non-taxable b e n e f i t s and used to f i n a n c e e x t r a s a l a r y , d i v i d e n d s , or repayment of shareholder's l o a n s . The l a t t e r amount i s U z I , as can be seen from the c o u n t e r p a r t s f o r non-taxable P r a t h e r than t a x a b l e b e n e f i t s of (25b), (26b) and (27b). As ZX f o r T , a s i m i l a r e x p l a n a t i o n may be used to show why t h i s i s the change i n t o t a l tax r e s u l t i n g from a $1 decrease i n expenditure on t a x a b l e b e n e f i t s and a consequent i n c r e a s e i n expenditure on non-taxable b e n e f i t s . 2.3 APPLICATIONS OF THE NECESSARY CONDITIONS One q u e s t i o n t h a t a r i s e s from the necessary c o n d i t i o n s i s whether i t i s ever opt i m al to purchase t a x a b l e b e n e f i t goods or non-taxable b e n e f i t goods p e r s o n a l l y r a t h e r than through the c o r p o r a t i o n . An obvious s i t u a t i o n i n which t h i s c o u l d happen i s i f the owner i s prevented by the reasonableness c o n s t r a i n t s (16) or (17) from buying a l l t h a t he wants of these goods through'the c o r p o r a t i o n . The more d i f f i c u l t q u e s t i o n i s whether there are any other s i t u a t i o n s i n which t h i s i s o p t i m a l . From (23a), (25a), (26a) and (27a), i t i s optimal to purchase taxable b e n e f i t goods p e r s o n a l l y even though the reasonableness c o n s t r a i n t i s not b i n d i n g o n l y i f a l l of the f o l l o w i n g c o n d i t i o n s are met: 50 p X \ p ^ (1 + T*5) unless S = 0 or S + r p ^ / = S 1 1^ (28a) p X \ p X (1 + T*0) unless ^ + Y3" = 0 or D r + D1^ = 0 or (N* 0 > O a n d ^ + Y 1 - (4/3) E F = n) (28b) pX?<_ p ^ (1 + T^) unless Y S + Y L = 0 o r L + D K= L 1"^ (28c) Assuming t h a t the p r i c e s a t which the owner and the f i r m can purchase these goods are i d e n t i c a l , c o n d i t i o n s (28) r e q u i r e XS XD t h a t a l l o f the r a t e s of change of t o t a l taxes T , T and XL T be non-negative, u n l e s s the r e l e v a n t p e r t u r b a t i o n s are not f e a s i b l e . T h i s requirement i s u n l i k e l y t o be met. In p a r t i -c u l a r , r e d u c i n g s a l a r y and i n c r e a s i n g t a x a b l e b e n e f i t s w i l l always reduce t o t a l taxes i f the owner's p e r s o n a l marginal tax XS •+• + r a t e i s p o s i t i v e , s i n c e T = - t b (1-r) and r < 1. Reducing repayment of shareholder's loans and i n c r e a s i n g taxable b e n e f i t s i s a l s o l i k e l y to reduce t o t a l taxes. The r e l e v a n t change i n XL — — + t o t a l taxes (T ) i s d e f i n e d as r t b - u , which has a maximum valu e of .0014 i f 1980 B.C. p e r s o n a l and c o r p o r a t e tax r a t e s are used and r i s assumed to be o n e - t h i r d (based on the computa-t i o n of the minimum standby charge f o r l e a s e d c a r s ) . T h i s shows t h a t any s a v i n g r e a l i z e d by buying t a x a b l e b e n e f i t goods perso-n a l l y can be no more than $1.40 per thousand d o l l a r s of expen-d i t u r e . The c o n c l u s i o n i s t h a t i t i s u n l i k e l y t o be o p t i mal to purchase t a x a b l e b e n e f i t goods p e r s o n a l l y , u n l e s s the reasonable-ness c o n s t r a i n t on t a x a b l e b e n e f i t s i s b i n d i n g or both s a l a r y 51 and repayment o f shareholder's loans cannot be decreased. A s i m i l a r c o n c l u s i o n a p p l i e s to the purchase o f non-taxable b e n e f i t goods. Another use f o r the necessary c o n d i t i o n s i s t o expl o r e f u r t h e r the optimal combination o f s a l a r y , t a x a b l e d i v i d e n d s and repayment of loans from the owner, assuming t h a t the q u a n t i t i e s o f t a x a b l e and non-taxable b e n e f i t s are chosen exogenously. The way t h a t t h i s can be done i s to use a c t u a l - + - + - + - + v a l u e s f o r the ten parameters u , u , d , d , c , c , b , b , t and t + to c a l c u l a t e the r a t e s of change of t o t a l taxes and the cumulative deduction account which appear i n c o n d i t i o n s (22). T h i s shows which combinations o f the ten parameters s a t i s f y (22) and can be used t o develop an a l g o r i t h m which c a l c u l a t e s the op t i m a l combination o f the three forms of cash compensation, g i v e n v a l u e s f o r the oth e r parameters o f the model. T h i s has been done f o r the values o f the ten parameters a p p l i c a b l e i n B r i t i s h Columbia and O n t a r i o i n 1980. The r e s u l t i n g a l g o r i t h m i s q u i t e complicated and n o n - i n t u i t i v e , so i t i s perhaps more worthwhile to pr e s e n t a s e r i e s o f simpl e r a l g o r i t h m s which apply to the most common s i t u a t i o n s . Four assumptions are made to s i m p l i f y the problem: the cumulative deduction account c o n s t r a i n t , (14), i s not b i n d i n g ; the employment income c o n s t r a i n t , ( 2 1 ) , i s not b i n d i n g ; the corpo-r a t i o n has a c t i v e business income from non-manufacturing g a c t i v i t i e s , so i t s c o r p o r a t e tax r a t e s are u = 0.2575 and 52 u = 0.528; and the c o r p o r a t i o n ' s RDTOH balance i s zero, so no t a x a b l e d i v i d e n d s are e l i g i b l e f o r the d i v i d e n d refund. The l a s t assumption i s r e l a x e d a t the end. The v a r i a b l e which i s used t o c l a s s i f y b usiness s i t u a t i o n s i s "gross c o r p o r a t e income," which i s d e f i n e d as v g v b X r „f Z _ f Y ^ = y - p x - p z or the c o r p o r a t i o n ' s a c t i v e business income be f o r e deducting the owner's s a l a r y . The three common business s i t u a t i o n s which are analyzed i n d e t a i l a r e : the " l a r g e b u s i n e s s , " which has a gross c o r p o r a t e income over $223,424; the "medium-sized b u s i n e s s " which has a gross c o r p o r a t e income between $157,621 and $223,424; and the "small b u s i n e s s " which has a gross c o r -porate income between $7,621 and $150,000. T h i s leaves some gaps i n coverage, but .they are not very important. The d o l l a r f i g u r e s which are used t o d e f i n e the c a t e g o r i e s depend on some assumptions, but they should convey the c o r r e c t order of mag-n i t u d e . The amount $7,621 i s the minimum amount of s a l a r y f o r which any amount of t a x a b l e d i v i d e n d s cannot reduce b a s i c f e d e r a l tax below $200, assuming t h a t the owner's exemptions and deductions are the minimum p o s s i b l e ($2,990), and assuming t h a t the owner has no other income. The amount $73,424 i s the mimimum amount of s a l a r y which makes the owner's p e r s o n a l m a r g i n a l tax r a t e g r e a t e r than the hig h c o r p o r a t e r a t e , under the same assumptions. In the l a r g e business category, the 53 gross c o r p o r a t e income i s l a r g e enough so t h a t paying out $73,424 i n s a l a r y does not reduce a c t i v e b u s i n e s s income 2 1 to $150,000. For a medium-sized b u s i n e s s , the amount of s a l a r y which i s r e q u i r e d to reduce a c t i v e business income to $150,000 i s between $7,621 and $73,424. A s m a l l business has a c t i v e business income under $150,000 r e g a r d l e s s of how much s a l a r y i s p a i d , and a s a l a r y of $7,621 does not reduce a c t i v e b u s i n e s s income t o z e r o . F i g u r e 2 i l l u s t r a t e s the o p t i m a l c h o i c e of s a l a r y , t a x a b l e d i v i d e n d s and repayment of loans from the owner f o r a l a r g e b u s i n e s s . The arrows i n d i c a t e an expansion path f o r s a l a r y and t a x a b l e d i v i d e n d s as the amount o f money the c o r p o r a t i o n has to d i s t r i b u t e (M i n (10)) i n c r e a s e s . The f o l l o w i n g d i r e c t i o n s i n d i c a t e how the f i g u r e can be used: C a l c u l a t e L* such t h a t S = 73,424 w i t h t a x a b l e — —K d i v i d e n d s equal to zero. I f L* L + D , t h i s — —K i s the optimum. I f not, s e t L* = L + D and continue a l o n g the expansion path u n t i l the c o r -porate budget c o n s t r a i n t i s s a t i s f i e d . In these d i r e c t i o n s and the ones t h a t f o l l o w f o r other business c a t e g o r i e s , L* stands f o r the sum of c a p i t a l d i v i d e n d s and repayment of loans from the owner, f o r the reasons d i s c u s s e d p r e v i o u s l y . 54 150;000, > > > > > > ) > > > > > > > > > > ) > > Salary 73,424 Taxable Dividends FIGURE 2: F i n a n c i a l Expansion Path f o r a Large Business 55 The i n t u i t i o n behind t h i s a l g o r i t h m can be e x p l a i n e d as f o l l o w s . I f no s a l a r y i s p a i d , the f i r m w i l l have the amount of i t s gross c o r p o r a t e income over $150,000 taxed a t the h i g h r a t e (52.8%) and the owner's marginal tax r a t e w i l l be l e s s 2 2 than the c o r p o r a t e r a t e . An i n c r e a s e i n s a l a r y which i s r e t u r n e d to the f i r m i n the form of a l o a n from the owner w i l l reduce t o t a l taxes, s i n c e the decrease i n c o r p o r a t e tax w i l l be l e s s than the i n c r e a s e i n p e r s o n a l tax. T h i s i s t r u e u n t i l the owner's marginal tax r a t e f i r s t exceeds the c o r p o r a t e r a t e , which occurs a t a s a l a r y of $73,424 under the assumptions made. I n c r e a s i n g s a l a r y and d e c r e a s i n g repayment of share-h o l d e r ' s loans beyond t h i s p o i n t i n c r e a s e s t o t a l taxes. The next step i s to check i f the c o r p o r a t i o n has money l e f t over to d i s t r i b u t e a f t e r paying out t h a t amount of s a l a r y . I f not, then the o n l y other p o s s i b l e adjustments are to i n c r e a s e t a x a b l e d i v i d e n d s and decrease s a l a r y , which i n c r e a s e s t o t a l taxes s i n c e the i n c r e a s e i n a c t i v e business income i s taxed at the h i g h c o r p o r a t e r a t e , or t o i n c r e a s e t a x a b l e d i v i d e n d s and r e t u r n the funds as a l o a n from the owner, which i n c r e a s e s t o t a l taxes s i n c e the p e r s o n a l marginal tax r a t e on d i v i d e n d s i s p o s i t i v e a t t h i s l e v e l of p e r s o n a l t a x a b l e income. The c o n c l u s i o n i n t h i s case i s t h a t the optimum has been reached. I f there i s money l e f t over, then the f i r s t c h o i c e s are to repay a l l loans from the owner and pay out as much i n c a p i t a l d i v i d e n d s as i s allowed, s i n c e these payments i n v o l v e no'' e x t r a 56 tax burden. A f t e r t h i s route has been exhausted, the next c h o i c e i s t o pay out more s a l a r y u n t i l a c t i v e b u s i n e s s income has been reduced to $150,000, i . e . , u n t i l S = Y g - 150,000. 2 3 Beyond t h i s p o i n t f u r t h e r i n c r e a s e s i n s a l a r y do not reduce c o r p o r a t e tax by as much because the low c o r p o r a t e r a t e (25.75%) i s i n e f f e c t , so t a x a b l e d i v i d e n d s are the b e s t way to remove any remaining funds. F i g u r e 3 shows t h a t the f i n a n c i a l p o l i c y of a medium-sized business t y p i c a l l y i n v o l v e s a g r e a t e r p r o p o r t i o n of c o r p o r a t e funds f l o w i n g out as t a x a b l e d i v i d e n d s than i s the case f o r a l a r g e b u s i n e s s . The d i r e c t i o n s f o r the use of t h i s f i g u r e a r e : C a l c u l a t e L* such t h a t S = Y g - 150,000 wit h — —K zero t a x a b l e d i v i d e n d s . I f L* <_ L + D , t h i s — —K i s the optimum. I f not, s e t L* = L + D and continue on the expansion path u n t i l the c o r -porate budget c o n s t r a i n t i s s a t i s f i e d . The d i f f e r e n c e between t h i s s i t u a t i o n and the p r e v i o u s one i s t h a t the p o i n t a t which the low c o r p o r a t e r a t e s t a r t s (Y°J _ $150,000) i s reached b e f o r e the s a l a r y i n c r e a s e s have pushed the owner's marginal tax r a t e above the high c o r p o r a t e r a t e . A t t h i s p o i n t the owner's mar g i n a l tax r a t e w i l l be above the low c o r p o r a t e r a t e , however, so paying e x t r a s a l a r y 57 Y 8 -150,000 > > ) > > ) > ) ) ) > > > ) > > > > Salary Taxable Dividends FIGURE 3: F i n a n c i a l Expansion Path f o r a Medium-Sized Business 58 and having i t r e t u r n e d as a l o a n from the owner i n c r e a s e s t o t a l taxes. I f the c o r p o r a t i o n does not have money l e f t over a f t e r paying the i n d i c a t e d amount of s a l a r y , then f o r the same reasons as f o r the l a r g e business t h i s i s the o p t i -mum. I f t h e r e i s money l e f t over, then the expansion path beyond t h i s p o i n t i s a l s o the same as f o r the l a r g e b u s i n e s s , again f o r the same reasons. The o p t i m a l f i n a n c i a l p o l i c y o f a s m a l l b u s i n e s s i s i l l u s t r a t e d i n F i g u r e 4. As may be apparent from the f i g u r e , the c a l c u l a t i o n and e x p l a n a t i o n of the optimal f i n a n c i a l p o l i c y f o r t h i s type of b u s i n e s s i s more complicated than f o r the p r e v i o u s two. Taxable d i v i d e n d s are g e n e r a l l y p r e f e r r e d over s a l a r y , but s a l a r y s t i l l has a s i g n i f i c a n t r o l e . The d i r e c t i o n s f o r the use of F i g u r e 4 a r e : Follow the i n d i c a t e d path u n t i l the value of L* i m p l i e d by the c o r p o r a t e budget c o n s t r a i n t f a l l s to L m i n , or u n t i l t a x a b l e d i v i d e n d s reach $10,157 and s a l a r y reaches $7,621. In the former case, the optimum has been reached. In the l a t t e r case, c a l -c u l a t e the v a l u e of L* t h a t i s i m p l i e d by the c o r p o r a t e budget c o n s t r a i n t a t t h i s p o i n t . I f i t — —K i s l e s s than or equal to L + D , t h i s p o i n t i s the — —K optimum; otherwise, s e t L* = L + D and continue along the expansion path u n t i l the c o r p o r a t e budget c o n s t r a i n t i s s a t i s f i e d . 59 Salary FIGURE 4: F i n a n c i a l Expansion Path for a Small Business 60 To understand t h i s a l g o r i t h m , the most important f a c t t o keep i n mind i s t h a t a l l of the a c t i v e b u s i n e s s income of a sm a l l b u s i n e s s i s taxed a t the low co r p o r a t e r a t e . As a DS r e s u l t , the c a l c u l a t i o n s f o r T show t h a t i n c r e a s i n g t a x a b l e d i v i d e n d s and d e c r e a s i n g s a l a r y , keeping the amount of funds d i s t r i b u t e d by the company const a n t , always decreases t o t a l taxes i f b a s i c f e d e r a l tax i s over $200. Another r e s u l t i s SD t h a t the c a l c u l a t i o n s f o r T show t h a t the r e v e r s e p e r t u r b a t i o n of i n c r e a s i n g s a l a r y and d e c r e a s i n g t a x a b l e d i v i d e n d s always decreases t o t a l taxes i f b a s i c f e d e r a l tax i s under $200. The c o n c l u s i o n i s t h a t the o n l y way t h a t s a l a r y and t a x a b l e d i v i -dends can both be p o s i t i v e i n the optimum i s i f b a s i c f e d e r a l tax e x a c t l y equals $200. The other two types of s o l u t i o n s occur a t c o r n e r s : s a l a r y p o s i t i v e and t a x a b l e d i v i d e n d s zero w i t h b a s i c f e d e r a l tax not over $200, or s a l a r y zero and t a x a b l e d i v i d e n d s p o s i t i v e w i t h b a s i c f e d e r a l tax not under $200. The expansion path t h e r e f o r e i s composed of th r e e segments c o r r e s -ponding t o the three types of s o l u t i o n s . The f i r s t o f these i s w i t h a p o s i t i v e amount of s a l a r y and zero t a x a b l e d i v i d e n d s . T h i s v e r t i c a l segment o f the expansion path ends when b a s i c f e d e r a l tax h i t s $200, which occurs a t a s a l a r y of $4,802 i f the owner has no ot h e r income and minimum exemptions and deduc-t i o n s . The second segment begins a t t h i s p o i n t and continues u n t i l the p o i n t of zero s a l a r y and $33,783 i n ta x a b l e d i v i d e n d s i s reached, a f t e r which b a s i c f e d e r a l tax r i s e s above $200, and 61 the t h i r d segment s t a r t s . The t h i r d segment f o l l o w s the h o r i z o n t a l a x i s , i n d i c a t i n g a p o s i t i v e amount of t a x a b l e d i v i d e n d s and zero s a l a r y . The second segment i s c h a r a c t e r i z e d by a constant b a s i c f e d e r a l tax of $200, which from B.C. and On t a r i o 1980 tax r a t e s i m p l i e s t h a t t o t a l p e r s o n a l income tax i s cons t a n t a t $88. Thus many owners of busin e s s e s i n t h i s category w i l l be paying almost n o t h i n g i n p e r s o n a l income tax. From the f i g u r e , i t can be seen t h a t t h i s segment f i r s t r i s e s , then reaches a wide p l a t e a u , and f i n a l l y f a l l s . The r i s i n g s e c t i o n , which ends when t a x a b l e d i v i d e n d s reach $7,749, occurs because i n t h i s r e g i o n the p e r s o n a l marginal tax r a t e on ta x a b l e d i v i d e n d s i s n e g a t i v e . T h i s means t h a t i n c r e a s e s i n t a x a b l e d i v i d e n d s must be matched by i n c r e a s e s i n s a l a r y t o keep b a s i c f e d e r a l tax a t $200, which accounts f o r the p o s i t i v e s l o p e . The p l a t e a u i s the r e g i o n i n which the marg i n a l f e d e r a l tax r a t e on t a x a b l e income i s 25%, i . e . , t = t + = 0.25, s i n c e i n t h i s r e g i o n the d i v i d e n d gross-up and tax c r e d i t system produces a zero p e r s o n a l m a r g i n a l tax r a t e on t a x a b l e d i v i d e n d s . The p l a t e a u ends when ta x a b l e d i v i d e n d s reach $10,157, a f t e r which the marg i n a l p e r s o n a l tax r a t e on ta x a b l e d i v i d e n d s i s p o s i t i v e . T h i s means t h a t i n c r e a s e s i n ta x a b l e d i v i d e n d s must be accompanied by decreases i n s a l a r y to keep b a s i c f e d e r a l tax a t $200, so t h i s segment has a negative s l o p e throughout. F i n a l l y , s a l a r y reaches zero and the second segment ends. 6 2 Whether the optimum f o r a p a r t i c u l a r s m a l l business l i e s i n the f i r s t , second or t h i r d segments depends on the amount of funds a v a i l a b l e f o r d i s t r i b u t i o n and the l i m i t s w i t h i n which the repayment of loans from the owner can v a r y . An optimum to the l e f t o f p o i n t A i s p o s s i b l e o n l y i f the c o r p o r a t e bud-get c o n s t r a i n t f o r c e s c a p i t a l d i v i d e n d s to be zero and loans from the owner t o be a t the minimum, i . e . , L* = L m i n , because moving f u r t h e r along the expansion path i n t h i s r e g i o n reduces t o t a l taxes. In the f i r s t segment t h i s i s because c o r p o r a t e tax i s f a l l i n g by more than p e r s o n a l tax i s r i s i n g , w h i l e i n the p a r t o f the second segment to the l e f t of p o i n t A i t i s because c o r p o r a t e tax i s f a l l i n g and p e r s o n a l tax i s constant. On the o t h e r hand, an optimum to the r i g h t of p o i n t B i s pos-s i b l e o n l y i f the c o r p o r a t e budget c o n s t r a i n t f o r c e s c a p i t a l d i v i d e n d s and repayment of loans from the owner to be a t t h e i r — —K maximum, i . e . , L* = L + D , because t o t a l taxes are r a i s e d by moving f a r t h e r along the expansion path i n t h i s r e g i o n . In the t h i r d segment, t h i s i s because p e r s o n a l tax i s r i s i n g , w h i l e i n the p a r t of the second segment to the r i g h t of p o i n t B, t h i s i s because p e r s o n a l tax i s constant and c o r p o r a t e tax i s r i s i n g . An optimum i n the second segment between p o i n t s A and B may occur w i t h c a p i t a l d i v i d e n d s and repayment of loans from the owner at any f e a s i b l e l e v e l s . The owner i s i n d i f f e r e n t among a l l p o i n t s i n the p l a t e a u area of the second segment 63 because t o t a l taxes are constant i n t h i s r e g i o n . I f dynamic c o n s i d e r a t i o n s are invoked, however, there i s reason to b e l i e v e t h a t the owner would p r e f e r to be as c l o s e to p o i n t B as i s allowed by the amount of funds a v a i l a b l e and the minimum c o n s t r a i n t s on c a p i t a l d i v i d e n d s and repayment of loans from the owner. The reason i s t h a t movements towards p o i n t B i n t h i s r e g i o n i n v o l v e d e c r e a s i n g c a p i t a l d i v i d e n d s or repayment o f loans from the owner, which allows more funds to be removed on a t a x - f r e e b a s i s from the c o r p o r a t i o n i n the f u t u r e . On the b a s i s of t h i s argument, the a l g o r i t h m above s p e c i f i e s t h a t a l l p o i n t s to the l e f t o f p o i n t B w i l l be used on l y i f r e q u i r e d by the c o n s t r a i n t s , i . e . , L* = L m i n . F i g u r e 5 shows how r e l a x i n g the assumption of a zero RDTOH balance a f f e c t s the r e s u l t s f o r a s m a l l b u s i n e s s . The s o l i d path i s the same path as i n F i g u r e 4, but the broken path i s new. The d i r e c t i o n s f o r the use of t h i s f i g u r e are: Follow the broken path u n t i l : (a) L* = L m i n ; (b) t a x a b l e d i v i d e n d s equal D ; or (c) t a x a b l e d i v i d e n d s equal $48,949, whichever comes f i r s t . I f (a) i s f i r s t , t h i s p o i n t i s the optimum.. I f -t-b). i s f i r s t , ^increase s a l a r y from t h i s p o i n t , s t o p p i n g f o r the optimum o n l y i f L* = L m i n , u n t i l the s o l i d path i s reached. I f t h i s i n t e r s e c t i o n p o i n t i s to the l e f t o f p o i n t B, f o l l o w i n g the 64 Salary FIGURE 5: Financial Expansion Path for a Small Business with Non-Zero RDTOH 65 p r e v i o u s f i g u r e w i l l l e a d one to the optimum. I f not, c a l c u l a t e L* a t t h i s p o i n t . I f L* <_ _ _ 1^ L + D , t h i s i s the optimum; otherwise s e t L* = L + D and f o l l o w the s o l i d path from t h i s p o i n t u n t i l the budget c o n s t r a i n t i s s a t i s f i e d . I f (c) i s f i r s t , c a l c u l a t e L* a t t h i s p o i n t . I f —K L* _< L + D , t h i s i s the optimum; otherwise s e t _ L* = L + D and i n c r e a s e t a x a b l e d i v i d e n d s u n t i l the budget c o n s t r a i n t i s s a t i s f i e d . The i n t u i t i o n behind the new expansion path, which i s shown as a broken l i n e i n the f i g u r e , i s t h a t the a v a i l a b i -l i t y o f a d i v i d e n d refund i n c r e a s e s the d e s i r a b i l i t y of t a x a b l e d i v i d e n d s . An i n c r e a s e i n t a x a b l e d i v i d e n d s and a decrease i n s a l a r y now reduces t o t a l taxes whenever there i s any unused d i v i d e n d tax c r e d i t , r a t h e r than j u s t when b a s i c f e d e r a l tax i s over $200. Thus the expansion path i s d i v i d e d i n t o three segments as b e f o r e , but the second segment i s now a l l combinations of s a l a r y and t a x a b l e d i v i d e n d s i n which t o t a l p e r s o n a l income tax i s zero r a t h e r than $88. Corporate income tax i s now f a l l i n g throughout the second segment, because the i n c r e a s e d d i v i d e n d refund more than compensates f o r the i n c r e a s e i n c o r p o r a t e tax due to s a l a r y r e d u c t i o n s which occur i n the downward-sloping p a r t of t h i s segment. 66 T h i s i m p l i e s t h a t t o t a l taxes are f a l l i n g throughout the second segment. T o t a l taxes are f a l l i n g i n the t h i r d seg-ment a l s o u n t i l the i n c r e a s e i n p e r s o n a l tax outweighs the decrease i n the co r p o r a t e tax from a r i s i n g d i v i d e n d r e f u n d , which occurs a t $48,9 49 of t a x a b l e d i v i d e n d s . The r e s u l t i s t h a t an optimum may be reached t o the l e f t of t h i s p o i n t o n l y i f the d i v i d e n d refund i s exhausted f i r s t , o r i f the minimum c o n s t r a i n t s on c a p i t a l d i v i d e n d s and repayment of loans from the owner become b i n d i n g . C l e a r l y , the d i v i d e n d refund system does achieve i t s g o a l of encouraging the payment of ta x a b l e d i v i d e n d s . Although the expansion path i n t h i s f i g u r e i s s i m i l a r to the pre v i o u s one, the p o i n t t h a t i s reached i n the optimum i s l i k e l y t o be much f a r t h e r along, w i t h a l a r g e r amount of ta x a b l e d i v i d e n d s . The above statements r e q u i r e some m o d i f i c a t i o n i f the RDTOH balance i s s m a l l enough t h a t f o l l o w i n g the broken path d r i v e s the RDTOH balance t o zero b e f o r e e i t h e r the $48,949 l e v e l of t a x a b l e d i v i d e n d s i s reached or the minimum cons-t r a i n t on c a p i t a l d i v i d e n d s and repayment of loans from the owner becomes b i n d i n g . I f t h i s happens the zero-RDTOH path from F i g u r e 4 a p p l i e s t o any f u t u r e i n c r e a s e s i n ta x a b l e d i v i d e n d s . T h i s i s shown as the s o l i d path i n F i g u r e 5. To get to t h i s path, s a l a r y may have t o be i n c r e a s e d t o r a i s e b a s i c f e d e r a l tax from zero t o $200. These i n c r e a s e s i n s a l a r y reduce t o t a l taxes because i n t h i s range of b a s i c 67 f e d e r a l tax the owner's marginal tax r a t e i s l e s s than the corp o r a t e r a t e . I t i s u s e f u l t o compare the above algorithms f o r s a l a r y -d i v i d e n d c h o i c e t o the recommendations made i n the l i t e r a t u r e by tax p r a c t i t i o n e r s . The s t a t e o f the a r t i n t h i s l i t e r a t u r e i s the work of Kwan and Murray (1981) and Cadesky and Kwan (1981) who d i r e c t t h e i r a t t e n t i o n p r i n c i p a l l y t o the s i t u a t i o n o f a "small b u s i n e s s . " T h e i r recommendations agree i n most r e s p e c t s w i t h the r e s u l t s shown i n F i g u r e 4 above. The major exceptions are t h a t the authors do not c o n s i d e r c a p i t a l d i v i -dends o r the repayment of loans from the owner, and the amount t h a t loans from the owner can be i n c r e a s e d i s not r e s t r i c t e d as i n c o n s t r a i n t (20). A l s o , s i n c e t h e i r r e s u l t s were obtained by numerical c a l c u l a t i o n r a t h e r than mathematical o p t i m i z a t i o n , t h e r e i s l e s s i n s i g h t i n t o why the a l g o r i t h m y i e l d s the c o r -r e c t r e s u l t . The p e r t u r b a t i o n argument d e r i v e d from the Kuhn-Tucker c o n d i t i o n s p r o v i d e s the reason: a g i v e n combination o f s a l a r y and t a x a b l e d i v i d e n d s cannot be an optimum i f i n c r e a s i n g s a l a r y and d e c r e a s i n g t a x a b l e d i v i d e n d s , o r v i c e v e r s a , decrea-ses t o t a l - t a x e s ' p a i d without v i o l a t i n g any of the c o n s t r a i n t s of the problem. N O T E S 1. Two types o f f r i n g e b e n e f i t s which are not i n c l u d e d i n the model ar e : f r i n g e b e n e f i t s which are non-taxable to the employee i f they are purchased by the c o r p o r a t i o n and which are d e d u c t i b l e t o the owner i f they are pur-chased p e r s o n a l l y , such as moving expenses, and t u i t i o n f e e s ; and f r i n g e b e n e f i t s which are non-deductible to the c o r p o r a t i o n , such as c l u b f e e s . See Pound (1980) and Zimmer (19 80). 2. Income tax ev a s i o n through f a i l i n g to r e p o r t t a x a b l e b e n e f i t s on the owner's tax r e t u r n can a l s o be co n s i d e r e d a non-taxable b e n e f i t i n terms of t h i s model. 3. Income from sources other than the c o r p o r a t i o n the owner c o n t r o l s c o u l d be i n t r o d u c e d without a f f e c t i n g the model s i g n i f i c a n t l y . 4. T h i s ignores a number of f e d e r a l and p r o v i n c i a l tax c r e d i t s . 5. I t i s not d i f f i c u l t to extend the model t o cover the Quebec p r o v i n c i a l income tax s t r u c t u r e . 6. The f r a c t i o n t h r e e - e i g h t h s comes from the f a c t t h a t the d i v i d e n d tax c r e d i t i s one-quarter of grossed-up t a x a b l e d i v i d e n d s , and grossed-up t a x a b l e d i v i d e n d s are t h r e e -halves of t a x a b l e d i v i d e n d s . 7. The d i v i d e n d s r e c e i v e d are termed " p o r t f o l i o " d i v i d e n d s because they are assumed not to be from connected corpo-r a t i o n s . 8. T h i s f o r m u l a t i o n of the model excludes c e r t a i n c o r p o r a t e tax c r e d i t s , f o r example the investment tax c r e d i t . 9. A l l a c t i v e business income and n o n - q u a l i f y i n g business income i s assumed t o be earned i n Canada and a l l i n v e s t -ment income i s assumed to be from Canadian sources. 10. The model does not apply to businesses e a r n i n g income from the e x t r a c t i o n of n a t u r a l resources because of the many s p e c i a l p r o v i s i o n s which would have to be modelled. 11. I t i s assumed t h a t the c o r p o r a t i o n i s not " a s s o c i a t e d " w i t h any other c o r p o r a t i o n , so i t does not have t o share the b u s i n e s s l i m i t and the t o t a l business l i m i t . 68 69 12. A c t i v e business l o s s e s and n o n - q u a l i f y i n g business l o s s e s are excluded from the model s i n c e Y and Y are c o n s t r a i n e d to be non-negative. 13. The model ignores any d i f f e r e n c e between the t a x a t i o n year of the c o r p o r a t i o n and of i t s owner. 14. One problem w i t h t h i s c o n s t r a i n t i s t h a t the gross amount may not be known u n t i l the f i n a n c i a l statements are prepared, which w i l l be a f t e r the end of the f i s c a l year, but the owner may be able t o make a f a i r l y a c c urate guess a t i t . 15. Brooks (1978). 16. See Kwan and Murray (1981), Ness and Vogel (1976), and Sommerfeld (1978), p. 317. In the U.S., s a l a r i e s which pass the reasonableness t e s t are sometimes a t t a c k e d as d i s g u i s e d d i v i d e n d s . 17. Moore (19 77). 18. P e r s o n a l communication from M i c h a e l J . O'Keefe, F a c u l t y of Law, U n i v e r s i t y of B r i t i s h Columbia. 19. See I n t r i l i g a t o r (1971). I t should be noted t h a t the Kuhn-Tucker c o n d i t i o n s are necessary c o n d i t i o n s f o r an optimum o n l y i f the c o n s t r a i n t q u a l i f i c a t i o n i s s a t i s f i e d . One c o n d i t i o n under which t h i s w i l l be t r u e i s i f a l l of the c o n s t r a i n t s are l i n e a r . Only two of the twenty c o n s t r a i n t s i n t h i s problem are n o n - l i n e a r , (6) and (12), so i t i s probable t h a t the Kuhn-Tucker c o n d i t i o n s are necessary f o r t h i s problem. 20. Another circumstance i n which p e r s o n a l purchase might be opt i m a l i s i f the p r i c e f a c i n g the owner i s s u b s t a n t i a l l y l e s s than the p r i c e f a c i n g the f i r m . _ c 21. If; Y i s not equal to $150,000, the c o r r e c t f i g u r e f o r Y should be s u b s t i t u t e d i n the c a l c u l a t i o n of the category l i m i t s f o r gross business income. 22. The hig h c o r p o r a t e r a t e was 52.8% i n B.C. i n 1980 and 51.8% i n O n t a r i o . T h i s s m a l l d i f f e r e n c e does not a f f e c t the expansion paths shown. — S 23. T h i s assumes t h a t Y =±= 150,000. I f i t i s not, the c o r r e c t v alue should be s u b s t i t u t e d i n t h i s statement. CHAPTER 3 SIMULATION RESULTS T h i s chapter develops a method of f i n d i n g numerical s o l u t i o n s to the model and a p p l i e s t h i s method to fou r problems i n the t a x a t i o n of c l o s e l y - h e l d c o r p o r a t i o n s : c a l -c u l a t i o n of the e f f e c t i v e p r i c e s of tax a b l e and non-taxable b e n e f i t s ; e s t i m a t i o n o f the foregone revenue from the small b u s i n e s s deductions; i n t e g r a t i o n of the corporate and per-sona l income taxes; and the use of r e g i s t e r e d r e t i r e m e n t savings plans and d e f e r r e d p r o f i t - s h a r i n g p l a n s . 3.1 THE LINEAR PROGRAMMING ALGORITHM L i n e a r programming i s an a t t r a c t i v e way to sol v e con-s t r a i n e d o p t i m i z a t i o n problems because i t i s r e l a t i v e l y e f f i c i e n t c o m p u t a t i o n a l l y , and because i t guarantees t h a t a g l o b a l optimum w i l l be achieved. T h i s method cannot be a p p l i e d d i r e c t l y to the problem a t hand because of the r e q u i -rement t h a t both the o b j e c t i v e f u n c t i o n and the c o n s t r a i n t s must be l i n e a r , and n e i t h e r of these c o n d i t i o n s i s s a t i s f i e d . The n o n l i n e a r o b j e c t i v e f u n c t i o n can be e l i m i n a t e d by assuming t h a t goods purchases are exogenous, thus r e d u c i n g the problem to one of maximizing the owner's a f t e r - t a x income o r min i m i z i n g the t o t a l amount of cor p o r a t e and p e r s o n a l income tax p a i d . The n o n l i n e a r c o n s t r a i n t s (6) and (12) can be e l i m i n a t e d by bre a k i n g the main problem i n t o f o u r sub-problems, where each sub-problem has l i n e a r c o n s t r a i n t s . The f o u r sub-problems are 70 71 d e f i n e d by the amount of t a x a b l e d i v i d e n d s p a i d and the s i z e of b a s i c f e d e r a l tax, such t h a t t o t a l tax i s c o r r e c t l y d e f i n e d i n the l i s t e d r e g i o n and may be o v e r s t a t e d o u t s i d e t h a t region; (a) t a x a b l e d i v i d e n d s < D r, b a s i c f e d e r a l tax _< 200 (b) " " > D r, " " " - 200 (.c) " " - D r, " " " > 200 (d) " " > D r, " " " > 200 In case ( a ) , the problem i s t o maximize S + L + + D r + D n r - (1 + p) [B± + B 2) +: B1 (29) s u b j e c t t o B x < 200 (30) D n r = 0 (31) B + B« > E t- Y? - (3/8) (D r + D n r) (32) 1 . i = l X 1 and c o n s t r a i n t s (8) to (11), (13) to (15), and (18) to (21). Case (b) i s the same, except t h a t c o n s t r a i n t (11) i s un-necessary s i n c e (31) i s replaced.by: D r = D r (33) In case ( c ) , the d e f i n i t i o n of the f e d e r a l tax r e d u c t i o n i s changed, so the problem i s to maximize S + L + D K + D r + D n r - (1 + p) (B x + B 2) + 0.09 B 1 (34) 72 s u b j e c t to (8) t o (11), (13) to (15), (18) to (21), (31), (32), and: B± < 5,556 (35) Case (d) i s the same as ( c ) , except t h a t (11) and (32) are r e p l a c e d by (33) . A f t e r the f o u r sub-problems have been s o l v e d , the s o l u t i o n to the main problem can be found by t a k i n g the maximum of the s o l u t i o n s to the sub-problems., In order t o use the l i n e a r programming a l g o r i t h m f o r the s i m u l a t i o n s r e p o r t e d i n t h i s c hapter, a number of s p e c i f i c assumptions were made about the parameters of the model. Cor-p o r a t i o n s were assumed to be o f f i v e types: s m a l l manufac-t u r i n g , s m a l l non-manufacturing, s m a l l n o n - q u a l i f y i n g b u s i n e s s , l a r g e manufacturing, and l a r g e non-manufacturing. A " s m a l l " c o r p o r a t i o n i s d e f i n e d i n t h i s chapter to be one w i t h Y = 150,000, i . e . , the l e s s e r of the two l i m i t s t o the s m a l l b u s i -ness de d u c t i o n i s $150,000. A " l a r g e " c o r p o r a t i o n has a cumu-l a t i v e d eduction account balance c a r r i e d over from the p r e v i o u s year of over $750,000, so Y = 0 . Large n o n - q u a l i f y i n g b u s i -nesses f i t i n t o the same category as l a r g e non-manufacturing c o r p o r a t i o n s s i n c e they are s u b j e c t to the same co r p o r a t e tax r a t e . W i t h i n these f i v e c a t e g o r i e s , there are c o r p o r a t i o n s of many d i f f e r e n t s i z e s and d i s t r i b u t i o n p o l i c i e s , so s i m u l a t i o n s are performed f o r l e v e l s of gross c o r p o r a t e income (Y g) from $10,000 to $200,000, w i t h 60%, 80% or 100% of t h a t amount d i s t r i b u t e d . Taxable and non-taxable b e n e f i t s are exogenous 73 i n t h i s chapter, so amounts d i s t r i b u t e d to the owner can be s a l a r y , t a x a b l e d i v i d e n d s , c a p i t a l d i v i d e n d s or repayment of loans from the owner. The minimum amount of s a l a r y i s assumed to be zero. No tax a b l e d i v i d e n d s q u a l i f y f o r a d i v i d e n d refund, s i n c e the c o r p o r a t i o n i s assumed to have no Canadian investment income or income from p o r t f o l i o d i v i d e n d s . The maximum amount of c a p i t a l d i v i d e n d s i s assumed to be zero, as i s the maximum amount of loans from the owner t h a t can be r e -p a i d . Loans from the owner may be i n c r e a s e d , but by no more than the c o r p o r a t i o n ' s u n d i s t r i b u t e d a f t e r - t a x p r o f i t ( i . e . , L m i n = - ( Y g - M) ). T h i s assumption i s e q u i v a l e n t t o c o n s t r a i n t (20), w i t h t a x a b l e and non-taxable b e n e f i t s exogenous, i f the c o r p o r a t i o n has no r e t a i n e d earnings c a r r i e d over from the pr e v i o u s year. The c o r p o r a t i o n i s assumed not to impose the c o n s t r a i n t (14) on the cumulative deduction account balance a t the end of the year, which i s a reasonable p o l i c y i f the c o r p o r a t i o n i s e i t h e r too smal l o r too l a r g e to be concerned about the $750,000 l i m i t . 1980 B.C. tax r a t e s are used f o r the c o r p o r a t i o n and the owner. The owner i s assumed to have exemptions and deductions of $2,990, net of any a d d i t i o n to h i s income from t a x a b l e b e n e f i t s . 3.2 FOUR APPLICATIONS The f i r s t a p p l i c a t i o n of the l i n e a r programming a l g o r i t h m i s to the c a l c u l a t i o n of e f f e c t i v e p r i c e s f o r tax a b l e and non-tax a b l e b e n e f i t s . The Kuhn-Tucker c o n d i t i o n s showed t h a t owners of c l o s e l y - h e l d c o r p o r a t i o n s choose the amount of i n - k i n d 74 b e n e f i t s i n the same way t h a t other consumer goods are chosen, except t h a t the r e l e v a n t p r i c e s f o r i n - k i n d b e n e f i t s are "tax-a d j u s t e d " p r i c e s , i . e . , the p r i c e p a i d f o r the good by the c o r p o r a t i o n l e s s the tax s a v i n g from buying i t . Tax-adjusted p r i c e s can be c a l c u l a t e d u s i n g l i n e a r programming by c a l c u l a -t i n g the r e d u c t i o n i n t o t a l c o r p o r a t e and p e r s o n a l taxes p a i d caused by an i n c r e a s e i n i n - k i n d b e n e f i t s and s u b t r a c t i n g t h i s from the market p r i c e . These p r i c e s are not e x a c t l y the same as i n the Kuhn-Tucker c o n d i t i o n s because here the change i n i n - k i n d b e n e f i t s i s a d i s c r e t e change, w i t h o p t i m i z i n g behaviour both b e f o r e and a f t e r . The d i f f e r e n c e between the "before" and " a f t e r " problems i s t h a t the i n c r e a s e i n expenditure on i n - k i n d b e n e f i t s i s s u b t r a c t e d from both gross c o r p o r a t e income and the amount o f money the f i r m has to d i s t r i b u t e . In the case o f t a x a b l e b e n e f i t s , o n e - t h i r d of the i n c r e a s e i n expendi-t u r e i s added to the owner's t a x a b l e income, where the o n e - t h i r d i s an e s timate based on the minimum standby charge f o r l e a s e d c a r s . Tables I and II r e p o r t the r e s u l t s of s i m u l a t i o n s of a $10 i n c r e a s e i n non-taxable and t a x a b l e b e n e f i t s r e s p e c t i v e l y . The key f i n d i n g i s t h a t the t a x - a d j u s t e d p r i c e s are very low. An owner buying non-taxable b e n e f i t s through h i s c o r p o r a t i o n i s spending f i f t y - c e n t d o l l a r s , s i n c e the e f f e c t i v e p r i c e of a $10 non-taxable b e n e f i t i s o f t e n $5 or l e s s , and purchases of TABLE I : Tax-Adjusted Price of a $10 Non-Taxable Benefit Gross Corporate Income Percent Distributed Small Mfg. Corp. Small Non-Mfg. Corp. Non-Qual. Business Corp. Large Mfg. Corp. Large Non-Mfg. Corp. Sole Proprietor 10,000 60 8.51 8.10 7.26 7.26 7.26 7.26 10,000 80 8.51 8.10 7.26 .7.26 7.26 7.26 25,000 60 7.95 7.42 6.22 6.22 6.22 6.22 25,000 80 7.95 7.42 6.22 6.22 6.22 6.22 50,000 60 7.31 7.08 6.05 5.35 4.82 4.82 50,000 80 7.23 6.60 5.39 5.35 4.82 4.82 100,000 60 6.06 5.66 5.39 5.35 4.72 4.38 100,000 80 5.70 5.32 4.82 4.82 4.72 4.38 200,000 60 4.38 4.38 4.82 4.82 4.72 3.81 200,000 80 3.81 3.81 3.81 3.81 3.81 3.81 U l TABLE II: Tax-Adjusted Price of a $10 Taxable Benefit C Gross Small Small Non-Qual. Large Large Corporate Percent Mfg. Non-Mfg. Business Mfg. Non-Mfg. Soil Income Distributed Corp. Corp. Corp. Corp. Corp. Proprietor 10,000 60 8.98 8.69 8.12 8.12 8.12 7.26 10,000 80 8.98 8.69 8.12 8.12 8.12 7.26 25,000 60 8.59 8.23 7.40 7.40 7.40 6.22 25,000 80 8.59 8.23 7.40 7.40 7.40 6.22 50,000 60 8.10 7.99 7.29 6.81 6.44 4.82 50,000 80 8.10 7.66 6.84 6.81 6.44 4.82 100,000 60 7.69 7.29 6.84 6.81 6.37 4.38 100,000 80 7.35 6.97 6.44 6.44 6.37 4.38 200,000 60 6.14 6.14 6.44 6.44 6.37 3.81 200,000 80 5.75 5.75 5.75 5.75 5.75 3.81 <1 CM 77 t a x a b l e b e n e f i t s are e f f e c t i v e l y made wit h s i x t y or seventy-cent d o l l a r s . None of the t a x - a d j u s t e d p r i c e s i s above the market p r i c e o f $10, so i t i s p r e f e r a b l e to purchase these goods through the c o r p o r a t i o n r a t h e r than p e r s o n a l l y . Tax-ad j u s t e d p r i c e s are lower f o r c o r p o r a t i o n s w i t h high gross c o r p o r a t e incomes and a h i g h percentage d i s t r i b u t e d , due to the p r o g r e s s i v i t y o f the p e r s o n a l income tax. The e f f e c t i v e p r i c e s are a l s o lower f o r c o r p o r a t i o n s w i t h higher c o r p o r a t e tax r a t e s , s i n c e t h i s i n c r e a s e s the value o f the deduction f o r expenditure on i n - k i n d b e n e f i t s . The t a b l e s are arranged so t h a t c o r p o r a t e tax r a t e s r i s e from l e f t to r i g h t . The l a s t column of the two t a b l e s g i v e s t a x - a d j u s t e d p r i c e s f o r a s o l e p r o p r i e t o r f o r comparison. Unincorporated business owners are taxed on the p r o f i t s of t h e i r b u s i n e s s e s , so the percentage d i s t r i b u t e d has no e f f e c t on t h e i r tax p o s i t i o n , and hence no e f f e c t on t h e i r t a x - a d j u s t e d p r i c e s . The d i s t i n c t i o n between t a x a b l e and non-taxable b e n e f i t s a l s o has no r e l e v a n c e , s i n c e t a x a b l e b e n e f i t s can only be imputed to employees. In e f f e c t a l l i n - k i n d b e n e f i t s are non-taxable to u n i n c o r p o r a t e d b u s i n e s s e s , which makes t a x a b l e b e n e f i t goods much cheaper to u n i n c o r p o r a t e d businesses than to corpo-r a t i o n s . The t a x - a d j u s t e d . p r i c e s of non-taxable b e n e f i t s t o uni n c o r p o r a t e d businesses are on a par wit h c o r p o r a t i o n s i n the three h i g h e s t r a t e c a t e g o r i e s . One problem w i t h these 78 comparisons i s t h a t the range of i n - k i n d b e n e f i t s may be s m a l l e r f o r u n i n c o r p o r a t e d b u s i n e s s e s than f o r c o r p o r a t i o n s , p a r t i c u l a r l y i n the case of t a x a b l e b e n e f i t goods. The reason i s t h a t the Department of N a t i o n a l Revenue c o u l d r u l e t h a t a car or other v e h i c l e used by an u n i n c o r p o r a t e d business owner p r i m a r i l y f o r p e r s o n a l p l e a s u r e i s a p e r s o n a l l i v i n g expense and not d e d u c t i b l e , but no such problem seems to e x i s t f o r c o r p o r a t i o n s . A second a p p l i c a t i o n of the l i n e a r programming a l g o r i t h m i s t o the e s t i m a t i o n of the foregone revenue, or tax expendi-t u r e , from the s m a l l b u s i n e s s d e d u c t i o n . The c o n v e n t i o n a l approach used.by the Department of Finance and others i s to apply the i n c r e a s e i n the c o r p o r a t e tax r a t e to the amount of a c t i v e business income and n o n - q u a l i f y i n g business income t h a t i s p r e s e n t l y taxed a t the s m a l l business r a t e . The weakness of t h i s approach i s t h a t i t ignores economic responses to the tax change, which i n c l u d e the p o s s i b l e d e c i s i o n of new f i r m s to not become i n c o r p o r a t e d , the g e n e r a l e q u i l i b r i u m e f f e c t s on the s i z e of the s m a l l business s e c t o r , and c o r p o r a t i o n s ' adjustments i n t h e i r f i n a n c i a l p o l i c y . I t i s p o s s i b l e to get an i d e a of the magnitude of the e r r o r i n v o l v e d in. i g n o r i n g the l a s t type of response by c a l c u l a t i n g the o p t i m a l f i n a n c i a l p o l i c y of h y p o t h e t i c a l c o r p o r a t i o n s both before and a f t e r the tax change. The i n c r e a s e i n t o t a l p e r s o n a l and c o r p o r a t e 79 income taxes i s the " t r u e " tax expenditure, which may be compared to the c o n v e n t i o n a l e s t i m a t e . Table I I I r e p o r t s the r e s u l t s from s i m u l a t i n g the e l i m i n a -t i o n of the s m a l l business deduction and the B.C. s m a l l business r a t e r e d u c t i o n f o r s m a l l e r non-manufacturing corpora-tions.''' I t appears t h a t the e r r o r i n v o l v e d i n i g n o r i n g the " f i r s t - o r d e r " b e h a v i o u r a l response i s l a r g e ; the " t r u e " tax expenditure ranges from 35% to 79% of the c o n v e n t i o n a l e s t i m a t e . The over-estimate of the tax expenditure tends to be g r e a t e r the h i g h e r i s the percentage of c o r p o r a t e income d i s t r i b u t e d . The reason i s t h a t the major e s t i m a t i o n e r r o r comes from c o r p o r a t i o n s r e d u c i n g t h e i r t a x a b l e income by d i s t r i b u t i n g funds to shareholders i n s a l a r y r a t h e r than t a x a b l e d i v i d e n d s . T h i s i n c r e a s e s p e r s o n a l income tax due to the l o s s of the d i v i d e n d tax c r e d i t , so tax revenues do r i s e , but not by as much as was expected. Of course, the c o n c l u s i o n t h a t c o n v e n t i o n a l estimates of the tax expenditure are o v e r - s t a t e d r e s t s on a p a r t i a l e q u i l i b r i u m framework, s i n c e the g e n e r a l e q u i l i b r i u m e f f e c t s on the economy as a whole c o u l d c o n c e i v a b l y work i n the o p p o s i t e d i r e c t i o n . Even so, i t would be u s e f u l to use t h i s approach to o b t a i n an aggregate estimate of the tax expenditure from the s m a l l b u s i n e s s deduction, which the Department of Finance estimates u s i n g the c o n v e n t i o n a l method to be $1.2 b i l l i o n f o r 19 79, but t h i s i s i m p o s s i b l e without knowing the proper weights to apply to the i n d i v i d u a l f i r m f i g u r e s . A t h i r d a p p l i c a t i o n i s to the measurement of the i n t e -g r a t i o n of c o r p o r a t e and p e r s o n a l income taxes on the business 80 TABLE ' s i l l : Two Methods of Estimating the Tax Expenditure from the Federal and B.C. Small Business Rate Reductions Gross Corporate Income Percent Distributed "True" Tax Expenditure Conventional Tax Expendi-ture Estimate True as % of Conventional 10,000 60 409 983 42 10,000 80 409 983 42 25,000 60 1,659 4,702 35 25,000 80 1,659 4,702 35 50,000 60 6,618 11,529 57 50,000 80 5,647 12,549 45 100,000 60 17,908 27,050 66 100,000 80 12,956 27,050 48 200,000 60 31,875 40,575 79 200,000 80 18,776 40,575 46 81 income of c l o s e l y - h e l d c o r p o r a t i o n s . C o n v e n t i o n a l measures of i n t e g r a t i o n , such as those used by A l l a n (1965), King (1977) and McLure (1979), measure the t o t a l tax burden on r e t a i n e d earnings and income d i s t r i b u t e d t o shareholders i n a way t h a t i s inadequate f o r c l o s e l y - h e l d c o r p o r a t i o n s . One problem i s t h a t the tax burden on the r e t a i n e d earnings may not be simply the c o r p o r a t e r a t e , as i t i s f o r w i d e l y - h e l d c o r p o r a -t i o n s i f f u t u r e taxes a t the shareholder l e v e l are i g n o r e d . The reason i s t h a t i f the c o r p o r a t e r a t e exceeds the p e r s o n a l marginal r a t e , the owner of a c l o s e l y - h e l d corporation.:can d e c l a r e the intended amount of r e t a i n e d earnings as s a l a r y , w i t h the c o r p o r a t i o n t a k i n g back an e q u i v a l e n t amount as a l o a n from the owner. Thus the tax burden on the r e t a i n e d earnings of c l o s e l y - h e l d c o r p o r a t i o n s i s e f f e c t i v e l y the lower of the c o r p o r a t e tax r a t e and the owner's marginal tax r a t e . Another problem concerns the measurement of the tax burden on income d i s t r i b u t e d t o s h a r e h o l d e r s . Conventional measures assume t h a t d i s t r i b u t i o n s ' take the form of t a x a b l e d i v i d e n d s , w h i l e c l o s e l y - h e l d c o r p o r a t i o n s have other c h o i c e s , e s p e c i a l l y s a l a r y . One would expect d i s t r i b u t i o n s to be made i n the b e s t combination of compensation a l t e r n a t i v e s , where the b e s t combi-n a t i o n i s t h a t which r e s u l t s i n the lowest p o s s i b l e t o t a l tax burden. One way of d e a l i n g w i t h these problems i s to d e f i n e a new standard of i n t e g r a t i o n f o r b u s i n e s s income earned through c l o s e l y - h e l d c o r p o r a t i o n s . I n t e g r a t i o n may be s a i d to be 8 2 achieved i f the s o l e owner of a c o r p o r a t i o n pays the same t o t a l income taxes as an u n i n c o r p o r a t e d i n d i v i d u a l , where: both i n d i v i d u a l s take advantage of a l l tax p l a n n i n g opportu-2 n i t i e s ; both have the same amounts of each type of income; both r e t a i n the same amount of the cash flow i n the b u s i n e s s ; and the c o r p o r a t i o n may not repay any loans from the owner or d i s t r i b u t e income beyond the year's a f t e r - t a x p r o f i t . The advantages of t h i s d e f i n i t i o n are t h a t i t makes c l e a r what v a r i a b l e s are to be h e l d constant, i t allows f o r tax p l a n n i n g , and i t i s based on t o t a l : t a x burdens r a t h e r than the u s u a l marginal tax r a t e a n a l y s i s . I t s main disadvantage i s t h a t i t does not take i n t o account f u t u r e taxes a t the shareholder l e v e l when r e t a i n e d earnings are d i s t r i b u t e d . Departures from t h i s standard of i n t e g r a t i o n may be d e f i n e d i n terms of the d i f f e r e n c e i n the t o t a l taxes p a i d by the two b u s i n e s s owners; a d i f f e r e n c e f a v o u r i n g c o r p o r a t i o n owners may be c a l l e d "super-i n t e g r a t i o n , " f o l l o w i n g Jones (1979), and a d i f f e r e n c e i n the other d i r e c t i o n may be c a l l e d " s u b - i n t e g r a t i o n . " The s i m u l a t i o n s r e p o r t e d i n Tables IV and V make i t c l e a r t h a t the business income of c l o s e l y - h e l d c o r p o r a t i o n s i s u s u a l l y s u p e r - i n t e g r a t e d . Table IV- reports'- the absolute tax savings which are p o s s i b l e f o r a s o l e p r o p r i e t o r s w i t c h i n g to each of the f i v e types of c o r p o r a t i o n s , and Table V expresses these savings as a percentage of the tax burden on the s o l e TABLE IV: Tax Savings from Incorporation Gross Small Small Non-Qual. Large Large Corporate Percent Mfg. Non-Mfg. Business Mfg. Non-Mfg. Income D i s t r i b u t e d Corp. Corp. Corp. Corp. Corp. 10,000 60 613 409 - - -10,000 80 613 409 - - -10,000 110 613 409 - - -25,000 60 2,571 1,659 - - -25,000 80 2,571 1,659 - - -25,000 100 2,426 1,530 - - -50,000 60 8,771 6,618 1.639 196 -50,000 80 7,861 5,647 1,299 196 -50,000 100 5,926 3,925 - - -100,000 60 22,803 18,800 8,590 4,014 893 100,000 80 17,610 13,848 5,228 3,144 893 100,000 100 11,164 7,955 - - -200,000 60 46,727 41,233 26,892 18,559 9,359 200,000 80 31,317 26,504 14,823 11,529 7,729 200,000 100 15,765 10,952 — — — CO TABLE V: Percentage Decrease in Total Taxes from Incorporation Gross Small Small Non-Qual. Large Large Corporate Percent Mfg. Non-Mfg. Business Mfg. Non-Mfg. Income Distributed Corp. Corp. Corp. Corp. Corp. 10,000 60 43 29 - -10,000 80 43 29 - - -10,000 100 43 29 - - -25,000 60 41 27 - - -25,000 80 41 27 - - -25,000 100 39 25 - - -50,000 60 50 37 9 1 -50,000 80 44 32 7 1 -50,000 100 34 22 - - -100,000 60 51 42 19 9 2 100,000 80 39 31 12 7 2 100,000 100 25 18 - - -200,000 60 44 39 25 18 9 200,000 80 30 25 14 11 7 200,000 100 15 10 — — — 00 85 p r o p r i e t o r . The reasons why the business income of c l o s e l y -h e l d c o r p o r a t i o n s i s not s u b - i n t e g r a t e d , as i s normally the case f o r w i d e l y - h e l d c o r p o r a t i o n s , l i e i n the p o s s i b i l i t y of paying s a l a r y to the owner. For income d i s t r i b u t e d to the owner, s a l a r y has the same tax treatment as self-employment 3 income, so there i s no p o s s i b i l i t y of s u b - i n t e g r a t i o n . For r e t a i n e d e a r n i n g s , s u b - i n t e g r a t i o n c o u l d occur i f the c o r p o r a t e r a t e i s h i g h e r than the owner's mar g i n a l tax r a t e , but the income to be r e t a i n e d i n the c o r p o r a t i o n can be p a i d out as s a l a r y and loaned back to the c o r p o r a t i o n to a v o i d t h i s problem. Another c o n c l u s i o n from the two t a b l e s i s t h a t the degree of s u p e r - i n t e g r a t i o n i s g r e a t e s t f o r the lowest c o r p o r a t e tax r a t e s . S m aller manufacturing businesses can achieve about a 25-50% decrease i n taxes by i n c o r p o r a t i n g , compared to 20-40% f o r s m a l l e r non-manufacturing bus i n e s s e s and l e s s e r savings f o r o t h e r types of b u s i n e s s e s . For the three types of b u s i n e s -ses w i t h the h i g h e s t c o r p o r a t e tax r a t e s , the tax saving from i n c o r p o r a t i o n i s e n t i r e l y a t t r i b u t a b l e to reduced t a x a t i o n on r e t a i n e d e a r n i n g s . T h i s i s shown by the f a c t t h a t i f 100% of gross c o r p o r a t e income i s d i s t r i b u t e d , the tax s a v i n g i s zero. Smaller c o r p o r a t i o n s b e n e f i t from both reduced t a x a t i o n on r e t a i n e d earnings and s u p e r - i n t e g r a t i o n f o r d i s t r i b u t e d income; a s m a l l e r non-manufacturing business which d i s t r i b u t e s a l l of i t s $50,000 income can s t i l l save almost $4,000 by i n c o r p o r a t i n g , 86 which reduces i t s t o t a l taxes by 22%. The tax s a v i n g on d i s t r i b u t e d income i s mostly due to the d i v i d e n d gross-up and tax c r e d i t system, which was l i b e r a l i z e d i n 1978. Table VI shows t h a t a r e t u r n to. the- pre-1978 system would, reduce the tax savings from i n c o r p o r a t i o n f o r t h i s business from almost $4,000 to under $1,400, w i t h s i m i l a r r e d u c t i o n s f o r other businesses p u r s u i n g a f u l l - d i s t r i b u t i o n p o l i c y . The tax savings from i n c o r p o r a t i o n would s t i l l remain very s i g n i -f i c a n t f o r c o r p o r a t i o n s which d i s t r i b u t e l e s s o f t h e i r e a r n i n g s , because t h i s change has no e f f e c t on the reduced t a x a t i o n of r e t a i n e d e a r n i n g s . The tax savings from i n c o r p o r a t i o n r e p o r t e d i n Table IV may o v e r s t a t e the b e n e f i t s to i n c o r p o r a t i o n t o some extent. One reason i s t h a t the f u t u r e taxes payable by shareholders when the r e t a i n e d earnings are d i s t r i b u t e d are not i n c l u d e d , but t h i s i s not too s e r i o u s because of the d i v i d e n d gross-up and tax c r e d i t system. F i g u r e 4 of the l a s t chapter shows t h a t a shareholder w i t h no ot h e r income and minimum exemptions and deductions can r e c e i v e $33,783 i n d i v i d e n d s a t a c o s t of on l y $88 i n tax. Another reason why the f i g u r e s i n Table IV should be d i s c o u n t e d somewhat i s t h a t the g r e a t e r l e g a l and acc o u n t i n g c o s t s o f the c o r p o r a t e forms are not taken i n t o account. A reasonable estimate of these c o s t s i s $1,100 which can be s u b t r a c t e d from.the f i g u r e i n Table IV t o pr o v i d e estimates of TABLE VI: Tax Savings from Incorporation Under Pre-1978 Dividend Gross-Up and Tax Credit Gross Corporate Income Percent Distributed Small Mfg. Corp. Small Non-Mfg. Corp. Non-Qual. Business Corp. Large Mfg. Corp. Large Non-Mfg. Corp. 10,000 60 391 142 - -10,000 80 391 142 - - -10,000 100 391 142 - - -25,000 60 2,116 1,097 - - -25,000 80 1,960 954 - - -25,000 100 1,504 481 - - -50,000 60 7,852 5,698 1,639 196 50,000 80 5,849 3,829 1,299 196 -50,000 100 3,241 1,372 - - -100,000 60 20,131 16,380 8,590 4,014 893 100,000 80 13,958 10,576 5,228 3,144 893 100,000 100 6,664 3,329 - - -200,000 60 44,280 39,278 26,892 18,559 9,359 200,000 80 27,139 22,741 14,283 11,529 7,729 200,000 100 9,477 5,079 — — — OO — I 88 the net b e n e f i t s of i n c o r p o r a t i o n . H The i s s u e of c h o i c e of o r g a n i z a t i o n a l form i s d i s c u s s e d f u r t h e r i n Chapter 5. A f i n a l a p p l i c a t i o n of the a l g o r i t h m i s to the use of r e g i s t e r e d r e t i r e m e n t savings plans and d e f e r r e d p r o f i t s h a r i n g p l a n s . The f i r s t q u e s t i o n to study i s the e f f e c t on t o t a l taxes o f c o n t r i b u t i n g o n l y to an RRSP. 5 Zintmer (1980) has argued t h a t the b e n e f i t s of c o n t r i b u t i n g to an RRSP are s u f f i -c i e n t t o j u s t i f y m o d i f y ing the f i n a n c i a l p o l i c y of c l o s e l y - h e l d c o r p o r a t i o n s . He argues t h a t a l l income should be d i s t r i b u t e d as s a l a r y r a t h e r than t a x a b l e d i v i d e n d s u n t i l the l e v e l of earned income r e q u i r e d f o r the maximum RRSP c o n t r i b u t i o n i s reached. The tax b e n e f i t s from t h i s p o l i c y are q u a n t i f i e d f o r s m a l l e r c o r p o r a t i o n s i n Table VII. The f o u r t h and :seventh columns show the tax s a v i n g f o r s m a l l e r manufacturing and non-manufac-t u r i n g c o r p o r a t i o n s from r a i s i n g RRSP c o n t r i b u t i o n s from zero to $2,000 and r a i s i n g s a l a r y , i f necessary, to meet the t e s t t h a t c o n t r i b u t i o n s cannot exceed 20% of earned income. I t i s apparent t h a t the tax savings are u s u a l l y s m a l l r e l a t i v e to the s i z e of the c o n t r i b u t i o n and can even be n e g a t i v e , e s p e c i a l l y f o r s m a l l e r manufacturing c o r p o r a t i o n s . ^ Columns f i v e and e i g h t show t h a t the tax savings from r a i s i n g c o n t r i b u t i o n s from $2,000 to $5,500 are s i m i l a r l y s m a l l . For example, a sm a l l non-manufacturing c o r p o r a t i o n which d i s t r i b u t e s 80% of i t s $50,000 income has a tax s a v i n g from the f i r s t $2,000 i n c o n t r i -b u t i o n s of o n l y 17% of the c o n t r i b u t i o n s , and a f u r t h e r $3,500 TABLE VII.:: Tax Savings from RRSP Contributions by Owners of Smaller Corporations Gross Corporate Income SMALLER MANUFACTURING CORPORATIONS "SMALLER NON--MANUFACTURING CORPORATIONS . | Percent Distributed Salary RRSP = i f Tax Saving 0 RRSP 0 vs 2,000 Tax Saving RRSP 2,000 vs 5,500 Salary ; RRSP = i f 0 Tax Saving RRSP 0 vs 2,000 Tax Saving RRSP 2,000 vs 5,500 35,000 60 7,619 351 -1,311 7,619 476 -392 35,000 80 6,489 390 -1,118 7,040 518 -285 50,000 60 6,966 362 -1,188 7,380 537 -392 50,000 80 2,526 -92 -569 3,608 340 200 75,000 60 2,582 -84 -570 4,231 396 186 75,000 80 - -88 -185 - 261 567 100,000 60 - -164 -117 - 192 377 100,000 80 - 19 -68 - 468 560 200,000 60 50,000 1,123 1,966 50,000 1,123 1,966 200,000 80 50,000 1,238 2,167 50,000 1,238 2,167 Ob Vo 90 c o n t r i b u t i o n r a i s e s the tax sav i n g by o n l y 6% of the $3,500. The reason f o r the s m a l l tax savings can be found i n columns three and s i x o f the t a b l e , which show the o p t i m a l s a l a r i e s f o r the two types o f c o r p o r a t i o n s i n the absence of RRSP c o n t r i b u t i o n s . These s a l a r i e s are q u i t e low, and the tax c o s t of r a i s i n g them cuts i n t o the tax savings from the d e d u c t i b i -l i t y o f RRSP c o n t r i b u t i o n s . The op t i m a l s a l a r i e s f o r the three other types of c o r p o r a t i o n s are hi g h e r , so t h i s problem w i t h RRSP c o n t r i b u t i o n s o n l y occurs w i t h the two types of c o r p o r a t i o n s . An a l t e r n a t i v e t a x - s h e l t e r e d savings p l a n f o r owners of c l o s e l y - h e l d c o r p o r a t i o n s i s the d e f e r r e d p r o f i t - s h a r i n g p l a n . U n l i k e r e g i s t e r e d pension p l a n s , a d e f e r r e d p r o f i t - s h a r i n g p l a n can be s e t up s o l e l y f o r the b e n e f i t o f key share h o l d e r s of a c l o s e l y - h e l d c o r p o r a t i o n . The optimal RRSP-DPSP choice can be added on to the model by s p e c i f y i n g t h a t the owner wants to c o n t r i b u t e an exogenously-determined amount C to the two types of p l a n s . ^ T h i s amount i s to be a l l o c a t e d among RRSP R c o n t r i b u t i o n s (C ), DPSP c o n t r i b u t i o n s by the f i r m f o r the b e n e f i t of the owner ( C D ^ ) , and the owner's p e r s o n a l c o n t r i b u -t i o n s to the DPSP ( C D p ) : 8 C = C R + C D f + C D P (36) The l i m i t s f o r c o n t r i b u t i o n s are $5,500 f o r RRSP c o n t r i b u t i o n s , $3,500 f o r cor p o r a t e DPSP c o n t r i b u t i o n s , and $5,500 f o r p e r s o n a l 91 DPSP c o n t r i b u t i o n s : C R < 5,500 (37) 3,500 (38) < 5,500 (39) T h i s makes a t o t a l p o s s i b l e c o n t r i b u t i o n to t a x - s h e l t e r e d savings p l a n s o f $14,000, compared to $5,500 f o r u n i n c o r p o r a t e d b u s i n e s s owners and f o r employees who do not have access t o a DPSP. RRSP c o n t r i b u t i o n s and c o r p o r a t e DPSP c o n t r i b u t i o n s are a l s o l i m i t e d to 20% o f s a l a r y : Three of the c o n s t r a i n t s of the s i m u l a t i o n model have to be a l t e r e d to accommodate the three new v a r i a b l e s : c o r p o r a t e DPSP c o n t r i b u t i o n s have to be i n c l u d e d i n (10), the co r p o r a t e budget c o n s t r a i n t ; the d e d u c t i b i l i t y to the c o r p o r a t i o n of i t s DPSP c o n t r i b u t i o n s must be r e c o g n i z e d i n (15); and the p e r s o n a l d e d u c t i b i l i t y of RRSP c o n t r i b u t i o n s changes the d e f i n i t i o n of p e r s o n a l t a x a b l e income i n (9). P e r s o n a l DPSP c o n t r i b u t i o n s are not d e d u c t i b l e , so no a d d i t i o n a l change to (9) i s r e q u i r e d . S i m u l a t i o n s w i t h the augmented model can be performed u s i n g the same method as b e f o r e . Table VIII shows how the owners o f s m a l l e r manufacturing and non-manufacturing c o r p o r a t i o n s w i l l a l l o c a t e o p t i m a l l y t o t a l c o n t r i b u t i o n s o f $5,500, which C ••< 0.2 S (40) < 0.2 S (41) TABLE VTII: :Optimal A l l o c a t i o n of Tax-Sheltered Savings Plan C o n t r i b u t i o n s by Owners of Smaller Corporations Gross Corporate Income SMALLER MANUFACTURING' CORPORATIONS SMALLER NON-MANUFACTURING CORPORATIONS Percent D i s t r i b u t e d Percent A l l o c a t i o n C R:C DP:C D f Tax Saving Over Zero C o n t r i b u t i o n s Percent A l l o c a t i o n C R:C DP:C D f Tax Saving Over Zero C o n t r i b u t i o n s Tax Saving Over $5,500 RRSP Con t r i b u t i o n s . 35,000 60 35:31:35 781 50:0:50 1,070 84 35,000 80 33:34:33 916 50:0:50 1,219 233 50,000 60 34:32:34 884 50:0:50 1,131 145 50,000 80 50:0:50 640 50:0:50 1,361 540 75,000 60 50:0:50 647 50:0:50 1,418 582 75,000 80 50:0:50 937 50:0:50 1,552 828 100,000 60 50:0:50 861 50:0:50 1,330 569 100,000 80 50:0:50 1,229 50:0:50 1,930 1,028 200,000 60 0:0:100 3,089 0:0:100 3,089 3,089 200,000 80 0:0:100 3,406 0:0:100 3,406 3,406 93 i s the maximum RRSP c o n t r i b u t i o n . The o p t i m a l a l l o c a t i o n i s not t o put the whole $5,500 i n t o an RRSP, except i f gross co r p o r a t e income i s above the s m a l l business deduction l i m i t of $150,000. In most s i t u a t i o n s the o p t i m a l a l l o c a t i o n i s to d i v i d e t o t a l c o n t r i b u t i o n s evenly between the RRSP c o n t r i b u -t i o n and the c o r p o r a t e DPSP c o n t r i b u t i o n . A comparison of the l a s t two columns of the t a b l e shows t h a t t h i s u s u a l l y produces a t l e a s t double the tax s a v i n g . The reason why e q u a l i z i n g RRSP c o n t r i b u t i o n s and c o r p o r a t e DPSP c o n t r i b u t i o n s i s u s u a l l y the o p t i m a l p o l i c y i s t h a t t h i s i n s u r e s t h a t a l l c o n t r i b u -t i o n s are d e d u c t i b l e somewhere, w h i l e m i n i m i z i n g the amount of s a l a r y t h a t has t o be p a i d to s a t i s f y c o n s t r a i n t s (40) and (.41) . The t a b l e i n d i c a t e s t h a t p e r s o n a l DPSP c o n t r i b u t i o n s have a r o l e o n l y f o r lower-income s m a l l e r manufacturing corpo-r a t i o n s , but t h i s i s l i k e l y t o - u n d e r s t a t e t h e i r importance. U n l i k e RRSP c o n t r i b u t i o n s and c o r p o r a t e DPSP c o n t r i b u t i o n s , p e r s o n a l DPSP c o n t r i b u t i o n s are non-taxable when they are w i t h -drawn by the owner. T h i s advantage i s not i n c l u d e d i n the model. Table V I I I a l s o shows t h a t i f c o n t r i b u t i o n s to tax-s h e l t e r e d savings p l a n s are a l l o c a t e d o p t i m a l l y , the immediate tax savings to owners of s m a l l e r c l o s e l y - h e l d c o r p o r a t i o n s can . be q u i t e s i g n i f i c a n t . Optimal a l l o c a t i o n of c o n t r i b u t i o n s r a i s e s the tax savings to 20-25% o f the c o n t r i b u t i o n s , as compared to 0-15% for the all-RRSP p o l i c y . Even so, t h i s i s low compared 94 to what u n i n c o r p o r a t e d b u s i n e s s owners w i t h the same business income r e c e i v e . 1 0 For example, !a s o l e p r o p r i e t o r w i t h b u s i -ness income of $50,000 has a tax s a v i n g of 50% of a $5,500 RRSP c o n t r i b u t i o n . The reason i s t h a t t a x a b l e d i v i d e n d s p a i d by c l o s e l y - ^ h e l d c o r p o r a t i o n s are not counted as earned income f o r RRSP c o n t r i b u t i o n s . Owners o f n o n - q u a l i f y i n g b u s i n e s s c o r p o r a t i o n s and l a r g e r manufacturing and non-manufacturing corporations, do not have t h i s problem because t h e i r d i s t r i b u -t i o n s to shareholders are more l i k e l y to take the form of s a l a r y than t a x a b l e d i v i d e n d s , so they w i l l a l s o have higher savings from RRSP c o n t r i b u t i o n s . The i s s u e i n t h i s case i s whether c o r p o r a t e DPSP c o n t r i b u t i o n s w i l l produce even g r e a t e r s a v i n g s , which i s p o s s i b l e i f the owner's mar g i n a l tax r a t e i s l e s s than the c o r p o r a t e r a t e . N O T E S 1. The two changes are sim u l a t e d together because the lower B.C. r a t e i s t i e d l e g a l l y to the e x i s t e n c e of the smal l b u s i n e s s deduction. 2. For the c o r p o r a t i o n , income should be measured p r i o r to the deduction of the owner's s a l a r y . 3. A c t u a l l y , s a l a r y i s s l i g h t l y b e t t e r than self-employment income, s i n c e i t i s e l i g i b l e f o r the employment expense ded u c t i o n . 4. T h i s estimate was p r o v i d e d by Michael O'Keefe, F a c u l t y of Law, U n i v e r s i t y of B r i t i s h Columbia. 5. Spousal RRSPs are not c o n s i d e r e d i n t h i s a n a l y s i s . 6. Cadesky and Kwan (1981) a l s o r e p o r t examples of negative tax savings from RRSP c o n t r i b u t i o n s by owner-managers. 7. The use of an RRSP-DPSP combination has a l s o been suggested by Cadesky and Kwan (19 81). 8. T h i s a n a l y s i s excludes d e f e r r e d a n n u i t i e s , which are very s i m i l a r to p e r s o n a l c o n t r i b u t i o n s to DPSPs. T h i s has no e f f e c t on the r e s u l t s r e p o r t e d i n Table V I I I below. 9. The RRSP c o n t r i b u t i o n l i m i t i s lower i f the owner i s e n r o l l e d i n a r e g i s t e r e d pension p l a n . 10. I t i s a l s o low compared to the savings a v a i l a b l e to o r d i n a r y employees w i t h the same l e v e l of income. 95 CHAPTER 4 RELAXING THE KEY ASSUMPTIONS OF THE MODEL The key assumptions of the model presented i n Chapter 2 are t h a t the c o r p o r a t i o n i s owned by one i n d i v i d u a l and t h a t the owner maximizes h i s u t i l i t y f o r the c u r r e n t p e r i o d without regard f o r the f u t u r e impact of h i s d e c i s i o n s . T h i s chapter d i s c u s s e s the ways i n which these assumptions c o u l d be r e l a x e d and the problems t h a t are i n v o l v e d . The l a s t p a r t of the chapter addresses the q u e s t i o n of whether the optimal s t a t i c program developed i n Chapter 2 i s l i k e l y t o be d i f f e r e n t from the o p t i m a l dynamic program. 4.1 MULTIPLE OWNERS Re l a x i n g the assumption t h a t the c o r p o r a t i o n has onl y one owner c r e a t e s problems i n d e f i n i n g both the o b j e c t i v e f u n c t i o n t o be maximized and the c o n s t r a i n t s on the maximization. Three p o s s i b l e o b j e c t i v e f u n c t i o n s may be i d e n t i f i e d . 1 F i r s t , a dominant shareholder may maximize h i s own u t i l i t y without regard 2 f o r the i n t e r e s t s of the m i n o r i t y s h a r e h o l d e r s . The other s h a r e h o l d e r s ' p r e f e r e n c e s may a f f e c t the f i r m ' s f i n a n c i a l p o l i c y , but only i f the dominant shareholder does not s u f f e r as a r e s u l t . T h i s i s j u s t an i l l u s t r a t i o n of the f a c t t h a t m i n o r i t y s h a r e h o l d e r s i n c l o s e l y - h e l d c o r p o r a t i o n s may be i n a very d i f -f i c u l t p o s i t i o n i f the consensual b a s i s of decision-making breaks down. Second, i n a husband-wife or f a m i l y c o r p o r a t i o n , the owners may maximize f a m i l y u t i l i t y without any c o n f l i c t among t h e i r i n t e r e s t s . A b s t r a c t i n g from the c o m p l i c a t i o n s of taxable and non-taxable b e n e f i t s , the o b j e c t i v e f u n c t i o n may be simply 96 the sum of the a f t e r - t a x incomes of the f a m i l y members. T h i s i s the o b j e c t i v e f u n c t i o n used f o r f a m i l y farm c o r p o r a t i o n s i n Chapter 5. T h i r d , i n the g e n e r a l multi-owner s i t u a t i o n , the f i r m may maximize the v e c t o r of i t s owners' u t i l i t i e s . T h i s i s j u s t the weak statement t h a t any f i n a n c i a l p o l i c y chosen by a c l o s e l y - h e l d c o r p o r a t i o n may be expected t o be P a r e t o - o p t i m a l f o r the s e t of i t s owners, i . e . , i t i s not p o s s i b l e to make one owner b e t t e r o f f without making another owner worse o f f . T h i s assumption makes the problem of determining an op t i m a l f i n a n c i a l p o l i c y a "ve c t o r maximum problem" and a s o l u t i o n w i l l be an 3 " e f f i c i e n t " f i n a n c i a l p o l i c y . The s e t of e f f i c i e n t f i n a n c i a l p o l i c i e s may be found by maximizing each owner's u t i l i t y i n t u r n s u b j e c t t o the u t i l i t y l e v e l s o f a l l other owners being h e l d constant. T h i s s e t cannot n e c e s s a r i l y be obtained by maximizing weighted sums o f owners' u t i l i t i e s , even i f a l l p o s s i b l e weights are used, s i n c e some e f f i c i e n t s o l u t i o n s may not be d i s c o v e r e d . I t i s i n t e r e s t i n g t h a t the v e c t o r maximum approach t o the m u l t i -owner problem has not been mentioned i n the tax p r a c t i t i o n e r l i t e r a t u r e , although perhaps i t i s simply taken f o r granted i n p r a c t i c a l a p p l i c a t i o n s . The ad hoc approach advocated by Kwan and -.Murray (i9 81) does appear to be i n t h i s s p i r i t . D e f i n i n g the c o n s t r a i n t s on the f i n a n c i a l p o l i c y o f a c o r p o r a t i o n w i t h m u l t i p l e shareholders i s a d i f f i c u l t e x e r c i s e . The c o n s t r a i n t s t h a t are p e r c e i v e d probably w i l l vary among tax p r a c t i t i o n e r s and over time. The source o f the problem i s t h a t some areas o f the law are not c l e a r - c u t and the a d m i n i s t r a t i v e 98 p r a c t i c e o f Revenue Canada i s important i n d e f i n i n g the e f f e c t i v e c o n s t r a i n t s . An example of the problem i s s i d e payments among share-h o l d e r s . I t might be d e s i r a b l e t o d i r e c t d i v i d e n d s or s a l a r y to a low-income shareholder who would then make payments to the other s h a r e h o l d e r s . Revenue Canada c o u l d r e a s s e s s the h i g h e r -income s h a r e h o l d e r s t o i n c l u d e the amounts i n t h e i r incomes as i n d i r e c t b e n e f i t s or employment income. However, the amounts c o u l d be c o n s i d e r e d t o be g i f t s o r , more l i k e l y , w i l l simply escape d e t e c t i o n by Revenue Canada. Of course, t h i s type of i n c o m e - s p l i t t i n g i s most e a s i l y accomplished between a husband and w i f e because the m i n g l i n g of funds makes s i d e payments un-4 necessary. Another example i s the importance of "reasonableness" c o n s t r a i n t s , which can take many forms. The reasonableness c o n s t r a i n t on s a l a r y i s not g e n e r a l l y e n f o r c e d by Revenue Canada f o r f u l l - t i m e shareholder-employees, but there i s an attempt a t enforcement f o r employees who perform l i t t l e o r no s e r v i c e s f o r the c o r p o r a t i o n — p a r t i c u l a r l y spouses of s h a r e h o l d e r s . In such a circumstance, the a l t e r n a t i v e s to s a l a r y payments are reason-able amounts of d i r e c t o r s ' f e e s , i n t e r e s t on loans to the c o r p o r a t i o n , and r e n t a l fees on equipment l e a s e d to the corpo-r a t i o n . Another reasonableness c o n s t r a i n t a p p a r e n t l y a p p l i e s to d i v i d e n d s i n c e r t a i n s i t u a t i o n s . Revenue Canada has s t a t e d t h a t 99 the amount of d i v i d e n d s p a i d should be commensurate w i t h a reasonable r a t e of r e t u r n on investment i n the shares of the c o r p o r a t i o n . T h i s was a p p l i e d i n the T i t e l y case t o i n c l u d e i n the income of two o p t o m e t r i s t s almost $100,000 i n d i v i d e n d s t h a t t h e i r wives had r e c e i v e d on investment of $300. Revenue Canada's p o s i t i o n i s t h a t t h i s a l s o a p p l i e s t o a person who i s b a s i c a l l y an employee of the c o r p o r a t i o n but who has a minor s h a r e h o l d i n g i n t e r e s t . I t i s s a i d t o be unreasonable f o r an employee who c o u l d command a s a l a r y of $50,000 to r e c e i v e a s a l a r y of $500 and d i v i d e n d s o f $36,000 on shareholdings worth $1.00. Revenue Canada may a l s o apply t h i s d o c t r i n e t o l i m i t d i v i d e n d s to f a m i l y members f o l l o w i n g an e s t a t e f r e e z e . Perhaps the most important q u e s t i o n i n d e f i n i n g the cons-t r a i n t s on the f i n a n c i a l p o l i c y of a c o r p o r a t i o n w i t h m u l t i p l e s h a r e h o l d e r s i s whether there i s a c o n s t r a i n t s p e c i f y i n g the r e l a t i o n s h i p among the amounts of d i v i d e n d s r e c e i v e d by the v a r i o u s s h a r e h o l d e r s . Such a c o n s t r a i n t i s pr e s e n t i f there i s a s i n g l e c l a s s o f shares because d i v i d e n d s must then be p r o p o r t i o n a l t o share ownership. Kwan and Murray (19 81) and others have suggested having m u l t i p l e c l a s s e s of shares w i t h d i f f e r i n g ownership p r o p o r t i o n s . I f t h i s i s done, each share-h o l d e r can r e c e i v e a d i f f e r e n t div.idend/salary combination. However, many lawyers are wary of t h i s approach as they f e a r t h a t i t c o u l d be a t t a c k e d a& c o n f e r r i n g an i n d i r e c t b e n e f i t . 5 100 They advocate i n s t e a d , i n t e r p o s i n g h o l d i n g c o r p o r a t i o n s between each s h a r e h o l d e r and the o p e r a t i n g c o r p o r a t i o n . For example, i f Mr. A and Mr. B. j o i n t l y own Opco, Mr. A and Mr. B c o u l d each form a h o l d i n g c o r p o r a t i o n w i t h the shares being t r a n s f e r r e d u s i n g a S e c t i o n 85 t a x - f r e e r o l l o v e r . Opco 1s d i v i d e n d s now flow to the two h o l d i n g c o r p o r a t i o n s r a t h e r than the i n d i v i d u a l s h a r e h o l d e r s , and there i s no P a r t I tax because o f the i n t e r c o r p o r a t e nature o f the d i v i d e n d s . The two i n d i v i -d u a l s can then i n d i v i d u a l l y decide the amount of d i v i d e n d s they wish to d e c l a r e to themselves, and any e x t r a funds can be loaned back to Opco or used to purchase p o r t f o l i o investments. The o n l y problem i s t h a t d i v i d e n d s p a i d out o f the business earnings of Opco w i l l not reduce Opco's cumulative deduction account u n l e s s the h o l d i n g c o r p o r a t i o n s e l e c t to pay the 25% P a r t IV tax on the d i v i d e n d . 6 The P a r t IV tax i s refunded when the funds are flowed through t o the s h a r e h o l d e r s , but to the e x t e n t t h a t the shareholders wish to r e t a i n the funds i n the h o l d i n g corpo-r a t i o n s t h e r e i s an unpleasant c h o i c e between paying the P a r t IV tax and m i s s i n g the r e d u c t i o n i n the cumulative deduction account. For t h i s reason, and because o f the e x t r a c o s t s i n v o l v e d i n having a d d i t i o n a l c o r p o r a t i o n s , " d i v i d e n d s p r i n k l i n g " through m u l t i p l e share c l a s s e s i s more advantageous although i t i s a l s o more r i s k y . A l s o , i n some cases n e i t h e r of these methods may be necessary. Kwan and Murray (1981) r e p o r t some r e s u l t s which suggest t h a t there may not be much more tax c o s t to having j u s t 101 a s i n g l e share c l a s s and no h o l d i n g c o r p o r a t i o n s i f p r o f i t s are t o be d i s t r i b u t e d roughly i n p r o p o r t i o n to share ownership. 4.2 DYNAMIC DECISION-MAKING The other key assumption of the model presented i n Chapter 2 i s t h a t decision-making i s s t a t i c r a t h e r than dynamic. 7 The e x t e n s i o n t o dynamic decision-making may be co n s i d e r e d i n the context of a s i n g l e owner without l o s s of g e n e r a l i t y s i n c e there are no important i n t e r a c t i o n s between the multiple-owner and many-period i s s u e s , other than perhaps f o r e s t a t e f r e e z i n g and o t h e r t r a n s f e r s o f c o n t r o l w i t h i n the e x i s t i n g group of sh a r e h o l d e r s . With a s i n g l e owner, the o b j e c t i v e f u n c t i o n f o r the dynamic problem i s easy t o determine: i t i s simply the owner's i n t e r t e m p o r a l u t i l i t y f u n c t i o n , p o s s i b l y i n c l u d i n g a bequest motive. The c o n s t r a i n t s are a l s o g e n e r a l l y w e l l - d e f i n e d but they are much d i f f e r e n t from the s t a t i c problem because there are many new endogenous v a r i a b l e s . One of the most important new endogenous v a r i a b l e s i s the balance i n the cumulative deduction account, which d e t e r -mines the c o r p o r a t i o n ' s tax r a t e on busi n e s s income i n f u t u r e years through the l i n k t o the s m a l l b u s i n e s s deduction. The e x i s t e n c e of the t o t a l b usiness l i m i t t o the s m a l l business deduction encourages the d i s t r i b u t i o n of corpora t e p r o f i t s through t a x a b l e d i v i d e n d s and owner's s a l a r y as the c o r p o r a t i o n ' s cumulative deduction account balance approaches the l i m i t . The cumulative deduction account balance i s a l s o l i n k e d to the 102 f i r m ' s r e a l investment d e c i s i o n . Consider an i n c r e a s e i n investment i n one p e r i o d and a decrease i n the next p e r i o d such t h a t the f i r m ' s time p a t t e r n of c a p i t a l stock i s changed f o r o n l y the c u r r e n t p e r i o d . The change i n investment can be f i n a n c e d i n a t l e a s t two ways: decrease d i v i d e n d s i n the c u r r e n t p e r i o d and i n c r e a s e d i v i d e n d s i n the next p e r i o d , or i n c r e a s e o u t s i d e borrowing i n the c u r r e n t p e r i o d and reduce i t i n the next p e r i o d . I f the l a t t e r approach i s o p t i m a l , the user c o s t of c a p i t a l w i l l be a f f e c t e d by the cumulative d e d u c t i o n account balance s i n c e the value o f i n t e r e s t deductions i n c r e a s e s w i t h the c o r p o r a t e tax r a t e . Another way i n which the cumulative deduction account balance a f f e c t s the user c o s t of c a p i t a l . i s through the e f f e c t on the value of the stream of c a p i t a l c o s t allowance (tax d e p r e c i a t i o n ) deductions. T h i s may cause the r e n t a l p r i c e o f c a p i t a l t o d i f f e r from the user c o s t s i n c e l e a s i n g f i r m s may face a d i f f e r e n t c o r p o r a t e tax r a t e and s e t t h e i r charges a c c o r d i n g l y , which w i l l consequently g a f f e c t the lease-purchase d e c i s i o n . For a l l of these reasons, the cumulative deduction account c r e a t e s an important l i n k between the investment and f i n a n c i a l p o l i c i e s of c l o s e l y - h e l d c o r p o r a t i o n s . In a d d i t i o n to investment d e c i s i o n s , the l i t e r a t u r e on the d e t e r m i n a t i o n of f i r m behaviour on the b a s i s of u t i l i t y maximi-z a t i o n has s t u d i e d f i r m s ' l e n d i n g and borrowing behaviour. In 103 p a r t i c u l a r , S t i g l i t z (1973) has allowed f o r the simultaneous d e t e r m i n a t i o n of borrowing and l e n d i n g between the f i r m and the owner, as w e l l as borrowing and l e n d i n g by the f i r m and the owner from o u t s i d e sources. A dynamic model of a c l o s e l y -h e l d c o r p o r a t i o n c o u l d i n c l u d e a l l of these v a r i a b l e s , as w e l l as e q u i t y investment i n the f i r m by the owner and the d e t e r -m i n a tion o f the l e v e l of r e t a i n e d e a r n i n g s . The balance between i n t e r n a l and e x t e r n a l f i n a n c i n g i s p a r t i c u l a r l y i n t e -r e s t i n g f o r c l o s e l y - h e l d f i r m s s i n c e i t i s o f t e n s a i d t h a t small b usinesses are o v e r l y dependent on e x t e r n a l f i n a n c i n g . The r e l a t i v e s i z e s of i n t e r n a l and e x t e r n a l f i n a n c i n g can be expected to depend very much on the u l t i m a t e d i s p o s i t i o n of the f i r m , s i n c e on the s a l e of shares the r e t a i n e d earnings of the c o r p o r a t i o n are converted i n t o c a p i t a l gains f o r the owner. T h i s p o i n t has been noted by S t i g l i t z (1973) who has e x p l a i n e d the l e v e l of d i v i d e n d d i s t r i b u t i o n s p a r t l y i n terms of the tax burden on d i v i d e n d s r e l a t i v e t o the tax burden on c a p i t a l g a i n s . However, the s a l e of the business i s t r i c k y to model s i n c e the commodity t h a t i s s o l d can be the shares of the c o r p o r a t i o n or j u s t i t s a s s e t s . The c h o i c e w i l l depend on the tax p o s i t i o n s of the vendor and the purchaser. For a given t o t a l s a l e s p r i c e , the vendor w i l l normally p r e f e r a s a l e of shares while the purchaser w i l l p r e f e r a s a l e of a s s e t s . In a s a l e of a s s e t s , the a s s e t s are p r i c e d i n d i v i d u a l l y and the income from the s a l e i s taxed i n the hands of the c o r p o r a t i o n . A f t e r c o r p o r a t e tax 104 i s paid, there are two choices. The remaining funds may be paid out to shareholders as dividends and taxed i n t h e i r hands, after which the corporation w i l l be wound up, or the corpora-ti o n can invest the funds i n order to defer personal tax. A sale of shares i s more d i f f i c u l t to model because the purchaser acquires the corporation's f i n a n c i a l and tax charac-t e r i s t i c s as well as i t s operating assets, and so the s e l l i n g price of the shares w i l l depend on how these c h a r a c t e r i s t i c s are valued i n the market. What i s needed i s a share valuation function which has as i t s arguments the firm's f i n a n c i a l assets, outside borrowing, shareholder's loans, cumulative deduction account balance, c a p i t a l dividend account balance, and refundable dividend tax on hand. A reading of the business valuation l i t e r a t u r e suggests that there i s too much v a r i a t i o n to assume that such a function e x i s t s . Two examples w i l l i l l u s t r a t e t h i s point. On the cumulative deduction account balance, business valuators have two approaches. If the purchasers' market for a p a r t i c u l a r business i s dominated by firms which are i n e l i g i b l e g for the small business deduction, then the cumulative deduction account balance has no e f f e c t on the value of the shares. I f the purchasers' market i s not dominated by firms of th i s type, then the cumulative deduction account balance matters because i t affects the corporate tax rate used i n the valuation formula, 105 which i s u s u a l l y c a p i t a l i z a t i o n of a f t e r - t a x e a r n i n g s . The method of t a k i n g t h i s i n t o account, however, i s a s u b j e c t of c o n t r o v e r s y . 1 0 For these reasons, i t i s not c l e a r how the cumulative deduction account balance a f f e c t s share v a l u e . The v a l u a t i o n of the f i r m ' s f i n a n c i a l a s s e t s i s a l s o p r o b l e m a t i c , even though determining the market value of the a s s e t s themselves may be simple. The problem i s t h a t there may be tax consequences to the c o r p o r a t i o n on the s a l e of the a s s e t s , and f u r t h e r tax consequences when the proceeds are e x t r a c t e d from, the c o r p o r a t i o n by t a x a b l e d i v i d e n d s or other means. Some purchasers w i l l wish to immediately remove the funds and thereby i n c u r these " d i s t r i b u t i o n c o s t s , " w h i l e others w i l l wish to keep the a s s e t s i n the c o r p o r a t i o n . T h e r e f o r e , a l l t h a t i s s a i d i n the v a l u a t i o n l i t e r a t u r e i s t h a t some f r a c t i o n of the d i s t r i b u t i o n c o s t s w i l l be s u b t r a c t e d from the market value of the a s s e t s to a r r i v e a t the purchase p r i c e . 1 1 The s i z e of t h i s f r a c t i o n i s very important to the business owner from a p l a n n i n g p o i n t of view because i t d e t e r -mines the r e t u r n to accumulating f i n a n c i a l a s s e t s i n the c o r p o r a t i o n . I f a l l d i s t r i b u t i o n c o s t s are s u b t r a c t e d , the owner should p l a n to l i q u i d a t e a l l f i n a n c i a l a s s e t s p r i o r to the share s a l e , s i n c e i f he- s o l d the a s s e t s w i t h the c o r p o r a -t i o n he would be worse o f f by the amount of the c a p i t a l gains tax on the s a l e of the c o r p o r a t i o n which i s due to the f i n a n -c i a l a s s e t s . I f d i s t r i b u t i o n c o s t s are not s u b t r a c t e d a t a l l , 106 the r e t u r n to accumulating f i n a n c i a l a s s e t s i n the c o r p o r a -t i o n might be h i g h e r f o r a share s a l e than f o r an a s s e t s s a l e because t h i s e x t r a c a p i t a l gains tax might be l e s s than the d i s t r i b u t i o n c o s t s . Another important p a r t of a dynamic model of the f i n a n -c i a l p o l i c y of a c l o s e l y - h e l d c o r p o r a t i o n i s a s e t of v a r i a b l e s r e l a t e d to r e t i r e m e n t income p l a n n i n g . The new v a r i a b l e s are c o n t r i b u t i o n s t o , and withdrawals from, r e g i s -t e r e d r e t i r e m e n t savings p l a n s , r e g i s t e r e d pension p l a n s , and d e f e r r e d p r o f i t - s h a r i n g p l a n s . These v a r i a b l e s are c l o s e l y l i n k e d t o the f i n a n c i a l p o l i c y o f c l o s e l y - h e l d c o r p o r a t i o n s because saving- through these p l a n s i s an a l t e r n a t i v e to s a v i n g through the c o r p o r a t i o n i n the form of r e t a i n e d earn-i n g s . A l s o , i n most cases the c o n t r i b u t i o n l i m i t s are l i n k e d to the amount of the owner's s a l a r y and income from t a x a b l e b e n e f i t s , s u b j e c t to f i x e d c e i l i n g s . In Chapter 3 an attempt was made to determine the o p t i m a l a l l o c a t i o n of c o n t r i b u t i o n s among these p l a n s , but a dynamic model i s r e q u i r e d to determine the o p t i m a l l e v e l of t o t a l c o n t r i b u t i o n s . The work of Daly (19 81) on RRSPs i l l u s t r a t e s some of the r e s u l t s t h a t might be expected from such an e x e r c i s e . A dynamic model c o u l d a l s o allow f o r amounts which can be deducted as expenses by the c o r p o r a t i o n two or three years b e f o r e they are p a i d and the p e r s o n a l w i t h o l d i n g taxes have 107 to be r e m i t t e d t o the government. In the model presented i n Chapter 2, the deduction by the c o r p o r a t i o n f o r owner's s a l a r y occurs a t the same time as the p e r s o n a l tax on the funds i s p a i d . However, i t i s p o s s i b l e to o b t a i n the d e d u c t i o n two years i n advance f o r owner's s a l a r y and three years i n advance f o r other accrued but unpaid amounts such 12 as accrued i n t e r e s t on loans from s h a r e h o l d e r s . A f u l l dynamic model i s r e q u i r e d to assess a l l of the i m p l i c a t i o n s of t h i s p o s s i b i l i t y f o r f i n a n c i a l p o l i c y , but some i n s i g h t s may be o b t a i n e d from a few simple c a l c u l a t i o n s . Suppose t h a t i n 1980 the owner i s p l a n n i n g a f i n a n c i a l p o l i c y which w i l l maximize h i s u t i l i t y f o r the y e a r 1982. I f a s a l a r y i s accrued i n 1980 to be p a i d i n 1982, there w i l l be a s a v i n g of u per d o l l a r of accrued s a l a r y , assuming f o r i l l u s t r a t i o n t h a t the c o r p o r a t i o n i s taxed a t the s m a l l b u s i n e s s r a t e . I f the tax s a v i n g i s used to reduce o u t s i d e borrowing by the c o r p o r a t i o n a t the i n t e r e s t r a t e i , then i n 3 3 19 81 there w i l l be u {1 + i ( l - u )} more a f t e r - t a x income i n the c o r p o r a t i o n than there would be otherwise. By 1982 s s t h i s w i l l have grown to u {1 + i ( l - u ) } 2 . T h i s can be a S S made a p a r t o f the s t a t i c model by adding S u { l + i ( l - u ) } 2 to the amount to be d i s t r i b u t e d i n c o n s t r a i n t (10), where S a i s the amount of s a l a r y accrued two years b e f o r e . Accrued s a l a r y c l e a r l y dominates o r d i n a r y owner's s a l a r y i n f i n a n c i a l p o l i c y because of the time advantage i n the deduction, u n l e s s 108 the c o r p o r a t i o n ' s marginal tax r a t e r i s e s s u f f i c i e n t l y i n the i n t e r i m p e r i o d . A more d i f f i c u l t q u e s t i o n i s whether the c o r p o r a t i o n i s induced to s u b s t i t u t e accrued s a l a r y f o r tax a b l e d i v i d e n d s , r e l a t i v e to the d i v i d e n d - s a l a r y mix i n the absence of the a c c r u a l advantage. The answer can be found DS SD by c a l c u l a t i n g T and T as i n Chapter 2, but using the m o d i f i e d c o r p o r a t e tax r a t e suggested above. The most i n t e r e s t i n g case i s a s m a l l b u s i n e s s w i t h zero RDTOH. For i n t e r e s t r a t e s of 15% and 20%, t o t a l taxes can s t i l l be reduced by s u b s t i t u t i n g t a x a b l e d i v i d e n d s f o r s a l a r y i f b a s i c f e d e r a l tax i s over $200, and by s u b s t i t u t i n g s a l a r y f o r taxa b l e d i v i d e n d s i f b a s i c f e d e r a l tax i s under $200. There-f o r e , the a b i l i t y to accrue s a l a r y two years i n advance does not change the a l g o r i t h m f o r d i v i d e n d - s a l a r y c h o i c e d i s p l a y e d i n F i g u r e ~47, of Chapter 2. 4.3 STATIC VS. DYNAMIC MODELS The above d i s c u s s i o n demonstrates t h a t many aspects of f i n a n c i a l behaviour can onl y be examined with a dynamic model. The c r i t i c a l q u e s t i o n f o r t h i s study i s whether the s t a t i c model g i v e s c o r r e c t r e s u l t s f o r the behaviour i t p u r p o r t s to e x p l a i n . In o t h e r words, w i l l the o p t i m a l s t a t i c f i n a n c i a l p o l i c i e s developed i n Chapter 2 remain o p t i m a l i n a dynamic context? The i n t e r t e m p o r a l c o n s i d e r a t i o n s which are most l i k e l y to a f f e c t the op t i m a l f i n a n c i a l p o l i c y are the c a p i t a l d i v i d e n d and 109 s h a r e h o l d e r ' s loans accounts, the cumulative deduction account, and the use of d e f e r r e d income p l a n s . C a p i t a l d i v i d e n d s and repayment of shareholder's loans are u n l i k e t a x a b l e d i v i d e n d s and s a l a r y i n t h a t the former have s t r i c t l i m i t s on t h e i r use imposed by the balances i n the r e s p e c t i v e accounts h e l d by the f i r m . The unused p o r t i o n of these balances can be c a r r i e d over from year to year inde-f i n i t e l y , and thus there i s a t i m i n g q u e s t i o n : should the balances be used i n f u l l t o reduce taxes i n the c u r r e n t year, or should they be conserved f o r f u t u r e use? The s t a t i c model i n Chapter 2 attaches no c o s t to t h e i r use as a means of r e d u c i n g c u r r e n t taxes, so the o p t i m a l s t a t i c p o l i c y i s normally f u l l use i n the c u r r e n t year. Some i n d i c a t i o n of whether t h i s i s a l s o c o r r e c t i n a dynamic context i s p r o v i d e d by the f o l l o w i n g two-period p e r t u r b a t i o n : i n the f i r s t year, i n c r e a s e t a x a b l e d i v i d e n d s by $1 and decrease c a p i t a l d i v i d e n d s i n the amount r e q u i r e d by the c o r p o r a t e budget c o n s t r a i n t , and then r e v e r s e the procedure i n the second year. The owner's cash flow i s reduced d i r e c t l y by the change i n t o t a l taxes i n the two years, T^ L i n year one and T^ 0 i n year two. Assuming t h a t the owner compensates f o r the reduced cash flow i n year one by i n c r e a s i n g non-d e d u c t i b l e p e r s o n a l borrowing, the owner's cash flow i n year two i s i n c r e a s e d i f : - (1 -i- i ) T D L - T L D > 110 Thus the p e r t u r b a t i o n of c o n s e r v i n g the c a p i t a l d i v i d e n d account f o r a year i s b e n e f i c i a l o n l y i f h i s marginal tax r a t e on d i v i d e n d s has grown between the two years a t a r a t e g r e a t e r than the r a t e of i n t e r e s t . I f i n s t e a d the reduced cash flow i n year one was balanced by an i n c r e a s e i n d e d u c t i b l e borrowing or a r e d u c t i o n i n taxable investments, the c r i t e r i o n would be an i n c r e a s e i n the owner's marginal tax r a t e a t the a f t e r - t a x r a t e of i n t e r e s t . In e i t h e r case, i t seems reasonable to say t h a t with an indexed p e r s o n a l income tax system i t i s normally p r e f e r a b l e not to conserve the balances i n the c a p i t a l d i v i d e n d and share-h o l d e r ' s loans accounts f o r f u t u r e y e a r s . A second i n t e r t e m p o r a l c o n s i d e r a t i o n i s the cumulative deduction account. A p e r t u r b a t i o n i n f i n a n c i a l p o l i c y i n the c u r r e n t p e r i o d which reduces the balance i n t h i s account reduces taxes i n a l l f u t u r e years i n which the cumulative deduction account i s between $600,000 and $750,000 and some income i s taxed a t the l a r g e business r a t e . The problem i s to determine i f the c u r r e n t tax c o s t of d e v i a t i n g from the s t a t i c optimum i s j u s t i f i e d by the f u t u r e tax s a v i n g . One p e r t u r b a t i o n which reduces the cumulative deduction account of a s m a l l b u s i n e s s i s to s u b s t i t u t e s a l a r y f o r t a x a b l e d i v i d e n d s . Using 1980 B.C. tax r a t e s , a $100 i n c r e a s e i n s a l a r y and a compensating r e d u c t i o n i n t a x a b l e d i v i d e n d s reduces the cumulative deduction account balance of a s m a l l business by $ 1 . At best, t h i s w i l l allow $1 more income i n each future year to be taxed at the small business rate rather than the large business rate, which w i l l reduce taxes by 26 cents per year. Assuming an i n f i n i t e time horizon and a 10% discount rate, t h i s has a present value of $ 2 . 6 0 . This should be compared with the cost of deviating from the expansion path of Figure W i n thi s way, which i s from $ 7 . 3 0 to $ 1 1 . 5 6 , depending on the personal tax bracket of the owner. Hence, i t i s clear that the future tax saving cannot j u s t i f y the current tax cost i n thi s case. Instead of deviating from the expansion path, a small business can reduce i t s cumulative deduction account balance by moving further along the path. Less money would be dis t r i b u t e d in the form of c a p i t a l dividends and repayment of shareholders' loans, and more would be dis t r i b u t e d in salary and/or taxable dividends. Movements along the path to the l e f t of point B in Figure 4\ do not r e s u l t i n an increase i n current taxes, so the issue of a trade-off between current and future taxes only arises past that point. In the l a t t e r area, a $1 reduction i n the cumulative deduction account by moving further along the expansion path costs from 3 £ to 2 7 £ i n current taxes, depending on the p a r t i c u l a r part of the path. Since this can be quite cheap r e l a t i v e to the future tax saving of up to $ 2 . 6 0 , i t follows that intertemporal considerations can cause the firm to move farther along the expansion path than- i s implied by the s t a t i c model. However, $ 2 . 6 0 i s far too high an estimate of the present value of the future tax savings for most small 112 b u s i n e s s e s because a-$600,000 balance<in the cumulative deduction account might not be reached f o r many years and the $750,000 p o i n t may be passed s h o r t l y a f t e r t h a t , i . e . , the f u t u r e tax savings c o u l d be many years away and c o u l d l a s t o n l y a year or two. Consequently, moving f a r t h e r along the expansion path than i n the s t a t i c optimum co u l d be optimal i n a dynamic context, but perhaps on l y f o r a few f i r m s . A t h i r d i n t e r t e m p o r a l c o n s i d e r a t i o n i s the use of d e f e r r e d income p l a n s , n o t a b l y RRSPs and DPSPs. C o n t r i b u t i o n s to these plans can a l t e r the o p t i m a l s t a t i c f i n a n c i a l p o l i c y because of c o n s t r a i n t (21). RRSP and DPSP c o n t r i b u t i o n s are l i m i t e d to 20% of employment income, and owner's s a l a r y i s p a r t of employment income but d i v i d e n d s are not. However, the l i m i t s are not connected, so RRSP and DPSP c o n t r i b u t i o n s combined can be 40% of employment income. The extent to which t h i s c o n s t r a i n t w i l l boost s a l a r y above the amount i n the s t a t i c optimum depends on the shareholder's p r e f e -rences as w e l l as the c h a r a c t e r i s t i c s of d e f e r r e d income plans as investments. As investments, d e f e r r e d income plans have the major advantage t h a t tax i s ' d e f e r r e d i n income earned i n the p l a n s . On the other hand, r e t a i n i n g earnings i n a c l o s e l y - h e l d c o r p o r a t i o n may be almost as e f f e c t i v e as a tax s h e l t e r . In p a r t i c u l a r , the i n i t i a l amount saved w i l l be l a r g e r because i t has not borne p e r s o n a l tax; 113 investment returns in the form of business income will be taxed but only at the low small business rate; and the eventual withdrawal of the accumulated sum will be taxed at preferential rates as a dividend, rather than as ordinary income. N O T E S 1. Evans and Williamson (1978) and others have suggested m o d e l l i n g p r o f e s s i o n a l p r a c t i c e s as labour-managed f i r m s , w i t h the o b j e c t i v e f u n c t i o n b e i n g the average income per owner-employee. T h i s assumption may be use-f u l t o e x p l a i n some aspects of f i r m s ' behaviour, but i t i s too r e s t r i c t i v e f o r the p r e s e n t problem. 2. Kwan and Murray (1981). 3. See i n t r i l i g a t o r (1971), pp. 67-68. 4. Kwan and Murray (1981). 5. M i c h a e l O'Keefe of the F a c u l t y of Law, U n i v e r s i t y of B r i t i s h Columbia, has made t h i s p o i n t i n a p e r s o n a l .communication. 6. T h i s a r i s e s because the h o l d i n g c o r p o r a t i o n s are con-nected by not a s s o c i a t e d to Opco. See H a r r i s (1981) f o r f u r t h e r d e t a i l s . 7. Dynamic aspects of t h i s problem have been s t u d i e d by Reid (1979) and H i e r l i h y (1981). 8. The co r p o r a t e tax r a t e used by l e a s i n g f i r m s i n s e t t i n g t h e i r p r i c e s may be c l o s e to zero, s i n c e a c c o r d i n g to O s t f i e l d (1981) the l e a s i n g i n d u s t r y i n Canada does not at p r e s e n t have enough ta x a b l e income to u t i l i z e f u l l y c a p i t a l c o s t allowance c l a i m s . 9. Examples are p u b l i c companies, companies with non-r e s i d e n t ownership, and c l o s e l y - h e l d c o r p o r a t i o n s w i t h cumulative deduction account balances which are w e l l over $750,000. 10. See Campbell (1982), Chapter 5, pp. 52-55, and McQu i l l a n , Doherty and Donald (1979), p. 43. 11. Campbell (1982), chapter 5, p. 76. 12. See Reid (1982) and Crawford and G r a t i a s (1980) f o r d e t a i l s . The two year maximum d e f e r r a l p e r i o d i s c a l -c u l a t e d from the middle of the f i s c a l year i n which the a c c r u a l i s made to the time t h a t the w i t h h o l d i n g tax has to be p a i d a f t e r an e l e c t i o n has been f i l e d under S e c t i o n 114 -115 78(3). The middle of the f i s c a l year i s used as the s t a r t i n g p o i n t because i f the monthly c o r p o r a t e tax i n s t a l l m e n t s are each o n e - t w e l f t h of the c o r p o r a t e tax f o r the year, then the tax s a v i n g from the s a l a r y deduc-t i o n begins on average i n the middle o f the year. CHAPTER 5 EMPIRICAL APPLICATION TO FARM INCORPORATION DECISIONS The p r e v i o u s p a r t s of the t h e s i s have d e a l t with the d e t e r m i n a t i o n of the o p t i m a l f i n a n c i a l p o l i c y f o r a c l o s e l y - h e l d c o r p o r a t i o n , where the o p t i m a l p o l i c y i s the one t h a t maximizes i t s owner's u t i l i t y . A n a t u r a l e x t e n s i o n of t h i s work i s a study of the c h o i c e of an o r g a n i z a t i o n a l form f o r a b u s i n e s s , s i n c e the owner may be expected to make t h i s c h o ice by comparing the maximum u t i l i t y l e v e l s he c o u l d achieve under each o r g a n i z a t i o n a l form. Choice of o r g a n i z a t i o n a l form i s t h e r e f o r e the s u b j e c t of t h i s chapter. A theory i s developed and t e s t e d u s i n g a sample of Saskatchewan f a r m e r s . 1 S i m u l a t i o n i s used to f o r e c a s t the e f f e c t of two r e c e n t tax changes on the p r o p o r t i o n of farmers t h a t choose the corporate form of business o r g a n i z a t i o n . 5.1 THEORY The f i r s t i s s u e to address i n c o n s t r u c t i n g a theory of choice of o r g a n i z a t i o n a l form i s what the a l t e r n a t i v e s are. The three best-known forms are s o l e p r o p r i e t o r s h i p , p a r t n e r -s h i p , and c o r p o r a t i o n , but p a r t i c u l a r businesses may have more or l e s s c h o ice than t h i s . A l l three are ways of r e c e i v i n g self-employment income, so to choose any of them, Revenue Canada must be persuaded t h a t the income i s not income from employment. T h i s i s not a problem f o r farmers, but i t i s f o r the a t h l e t e s , c o r p o r a t e e x e c u t i v e s , u n i v e r s i t y p r o f e s s o r s and others who have i n r e c e n t years t r i e d to channel t h e i r income 116 117 -from r e n d e r i n g p e r s o n a l s e r v i c e s through a corporation.^" Another s i t u a t i o n i n which c h o i c e o f o r g a n i z a t i o n a l form i s r e s t r i c t e d i s the s i t u a t i o n o f many professionals., n o t a b l y d o c t o r s , d e n t i s t s and lawyers, who i n p r o v i n c e s other than A l b e r t a are b a r r e d by law from d i r e c t l y i n c o r p o r a t i n g t h e i r p r o f e s s i o n a l p r a c t i c e s . Some p r o f e s s i o n a l s have p a r t i a l l y circumvented t h i s by e n t e r i n g i n t o agreements wi t h "management c o r p o r a t i o n s " owned by t h e i r spouses, w i t h the c o r p o r a t i o n c h a r g i n g the p r o f e s s i o n a l p r a c t i c e a fee f o r a d m i n i s t e r i n g i t . ^ Farmers are not a f f e c t e d by t h i s r e s t r i c t i o n e i t h e r , and i n f a c t they have more a l t e r n a t i v e s than the b a s i c t h r e e . I t i s p o s s i b l e f o r a farmer t o be t r e a t e d as a s o l e p r o p r i e t o r f o r tax purposes even though he i s not working on h i s own. A common arrangement i s an i n f o r m a l p a r t n e r s h i p i n which each farmer c o n t r i b u t e s some equipment and labour, p o s s i b l y o n l y a t peak times o f the year. Such arrangements may i n v o l v e no w r i t t e n agreement and no cash changing hands. A l t e r n a t i v e l y , two or more s o l e p r o p r i e t o r s may work together under a "business agreement" or "farm o p e r a t i n g agreement" and share revenues, cash expenses, and f a c t o r s o f p r o d u c t i o n . The d i f -f e r e n c e between a business agreement and a t r a d i t i o n a l p a r t n e r -s h i p i s t h a t w i t h a busi n e s s agreement a l l a s s e t s are owned i n d i v i d u a l l y by the farmers, w h i l e i n a t r a d i t i o n a l p a r t n e r s h i p most or a l l of the as s e t s are owned by the p a r t n e r s h i p . 118 There are many tax and non-tax f a c t o r s t o c o n s i d e r i n choosing among the d i f f e r e n t types of u n i n c o r p o r a t e d o r g a n i -z a t i o n a l forms. 5 For example, a business agreement allows the farmers to i n d i v i d u a l l y choose the t i m i n g o f t h e i r c a p i t a l c o s t allowance c l a i m s , w h i l e a t r a d i t i o n a l p a r t n e r s h i p does not. However, i t i s i m p o s s i b l e to d i s t i n g u i s h among these forms e m p i r i c a l l y without d e t a i l e d knowledge of the i n d i v i d u a l s i t u a t i o n s . The Saskatchewan farm survey of 1978 o n l y asks i f the farm i s operated as a s o l e p r o p r i e t o r s h i p , p a r t n e r s h i p or c o r p o r a t i o n , and does not ask about the ownership o f the farming a s s e t s . T h i s means t h a t a farmer who i s p a r t of a business agreement cannot be d i s t i n g u i s h e d from other s o l e p r o p r i e t o r s , and a p a r t n e r s h i p i n which a l l a s s e t s are owned i n d i v i d u a l l y , which i s v e r y s i m i l a r t o a b u s i n e s s agreement, cannot be d i s t i n g u i s h e d from a t r a d i t i o n a l p a r t n e r s h i p . In view of t h i s b l u r r i n g of the d i s t i n c t i o n between s o l e p r o p r i e -t o r s h i p s and p a r t n e r s h i p s and the i n a b i l i t y t o s o r t out i n the data the d i f f e r e n t u n i n c o r p o r a t e d business arrangements, t h i s study focuses on the b i n a r y c h o i c e between any type of u n i n -c o r p o r a t e d b u s i n e s s form and a c o r p o r a t i o n . S t a t i s t i c s i n d i c a t e t h a t the g r e a t m a j o r i t y of farms i n Canada are u n i n c o r p o r a t e d , although the p r o p o r t i o n of farm c o r p o r a t i o n s has been i n c r e a s i n g . Census of a g r i c u l t u r e data show t h a t o n l y 2.2% of farms were i n c o r p o r a t e d i n 1971, but by 1976 t h i s had doubled to 4.4%. 7 Other S t a t i s t i c s Canada data i n d i c a t e t h a t the p r o p o r t i o n i n c o r p o r a t e d i s s t i l l 119 i n c r e a s i n g : from 1976 to 1979 the number of farm c o r p o r a t i o n s i n c r e a s e d by over one-quarter, w h i l e the t o t a l number of farms f e l l . Farm c o r p o r a t i o n s are e s p e c i a l l y common i n B.C. (7.9%) and uncommon i n Quebec (3.1%), w h i l e Saskatchewan i s near the n a t i o n a l average a t 4.3%. Of a l l Saskatchewan farm c o r p o r a t i o n s , 9 87% had most o r a l l o f the shares owned by one f a m i l y . T h i s p r o v i d e s a lower bound f o r the percentage of farm c o r p o r a t i o n s t h a t are c l o s e l y - h e l d , and i t suggests t h a t almost a l l farms are c l o s e l y - h e l d . b u s i n e s s e s , as w i d e l y - h e l d farm p a r t n e r s h i p s do not e x i s t i n Canada. There are e s s e n t i a l l y t w o . f a c t o r s f o r the owners of a c l o s e l y - h e l d b u s i n e s s to c o n s i d e r i n choosing an o r g a n i z a t i o n a l form: the v a l u e they p l a c e on having simple and t r a d i t i o n a l b u s i n e s s arrangements and the tax c o s t s or b e n e f i t s . Farmers who s t r o n g l y p r e f e r simple b u s i n e s s arrangements w i l l t y p i c a l l y choose to be u n i n c o r p o r a t e d . A c o r p o r a t i o n i s harder to under-stand because i t i s a separate l e g a l person from i t s owners. Brown, Elmgren and Minogue (1973) found t h a t many i n c o r p o r a t e d Saskatchewan farmers d i d not f u l l y understand c o r p o r a t e c r e a t i o n or s t r u c t u r e , and u n i n c o r p o r a t e d farmers probably have even l e s s understanding of the c o r p o r a t e form. The c o r p o r a t e form may a l s o be avoided because i t i s n o n - t r a d i t i o n a l . One Saskatchewan tax.accountant notes t h a t one s i g n i f i c a n t non-tax f a c t o r i s "...the s t r o n g f e e l i n g t h a t farmers have f o r t h e i r l a n d and the s e c u r i t y i t r e p r e s e n t s . Many are r e l u c t a n t to 120 ' a c t u a l l y t r a n s f e r t h e i r land t o a c o r p o r a t i o n or to enter i n t o l e a s i n g arrangements wi t h a corporation."" 1" 0 The second f a c t o r , the tax c o s t s or b e n e f i t s , i s probably the main reason why farmers i n c o r p o r a t e . T h i s o p i n i o n i s sup-po r t e d by Brown, Elmgren and Minogue (1973), who found t h a t t h i s was the most common reason g i v e n by the i n c o r p o r a t e d farmers i n t h e i r survey. T h i s f a c t o r has two a s p e c t s : the d i f f e r e n c e i n the t o t a l tax burden between the two o r g a n i z a -t i o n a l forms, and the c o s t s of changing between forms. I f c o s t s of change are i n f i n i t e , o r g a n i z a t i o n a l c h o i c e i s a once-a n d - f o r - a l l s e l e c t i o n by the owners o f a new b u s i n e s s , and so tax burdens over a m u l t i - y e a r p e r i o d must be c o n s i d e r e d i n the decision. 1" 1" I f c o s t s of change are zero, o r g a n i z a t i o n a l choice f o r each year can be decided independently on the b a s i s of r e l a t i v e tax burdens i n t h a t p e r i o d . In p r a c t i c e , becoming i n c o r p o r a t e d i s cheap but r e v e r t i n g to an u n i n c o r p o r a t e d form ( " d i s i n c o r p o r a t i o n " ) i s expensive. I n c o r p o r a t i o n c o s t s are c u r r e n t l y i n the $500 to $1,000 range and c o n s i s t of l e g a l c o s t s o n l y . There i s no tax c o s t because S e c t i o n 85 of the Income Tax Act allows the t r a n s f e r from the owners to t h e i r c o r p o r a t i o n t o take p l a c e at the c o s t of the p r o p e r t y f o r tax purposes. D i s i n c o r p o r a t i o n , however, may i n v o l v e s u b s t a n t i a l tax c o s t s because there i s no r o l l o v e r on the winding-up of a c o r p o r a t i o n . A l l t r a n s f e r s of c o r p o r a t e a s s e t s , whether to -121 the owner o r anyone e l s e , take p l a c e a t market value f o r tax purposes. T h i s c r e a t e s t a x a b l e c a p i t a l . g a i n s , r e c a p t u r e of c a p i t a l c o s t allowance, g a i n on the s a l e of i n v e n t o r y , and other income w i t h i n the c o r p o r a t i o n . There may a l s o be a s i g -n i f i c a n t tax l i a b i l i t y a t the shareholder l e v e l because the d i s t r i b u t i o n of the a f t e r - t a x proceeds from the a s s e t s a l e , a f t e r paying o f f l i a b i l i t i e s , i s taxed as a deemed d i v i d e n d . I t i s estimated t h a t the average Saskatchewan farmer would have d i s i n c o r p o r a t i o n c o s t s o f $35,000 i f he i n c o r p o r a t e d when 12 he s t a r t e d farming and d i s i n c o r p o r a t e d i n 1977. The problem posed f o r t h i s study i s t h a t i t i s i m p o s s i b l e to estimate d i s -i n c o r p o r a t i o n c o s t s f o r p a r t i c u l a r farmers without knowing the c o s t f o r tax purposes of the land and other farming a s s e t s . The o n l y f e a s i b l e approach i s to proceed as i f the c o s t s of changing o r g a n i z a t i o n a l form were t r i v i a l , assuming t h a t there are few farm c o r p o r a t i o n s whose ch o i c e of o r g a n i z a t i o n a l form has been a f f e c t e d by the c o s t s of change. I t i s known t h a t many farm c o r p o r a t i o n s e x i s t i n g now were i n c o r p o r a t e d i n the pre-1972 p e r i o d to minimize e s t a t e taxes, but i t i s d i f f i c u l t t o say how many o f these would p r e f e r t o be u n i n c o r p o r a t e d now 13 t h a t e s t a t e taxes have been a b o l i s h e d . E s t a t e p l a n n i n g i s another f a c t o r to c o n s i d e r i n the choice, of o r g a n i z a t i o n a l form. Before 1972 i n c o r p o r a t i o n was h e l p f u l i n e s t a t e p l a n n i n g , but from 1972 to 1978 the s i t u a t i o n 1.22 was more, mixed. The c a p i t a l gains tax i n t r o d u c e d i n 19 72.. p r o v i d e d f o r a deemed r e a l i z a t i o n and tax a t death u n l e s s a r o l l o v e r allowed a t r a n s f e r without tax. Such a r o l l o v e r was i n t r o d u c e d i n 1973 f o r the i n t e r v i v o s or testamentary t r a n s -f e r of l a n d or d e p r e c i a b l e p r o p e r t y used i n farming to a c h i l d of the farmer, but i t was not extended to c o r p o r a t e farms u n t i l 1978. T h i s made the tax c o s t of t r a n s f e r r i n g farm p r o p e r t y between generations h i g h e r f o r a c o r p o r a t i o n than f o r a s o l e p r o p r i e t o r s h i p or f o r a p a r t n e r s h i p i n which the farming, a s s e t s were i n d i v i d u a l l y owned. On the other hand, i n c o r p o r a ^ t i n g allowed a farmer t o decrease h i s g i f t tax or succession. 14 duty l i a b i l i t y through an e s t a t e f r e e z e . G i f t taxes and s u c c e s s i o n d u t i e s were a b o l i s h e d i n Saskatchewan e f f e c t i v e January 1, 19 77. Non-tax l e g a l and f i n a n c i a l f a c t o r s are important i n the c h o i c e of o r g a n i z a t i o n a l form f o r few farm b u s i n e s s e s . 1 5 The. l i m i t e d l i a b i l i t y o f a c o r p o r a t i o n does not help the farmer h i m s e l f or a s s i s t him i n r a i s i n g e q u i t y c a p i t a l because most f i n a n c i a l i n s t i t u t i o n s w i l l not g i v e a loan to a c l o s e l y - h e l d company by i t s e l f ; , they w i l l i n s i s t on a p e r s o n a l guarantee from the s h a r e h o l d e r s . Another reason why the c o r p o r a t e form o f f e r s no advantage i n r a i s i n g c a p i t a l i s t h a t a m i n o r i t y i n t e r e s t i n a c l o s e l y - h e l d c o r p o r a t i o n i s no more l i q u i d than a p a r t n e r s h i p i n t e r e s t . An u n i n c o r p o r a t e d farmer has l e g a l p r o t e c t i o n from s e i z u r e by c r e d i t o r s of farm machinery, but 12.3 •this i s not a b a r r i e r to i n c o r p o r a t i o n s i n c e the farmer may-continue to own the machinery p e r s o n a l l y and j u s t l ease i t to the c o r p o r a t i o n . B e t t e r access to long-term c r e d i t f o r c o r p o r a t i o n s i s the only non-tax l e g a l or f i n a n c i a l f a c t o r which i s of any importance to Saskatchewan farmers i n t h e i r c h o i c e of b u s i n e s s form. T h i s f a c t o r i s c i t e d as a reason f o r i n c o r p o r a t i o n by 13% of the respondents to the farm survey conducted by Brown, Elmgren and Minogue (19 73). For a few farmers, i n c o r p o r a t i o n may be h e l p f u l t o separate ownership from c o n t r o l i n e s t a t e p l a n n i n g s i t u a t i o n s i n which some of the c h i l d r e n have stayed i n farming and some have not. 5.2 DATA CONSTRUCTION I t i s d i f f i c u l t or i m p o s s i b l e to capture some of these f a c t o r s i n an e m p i r i c a l model of the determinants of o r g a n i -z a t i o n a l form. Tax c o s t s or b e n e f i t s can be measured, but proxy v a r i a b l e s must be found f o r the value a farmer p l a c e s on having simple and t r a d i t i o n a l b usiness arrangements. One such v a r i a b l e i s e d u c a t i o n . More educated farmers may be expected to o b j e c t l e s s to complex and unusual b u s i n e s s a r -rangements and they may a l s o be more aware of the p o t e n t i a l tax savings from i n c o r p o r a t i o n . Length of farming experience may a l s o have the same e f f e c t s , s i n c e on-the-job t r a i n i n g i s a s u b s t i t u t e f o r formal e d u c a t i o n i n some r e s p e c t s . On the o t h e r hand, o l d e r farmers may be more c o n s e r v a t i v e and thus may put a h i g h e r value on having t r a d i t i o n a l and simple b u s i n e s s arrangements. However, the impact of the age f a c t o r 124 i s i m p o s s i b l e to determine i n t h i s study because the data are at a s i n g l e p o i n t i n time and the c o s t s of d i s i n c o r p o -r a t i o n make the d e c i s i o n to i n c o r p o r a t e almost i r r e v e r s i b l e . A farmer may have i n c o r p o r a t e d i n the 1950's t o o b t a i n the tax savings a v a i l a b l e a t t h a t t i m e 1 7 and i t i s h i s age a t the time of i n c o r p o r a t i o n t h a t i s r e l e v a n t . The major problem i n c o n s t r u c t i n g the e m p i r i c a l model i s measuring the amounts of tax payable under the c o r p o r a t e and non-corporate o r g a n i z a t i o n a l , forms f o r p a r t i c u l a r farmers. As d i s c u s s e d above, a one-year s t a t i c a n a l y s i s i s used on the assumption t h a t the c o s t s of changing o r g a n i z a t i o n a l form are 18 t r i v i a l . T h i s i n v o l v e s e s t i m a t i n g both the tax payable under the farmer's a c t u a l o r g a n i z a t i o n a l form and the tax payable i f the a l t e r n a t i v e form had been chosen. Tax payable i n c l u d e s the p e r s o n a l income tax payable by both the farmer 1 9 and h i s spouse, p l u s c o r p o r a t e income tax i f the farm i s i n c o r p o r a t e d . S a les tax and p r o p e r t y tax are not i n c l u d e d i n the measure s i n c e they do not vary w i t h o r g a n i z a t i o n a l form. The t o t a l income tax payable i s r e l a t i v e l y easy to e s t i -mate f o r an u n i n c o r p o r a t e d farm. There are t h r e e s t e p s : estimate the farm's net income f o r tax purposes; a l l o c a t e the survey respondent h i s share, which w i l l be the whole amount unless he i s p a r t of a b u s i n e s s agreement or a p a r t n e r s h i p ; and combine t h i s f i g u r e w i t h non-farm income to estimate the t o t a l tax l i a b i l i t i e s of husband and w i f e . The net income of the farm f o r tax purposes i s i t s net cash income l e s s e stimated c a p i t a l c o s t allowance, s i n c e farmers normally 20 compute t h e i r income on a cash b a s i s . Net cash income i s the v a l u e of a l l a g r i c u l t u r a l products s o l d p l u s cash r e c e i p t s from custom work and r e n t a l or l e a s i n g of farm machinery and equipment, l e s s a l l cash expenses. Cash expenses i n c l u d e d on the survey are: i n t e r e s t on lo a n s , e x c l u d i n g p e r s o n a l 21 2 2 loans; cash wages p a i d t o h i r e d a g r i c u l t u r a l labour; 2 3 commercial f e r t i l i z e r s purchased; a g r i c u l t u r a l chemicals purchased; custom work and machine r e n t a l expenses; f u e l and o i l used f o r farm purposes; r e p a i r s and maintenance to farm v e h i c l e s and machinery;, feed and supplements purchased; v e t e r i n a r y s e r v i c e s ; twine and wire; m a t e r i a l s f o r fence r e p a i r s ; and r e p a i r s t o farm b u i l d i n g s . T h i s i n c l u d e s almost a l l farm cash expenses except l i v e s t o c k purchases, crop i n s u r a n c e and p r o p e r t y t a x e s . C a p i t a l c o s t allowance i s e s t i -2 A mated as 12% of the v a l u e of farm machinery and equipment. Survey respondents who are members of a business agreement or a p a r t n e r s h i p are assumed to have a share of the farm's net income f o r tax purposes equal t o t h e i r share o f the t o t a l 2 5 2 6 hours worked on the farm by a l l of the members, ' For t h i s purpose, i t i s assumed t h a t the respondent's spouse i s not a member and t h e r e f o r e does not share i n the farm's net 126 income. 2 1 The respondent's t a x a b l e income i s h i s share of farm income p l u s h i s non-farm income, l e s s the $100 standard de d u c t i o n , the b a s i c p e r s o n a l exemption, the age exemption 2 8 ( i f 65 or o v e r ) , and the married s t a t u s exemption. The respondent's e l i g i b i l i t y f o r the married s t a t u s exemption depends on h i s spouse's income, which i s estimated as the number of hours the spouse worked o f f the farm i n 1977 times the minimum wage ($3 a t the t i m e ) . From t h i s f i g u r e the spouse's income tax l i a b i l i t y i s a l s o c a l c u l a t e d , which i s added to t h a t of the respondent to get the t o t a l income tax l i a b i l i t y of the farm f a m i l y . The t o t a l amount o f income tax payable i f the farm i s i n c o r p o r a t e d i s more d i f f i c u l t t o estimate because i t i s not j u s t a mechanical c a l c u l a t i o n . Rather, i t i s the product of an o p t i m i z a t i o n process on the p a r t of the farmer's accountant, where the c h o i c e v a r i a b l e s are the farmer's s a l a r y , h i s spouse's 2 9 s a l a r y , and the amount of d i v i d e n d s to be p a i d per share. The g o a l i s the m i n i m i z a t i o n of t o t a l income taxes payable by the c o r p o r a t i o n , the farmer and h i s spouse. The s t a r t i n g p o i n t i s the survey respondent's share of the farm net income f o r tax purposes, w i t h the c a l c u l a t i o n performed as s e t out 3 0 above f o r an u n i n c o r p o r a t e d farm. I t i s assumed t h a t a c e r t a i n f r a c t i o n of t h i s amount i s a v a i l a b l e f o r d i s t r i b u t i o n as c o r p o r a t e income tax, d i v i d e n d s and s a l a r i e s t o the farm f a m i l y , and the farmer and h i s accountant a l l o c a t e t h i s i n the 127 way t h a t minimizes t o t a l income tax payable. The f r a c t i o n t h a t i s a v a i l a b l e f o r d i s t r i b u t i o n i s l i k e l y t o be i n v e r s e l y r e l a t e d to the respondent's share of farm net income, s i n c e more a f f l u e n t farmers may have l e s s need t o withdraw the funds to f i n a n c e c u r r e n t consumption. T h e r e f o r e , i t i s assumed t h a t the . f r a c t i o n a v a i l a b l e f o r d i s t r i b u t i o n i s a d e c r e a s i n g p i e c e w i s e - l i n e a r f u n c t i o n of the respondent's share of farm net income, beginning a t one f o r zero net income, d e c l i n i n g to 0.85 a t a net income of $20,000, d e c l i n i n g again to 0.65 a t a net income of $150,000, and then remaining cons-31 t a n t a t 0.65. These f i g u r e s are chosen a r b i t r a r i l y as there i s no r e l e v a n t s t a t i s t i c a l i n f o r m a t i o n , but s e n s i t i v i t y a n a l -y s i s l a t e r i n the chapter i n d i c a t e s t h a t the main f i n d i n g s are independent of the s p e c i f i c f i g u r e s . The amount of farm net income which i s not d i s t r i b u t e d i s e i t h e r r e - i n v e s t e d i n the bu s i n e s s or used by the c o r p o r a t i o n f o r o f f - f a r m investments. In h i s c h o i c e of a s a l a r y f o r h i s spouse, the farmer i s con-s t r a i n e d to pay no more than the maximum "reasonable" amount, which may be c o n s e r v a t i v e l y i n t e r p r e t e d as. the number of hours the spouse works on the farm times the minimum wage. No s i m i l a r l i m i t a p p l i e s t o the respondent's s a l a r y because Revenue Canada i s not concerned about the reasonableness of remuneration to 32 owner-operators of c l o s e l y - h e l d c o r p o r a t i o n s . As f o r d i v i -dends, the o n l y r e s t r i c t i o n i s t h a t the s h a r e - s t r u c t u r e of the c o r p o r a t i o n determines the r e l a t i o n s h i p between the amount of 128 -d i v i d e n d s p a i d t o the respondent as compared to h i s spouse. 3 3 I t i s assumed t h a t both are shar e h o l d e r s o f the c o r p o r a t i o n , and t h a t t h e i r s h a r e h o l d i n g s are such t h a t d i v i d e n d s p a i d t o 34 the respondent must be twice the amount p a i d t o h i s spouse. T h i s allows some degree of i n c o m e - s p l i t t i n g on d i v i d e n d s but probably not so much as t o i n v i t e an a t t a c k by Revenue Canada so i t may be a r e a l i s t i c share s t r u c t u r e . 3 5 The amounts of d i v i d e n d s and s a l a r i e s p a i d determine the p e r s o n a l income tax payable by the respondent and h i s spouse, where t h i s i s c a l c u -l a t e d as f o r an un i n c o r p o r a t e d farm except t h a t net farm income i s r e p l a c e d by s a l a r y and d i v i d e n d s r e c e i v e d from the farm 3 6 c o r p o r a t i o n . Corporate income tax payable i s c a l c u l a t e d by a p p l y i n g the co r p o r a t e r a t e s t r u c t u r e to co r p o r a t e t a x a b l e income, where t h i s i s the respondent's share o f farm net income l e s s the-ainbtflitof s a l a r i e s p a i d t o him and h i s spouse. The t o t a l of co r p o r a t e tax payable and p e r s o n a l tax payable i s the t o t a l income tax payable f o r a co r p o r a t e farm. The d e t a i l s of the tax m i n i m i z a t i o n problem f o r a co r p o r a t e farm, are g i v e n below. The o b j e c t i v e f u n c t i o n , t o t a l income tax payable, i s Fu, - R + P. + F - R +, P + 0.27*Y + 0.50*Y, (42) h.\ h h w w w s 1 where the s u b s c r i p t s h and w r e f e r to "husband" (the respondent, who a c t u a l l y can be o f e i t h e r sex) and "wife," F i s b a s i c f e d e r a l tax, R i s the f e d e r a l tax r e d u c t i o n , P i s Saskatchewan p r o v i n c i a l 129 tax, Y g i s c o r p o r a t e t a x a b l e income taxed a t the s m a l l business r a t e (27% i n 1977 i n Saskatchewan), and Y 1 i s c o r p o r a t e t a x a b l e income taxed a t the l a r g e business r a t e (50%)• The f i r s t 3 7 $150,000 i s taxed a t the s m a l l business r a t e , so: Y s - 150,000 (43) The remainder of co r p o r a t e t a x a b l e income must go i n t o the l a r g e - b u s i n e s s r a t e category: Y s + Y l = Y b - S h " Sw , ( 4 4 ) The r i g h t s i d e o f the equation i s j u s t an a l t e r n a t i v e d e f i n i t i o n o f c o r p o r a t e t a x a b l e income: the respondent's share of the net income of the farming b u s i n e s s (Y^) l e s s s a l a r i e s p a i d out to the husband and w i f e . The w i f e ' s s a l a r y cannot exceed the maximum reasonable amount, which was assumed above to be the minimum wage times the number of hours i n the year t h a t the w i f e worked on the farm: Sw <- §w ( 4 5 ) The amount a v a i l a b l e t o be p a i d out i n s a l a r i e s , d i v i d e n d s (D) and c o r p o r a t e income tax i s M: M = S h + S w + + D w + 0.27*Ys + 0.50*Y1 (46) As noted above, M i s assumed to be a s p e c i f i e d p i e c e w i s e - l i n e a r concave f u n c t i o n of the respondent's share of farm net income. The d i v i d e n d s of the husband are assumed to be twice t h a t of h i s w i f e : 1 3 0 D. = 2*D (47) h w 13 The husband's p e r s o n a l t a x a b l e income i s ^ Y h i ' w n e r e i = l Y, . i s the amount of h i s t a x a b l e income which f a l l s i n t o the h i i t h r a t e b r a c k e t . Except f o r the top b r a c k e t , which i s open-ended, each of these b r a c k e t s has a l i m i t on the amount of income t h a t can f a l l i n t o i t : Y, . < Y, . i = l , 2 ,...12 (4 8) h i — h i ' The husband's b a s i c f e d e r a l tax (F h) i s determined p a r t l y by the amount o f income t h a t f a l l s i n t o each of these b r a c k e t s : *h - I t.Y:. - (4/15)*D, (49) i = l 1 h i ' h B a s i c f e d e r a l tax i s computed by a p p l y i n g the f e d e r a l m a r g i n a l tax r a t e i n each b r a c k e t (t^) t o the amount o f t a x a b l e income f a l l i n g i n t o t h a t b r a c k e t , summing over b r a c k e t s , and sub-t r a c t i n g the d i v i d e n d tax c r e d i t . The f r a c t i o n 4/15 appears i n the d i v i d e n d tax c r e d i t because i n 19 7 7 the c r e d i t was 1/5 o f grossed-up d i v i d e n d s and the gross-up f a c t o r was 4/3. S i n c e the d i v i d e n d :tax c r e d i t i s not a ref u n d a b l e tax c r e d i t , i t can never make b a s i c f e d e r a l tax n e g a t i v e . T h i s f a c t i s re p r e s e n -ted by w r i t i n g (49) as an i n e q u a l i t y r a t h e r than an equation. The husband's Saskatchewan p r o v i n c i a l tax i s 58.5% of b a s i c f e d e r a l t ax: 0.585 F h = P h l + P h 2 (50) 1 3 1 The two "brackets" o f p r o v i n c i a l tax, P h l and P h 2 , e x i s t i n order t o allow f o r the 10% surtax on p r o v i n c i a l tax over $2,000. P h l - 2 ' 0 0 0 ( 5 1 ) P h > P h l + l . l * P h 2 " 120 (52) The f i n a l p r o v i n c i a l tax payable by the husband, a f t e r a l l o w i n g f o r the $120 non-refundable tax c r e d i t , i s P^. The remaining c o n s t r a i n t s of the problem pose some d i f -f i c u l t i e s from a computational p o i n t of view because there are four n o n - l i n e a r i t i e s . These are of the separable type, so one approach would be to s o l v e the m i n i m i z a t i o n problem by the method o f se p a r a b l e programming. T h i s i s c o m p u t a t i o n a l l y expensive f o r a sample of over three thousand farmers, but f o r -t u n a t e l y a cheaper s o l u t i o n technique employing l i n e a r program-ming may be used. The method i s to d i v i d e the main problem i n t o e i g h t sub-problems, where each sub-problem has the same o b j e c t i v e f u n c t i o n and the f e a s i b l e r e g i o n of the main problem i s equal 3 8 to the union of the f e a s i b l e r e g i o n s of the sub-problems. The s o l u t i o n t o the main problem i s t h e r e f o r e the minimum o f the minimized values of the o b j e c t i v e f u n c t i o n s of each of the sub-problems. Each of the sub-problems can be s o l v e d by l i n e a r programming, which i s a t t r a c t i v e because of the computational e f f i c i e n c y o f the l i n e a r programming a l g o r i t h m and because i t guarantees t h a t a g l o b a l optimum w i l l be achieved. I n t u i t i v e l y , -132 the reason why t h i s method of s o l v i n g the main problem works i s t h a t the f e a s i b l e r e g i o n of the main problem has s t r a i g h t s i d e s , even though i t i s non-convex, and so i t can be separated i n t o a number o f convex s e t s which become the f e a s i b l e r e g i o n s of the sub-problems. The e i g h t sub-problems are d e f i n e d by the s i z e of the married exemption of the husband and w i f e (E, and E ) and the s i z e of each spouse's f e d e r a l tax r e d u c t i o n h w ( R h a n d V : (a) = E = w 0, < 200, \ < 200 (b) \ - E = w o, R h < 200, R w > 200 (c) \ = E = w 0, >_ 200, R w < 200 (d) \ - E = w o, > 200, R w > 200 (e) E h > 0, *h < 200 (f) \ > 0, *h > 200 (g) E w > 0, R w < 200 (h) E w > 0, R w >_ 200 In the f i r s t f o u r cases, both spouses may have tax t o pay, so t h a t n e i t h e r can c l a i m a married s t a t u s exemption f o r the o t h e r . In the second f o u r cases, at most one spouse has tax to pay and t h a t spouse claims a c a r r i e d s t a t u s exemption f o r the o t h e r . W i t h i n each of these groups, the f o u r cases are d i s t i n g u i s h e d by the amount of the f e d e r a l tax r e d u c t i o n of the tax-paying s p o u s e ( s ) . ..1.3.3 The c o n s t r a i n t s a p p l y i n g i n each of the cases are d i f f e r e n t but an e x p l a n a t i o n of the c o n s t r a i n t s a p p l y i n g i n two cases should enable the reader to understand the o t h e r s . In case ( a ) , the t a x a b l e income o f the husband i s the sum of h i s s a l a r y , grossed-up d i v i d e n d s , and non-farm income (1^)/ l e s s the b a s i c p e r s o n a l e x c e p t i o n ($2,270) and the standard 39 deduction f o r medical and c h a r i t a b l e expenses ($100): 13 E Y h i > S h + (4/3)*D h + I h - 2,270 - 100 (53) T h i s i s an i n e q u a l i t y r a t h e r than an equation because taxable income can never f a l l below z e r o , even i f the r i g h t - h a n d s i d e i s n e g a t i v e (deductions exceed income). The husband's f e d e r a l tax r e d u c t i o n i s the l e s s e r of h i s b a s i c f e d e r a l tax and $200: R h < F h (54) R h < 200 (55) T h e r e f o r e sub-problem (a) has (42) as an o b j e c t i v e f u n c t i o n to be minimized s u b j e c t to the c o r p o r a t e c o n s t r a i n t s (43) to (47), the p e r s o n a l tax c o n s t r a i n t s (48) to (55) f o r the husband and t h e i r c o u n t e r p a r t s f o r the w i f e (changing o n l y the s u b s c r i p t s ) , and n o n - n e g a t i v i t y c o n s t r a i n t s on a l l v a r i a b l e s . In case ( f ) , the husband's c l a i m of a married s t a t u s e x c e p t i o n changes the c o n s t r a i n t d e f i n i n g h i s t a x a b l e income t o : \ 13:4 13 Z ; Y h i - S h + ( 4/ 3>* D h + I h " 2 , 2 7 0 " 1 0 0 " E h ( 5 6 ) i = l The maximum amount of the married s t a t u s exemption i s $1,99 0: E h .<_ 1,990 (57) Another l i m i t on the married s t a t u s exemption claimed by the husband i s the d i f f e r e n c e between $2,370 and h i s w i f e ' s net income: E. < 2,370 - (S + (4/3) *D + I ) (58) h — w ' w w In case ( f ) , the f e d e r a l tax r e d u c t i o n i s the l e s s e r of $500 and 9% of b a s i c f e d e r a l tax: R h < 500 (59) R h 1 0.09*F h (60) Thus f o r t h i s case the o b j e c t i v e f u n c t i o n i s again (1), except t h a t F = R = P = 0 s i n c e the w i f e i s not paying any tax, w w w v i v 2 i and the c o n s t r a i n t s are the c o r p o r a t e c o n s t r a i n t s (43) t o (47), the husband's p e r s o n a l tax c o n s t r a i n t s (48) to (52) and (56) to (.60), and n o n - n e g a t i v i t y c o n s t r a i n t s on a l l v a r i a b l e s . The c o n s t r a i n t s on the married s t a t u s exemption, i n c l u d i n g the n o n - n e g a t i v i t y c o n s t r a i n t , have the e f f e c t t h a t f o r many farmers some or a l l o f sub-problems (e) t o (h) w i l l have no 4 0 f e a s i b l e s o l u t i o n . T h i s i s not a problem, s i n c e . i f o n l y means t h a t n e i t h e r spouse has any married exemption c l a i m , but there i s a s i t u a t i o n i n which none of the sub-problems w i l l have a 135 f e a s i b l e s o l u t i o n : i f there i s a l o s s on the farming o p e r a t i o n , so t h a t i s n e g a t i v e . I t seems reasonable to assume t h a t i n t h i s s i t u a t i o n d i v i d e n d s and owners' s a l a r i e s w i l l both be zero, so c o r p o r a t e tax l i a b i l i t y i s zero and p e r s o n a l tax l i a b i l i t i e s are determined by each spouse's non-. , 4 1 farm income alone. The method presented above p r o v i d e s a measure of the d i f f e r e n c e i n tax burdens between c o r p o r a t e and non-corporate o r g a n i z a t i o n a l forms. The measure has the advantage of combi-ni n g the t h r e e major tax b e n e f i t s of the c o r p o r a t e form: the income flow-through b e n e f i t , the d e f e r r a l of tax on r e t a i n e d e a r n i n g s , and the i n c o m e - s p l i t t i n g b e n e f i t . The income flow-through b e n e f i t i s the tax s a v i n g from e a r n i n g income through a c o r p o r a t i o n and d i s t r i b u t i n g i t i n the same year to share-h o l d e r s u s i n g an o p t i m a l d i v i d e n d - s a l a r y mixture as opposed to e a r n i n g i t through an u n i n c o r p o r a t e d b u s i n e s s and removing i t from the b u s i n e s s as drawings. T h i s b e n e f i t was s u b s t a n t i a l l y i n c r e a s e d i n 1 9 7 8 w i t h the change i n the d i v i d e n d gross-up and 42 " tax c r e d i t system. The d e f e r r a l of tax on r e t a i n e d earnings a r i s e s because of the s a v i n g i n c u r r e n t taxes on income earned through a c o r p o r a t i o n and not d i s t r i b u t e d t o s h a r e h o l d e r s , as compared t o income earned by an u n i n c o r p o r a t e d business and r e t a i n e d i n the b u s i n e s s . T h i s i s a c u r r e n t tax s a v i n g p r o v i d e d t h a t the c o r p o r a t e tax r a t e i s l e s s than the p e r s o n a l marginal 136 tax r a t e of an un i n c o r p o r a t e d businessman, which i s u s u a l l y the case. I t i s onl y a d e f e r r a l and not a permanent tax sa v i n g to the extent t h a t the r e t a i n e d earnings bear f u r t h e r tax when they are u l t i m a t e l y p a i d out as d i v i d e n d s and taxed i n the hands of s h a r e h o l d e r s . Our measurement of the d i f f e r e n c e i n tax burdens between corpor a t e and non-corporate o r g a n i z a t i o n a l forms as the d i f f e r e n c e i n c u r r e n t taxes ignores t h i s second l e v e l o f t a x a t i o n , however, so the tax b e n e f i t s of d e f e r r a l are o v e r s t a t e d . On the o t h e r hand, the e r r o r i n v o l v e d may not be gr e a t i n pr e s e n t value terms i f the funds are l e f t i n the c o r -p o r a t i o n f o r many y e a r s . The t h i r d b e n e f i t o f the corpora t e form i s the p o s s i b i l i t y o f i n c o m e - s p l i t t i n g . Under a p r o g r e s s i v e p e r s o n a l income tax, e q u a l i z i n g t a x a b l e incomes of husband and w i f e may produce s u b s t a n t i a l tax s a v i n g s , even i f the married s t a t u s exemption has to be s a c r i f i c e d . A c o r p o r a t i o n makes t h i s p o s s i b l e through payments of s a l a r y and d i v i d e n d s to both spouses. An un i n c o r p o r a t e d business i s not n e a r l y as u s e f u l i n t h i s r e g a r d , as th e r e i s no co u n t e r p a r t t o spousal d i v i d e n d s , 4 3 and a spousal s a l a r y was not d e d u c t i b l e u n t i l 1980. Another v i r t u e of the proposed measure of the tax burden d i f f e r e n t i a l i s t h a t i t takes i n t o account two of the major disadvantages o f the co r p o r a t e form. The f i r s t of these i s t h a t the l o s s e s of an u n i n c o r p o r a t e d business can be used by the owner t o reduce h i s p e r s o n a l t a x a b l e income from other sources. 137 Any amount of l o s s e s can be so used, and i t can be done i n the year t h a t the l o s s i s i n c u r r e d . Losses i n a c o r p o r a t i o n do not reduce the owners' p e r s o n a l tax l i a b i l i t i e s u n t i l the c o r p o r a t i o n i s wound up or s o l d , and a t t h a t time the a l l o w a b l e l o s s i s o n l y one-half of the l o s s on share investment or share-h o l d e r s ' income to the c o r p o r a t i o n . The c o r p o r a t e l o s s e s can be c a r r i e d backward and forward w i t h i n l i m i t s t o reduce the c o r p o r a t i o n ' s income i n other y e a r s , but t h i s i s not as d e s i r a b l e as the a b i l i t y t o use the l o s s e s a t the p e r s o n a l l e v e l , s i n c e the p e r s o n a l marginal tax r a t e i s u s u a l l y higher and the c o r -p o r a t i o n may a l s o have l o s s e s i n other y e a r s . A second d i s -advantage of the c o r p o r a t e form i s t h a t i t i n v o l v e s e x t r a l e g a l and accounting c o s t s , of which the e x t r a c o s t s f o r tax compliance and tax p l a n n i n g are the most important. T h i s i s accounted f o r by a d j u s t i n g the measure of the tax burden d i f f e r e n t i a l to allow f o r an e x t r a $80 0 i n annual expenses f o r a c o r p o r a t i o n . One f a c t o r a f f e c t i n g r e l a t i v e tax burdens which c o u l d not be i n c l u d e d i n the measure i s the a v a i l a b i l i t y of c e r t a i n income-averaging d e v i c e s only to u n i n c o r p o r a t e d farmers. F u l l - t i m e u n i n c o r p o r a t e d farmers may use f i v e - y e a r b l o c k averaging f o r t h e i r farming income, and p r i o r to the 1981.budget u n i n c o r p o r a t e d farmers c o u l d purchase an income-averaging annuity c o n t r a c t (IAAC) i n the amount of t h e i r t a x a b l e c a p i t a l gains or recaptured c a p i t a l c o s t allowance, as might a r i s e on the s a l e of the farm. 138 " However, c o r p o r a t i o n s may engage i n some averaging on t h e i r own by a p p r o p r i a t e t i m i n g of s a l a r y and d i v i d e n d payments over the y e a r s . 5.3 ESTIMATION AND ANALYSIS The f o r e g o i n g a n a l y s i s suggests t h a t the f a c t o r s a f f e c t -i n g the p r o b a b i l i t y t h a t a farmer w i l l be i n c o r p o r a t e d are h i s years o f s c h o o l i n g and farming experience and the amount of 45 46 tax s a v i n g i n v o l v e d . ' In order to estimate how the p r o b a b i l i t y i s a f f e c t e d by these f a c t o r s , an e s t i m a t i o n t e c h -nique which i s a p p r o p r i a t e f o r d i s c r e t e dependent v a r i a b l e s i s r e q u i r e d , s i n c e the observed o r g a n i z a t i o n a l form i s e i t h e r 4 7 c o r p o r a t e o r non-corporate. One such technique i s p r o b i t a n a l y s i s , which assumes i n t h i s a p p l i c a t i o n t h a t a farmer's o r g a n i z a t i o n a l form i s determined by z = j 0 i f ,6 ,X i u ± ,< 0 1 "" 1 i f B'X. u. > 0 ( 6 1 ) I I -where Z^= 0 re p r e s e n t s a non-corporate farmer, Z^= 1 r e p r e -sents a co r p o r a t e farmer, i s a v e c t o r of o b s e r v a t i o n s on the independent v a r i a b l e s , v3 i s a v e c t o r of c o e f f i c i e n t s , and the d i s t u r b a n c e s u^ are independently d i s t r i b u t e d standard normal random v a r i a b l e s . The c o e f f i c i e n t s i n (61) were estimated by the method of maximum l i k e l i h o o d , which guarantees t h a t the estimates w i l l be c o n s i s t e n t , a s y m p t o t i c a l l y unbiased, asympto-48 t i c a l l y e f f i c i e n t and a s y m p t o t i c a l l y normally d i s t r i b u t e d . The r e l i a n c e on asymptotic r a t h e r than small-sample p r o p e r t i e s i s not a problem because of the l a r g e s i z e of the sample—3,017 1:3 9 farms, of which 106 are i n c o r p o r a t e d . The sample used d i f f e r s from the f u l l survey i n some r e s p e c t s , mainly i n t h a t 314 records were not usable because of e r r o r s i n the p r o d u c t i o n of the p u b l i c r e l e a s e tape, and a l s o 149 l a r g e l i v e s t o c k farms are not on the p u b l i c r e l e a s e tape f o r c o n f i d e n t i a l i t y reasons. The i n i t i a l e q u ation estimated i n c l u d e d b i n a r y v a r i a b l e s f o r the three c a t e g o r i e s of l e n g t h of farming e x p e r i e n c e , 5 0 years of s c h o o l i n g and i t s square, tax savings and i t s square, and i n t e r a c t i o n v a r i a b l e s between experience and tax savings and between e d u c a t i o n and tax s a v i n g s . The i n t e r a c t i o n e f f e c t s were i n c l u d e d i n the equation because edu c a t i o n and experience may be expected t o i n c r e a s e the p r o b a b i l i t y of the c o r p o r a t e form i f there are p o s i t i v e tax savings from i n c o r p o r a t i o n and decrease the p r o b a b i l i t y i f tax savings are n e g a t i v e . The r e s u l t s of t h i s e s t i m a t i o n are d i s p l a y e d i n Table IX. Most r e s u l t s are as expected: the e f f e c t of g r e a t e r experience i s p o s i t i v e , the e f f e c t of a d d i t i o n a l years of s c h o o l i n g (above 4.5 years) i s p o s i t i v e , and the e f f e c t of a d d i t i o n a l tax savings i s p o s i t i v e i n the r e l e v a n t range. However, the co-e f f i c i e n t s of the i n t e r a c t i o n v a r i a b l e s were unexpectedly n e g a t i v e . In a d d i t i o n , s i x of the nine v a r i a b l e s i n the equa-t i o n had c o e f f i c i e n t s which were not s i g n i f i c a n t l y d i f f e r e n t from zero a t the .05 l e v e l . 140 TABLE IX: I n i t i a l Problt Equation for Organizational Form Variable Coefficient. Asymptotic t-ratio (constant) -2.7405 -5.48 Years of schooling -0.2716 x IO - 1 -0.34 , Years of schooling squared 0.6089 x IO - 2 1.73 Tax savings ($000) 0.1246 2.81 Tax savings squared -0.5111 x 10"3 -3.60 6-15 yrs experience 0.1904 0.93 15+ yrs experience 0.4092 2.14 Tax savings x yrs of schooling -0.1588 -0.93 Tax savings x 6-15 yrs experience -0.2439 x 10 - 1 -0.60 Tax savings x 15+ yrs experience -0.4847 x 10 - 1 -1.20 The equation was r e - e s t i m a t e d and the f i n a l form, i n which a l l v a r i a b l e s are s i g n i f i c a n t l y d i f f e r e n t from zero, i n c l u d e d the const a n t , years of s c h o o l i n g squared, tax s a v i n g s , and tax savings squared. The c o e f f i c i e n t estimates are r e p o r t e d i n Table X. 1-41 TABLE X: Probit Equation for Organizational Form: Variable Coefficient Asymptotic t-ratio (constant) -2.4653 -23.10 Years of schooling squared 0.3915 x 10" -2 5.06 Tax savings ($000) 0.7052 x 10" -1 8.18 Tax savings squared -0.5634 x 10" -3 -4.51 *A11 coefficients are significant at the .001 level in a two-tailed test. A likelihood ratio test rejected the hypothesis that a l l co-efficients other than the constant are jointly zero at the .001 level of significance. Efron's R squared = 0.09. As b e f o r e , e d u c a t i o n and tax savings both had p o s i t i v e e f f e c t s on the p r o b a b i l i t y of a farm being i n c o r p o r a t e d . The e f f e c t of a d d i t i o n a l t a x . s a v i n g s does e v e n t u a l l y become n e g a t i v e , but not u n t i l a very h i g h l e v e l of tax savings ($62,500) i s reached. In order t o i n t e r p r e t the p r o b i t equation f u r t h e r , Table XI p r e s e n t s p r e d i c t i o n s of the p r o b a b i l i t y t h a t a farm w i l l be i n c o r p o r a t e d f o r d i f f e r e n t v a l u e s of the independent v a r i a b l e s . .142 TABLE XI: Predicted Probabilities of the Corporate Form Years of Schooling 6 8 10 12 ; 14 .' Tax Savings -2,500 .006 .008 .012 .019 .030 from Corporate 0 .010 .013 .019 .029 .045 Form ($> 2,500 .016 .021 .029 .042 .064 5,000 .024 .030 .041 .059 .087 15,000 .082 .100 .127 .166 .222 25,000 .181 .211 .254 .312 .387 The f i g u r e s i n the t a b l e may be compared wit h the '0 .024 p r o b a b i l i t y t h a t the average farmer i n the sample, who has 9.7 years of e d u c a t i o n and p o t e n t i a l tax savings of $1,794 w i l l be i n c o r p o r a t e d . The average tax s a v i n g i s m i s l e a d i n g , however, as the m a j o r i t y of farmers (51%) had tax savings i n the range of -$1,000 to zero, i n d i c a t i n g a s m a l l tax c o s t to adopting the c o r p o r a t e form. The d i s t r i b u t i o n of tax savings i s skewed t o the r i g h t , with about one-quarter of the sample f a l l i n g i n t o the zero to $2,500 range of tax s a v i n g s , and another o n e - f i f t h having tax savings over $2,500. 5 1 To determine i f the r e s u l t s above are s e n s i t i v e t o the assumption made e a r l i e r about the r e l a t i o n s h i p between farm net income (Y^) and the amount d i s t r i b u t e d (M), the p r o b i t equations were r e - e s t i m a t e d under the assumptions of a f l a t 75% or 85% of income d i s t r i b u t e d . The r e s u l t s d i d not change 143 s i g n i f i c a n t l y . Table XII shows the p r e d i c t e d p r o b a b i l i t i e s of i n c o r p o r a t i o n o b t a i n e d by e s t i m a t i n g the f i n a l form of the p r e v i o u s equation under the assumption of a f l a t 75% d i s t r i b u -t i o n of farm net income. The range of p r e d i c t e d p r o b a b i l i t i e s i s widened somewhat but the i n f e r e n c e s drawn are u n a f f e c t e d . TABLE XII: Predicted Probabilities of the Corporate Form with Alternative Distribution Assumption Years of Schooling 6 8 10 12 14 Tax Savings -2,500 .006 .008 .011 .017 .028 from Corporate 0 .010 .013 .018 .028 .043 Form ($) 2,500 .016 .021 .029 .042 .063 5,000 .024 .031 .043 .061 .089 15,000 .096 .108 .137 .178 .235 25,000 .195 .226 .270 .329 .405 The most s u r p r i s i n g aspect of the p r e d i c t e d p r o b a b i l i t i e s i n Table XI i s how low they are. For example, a farmer who has 12 years of s c h o o l i n g and p o t e n t i a l tax savings of $25,000 by being i n c o r p o r a t e d i n 19 77, and who probably would have s i g n i f i c a n t tax savings i n o t h e r years a l s o , has a p r e d i c t e d p r o b a b i l i t y of being i n c o r p o r a t e d of only 0.31. One e x p l a n a t i o n i s t h a t the f r e q u e n t changes i n the tax laws a f f e c t i n g c l o s e l y -h e l d c o r p o r a t i o n s i n the 19 70's have c r e a t e d a d i s e q u i l i b r i u m . Perhaps most farmers who can save taxes by adopting the c o r -porate form w i l l e v e n t u a l l y do so, but as of 19 77 many had not y e t caught on to the advantages. T h i s i n t e r p r e t a t i o n i s con-144 s i s t e n t w i t h the importance of e d u c a t i o n i n the choice of an o r g a n i z a t i o n a l form r e v e a l e d by Table XI, s i n c e s e v e r a l s t u d i e s have found t h a t more educated farmers adopt new t e c h n o l o g i e s 5 2 more q u i c k l y . The a l t e r n a t i v e view t h a t the education v a r i a b l e i s a proxy f o r the value d i f f e r e n t farmers p l a c e on s i m p l i c i t y i n o r g a n i z a t i o n a l form i s not as c o n v i n c i n g , e s p e c i a l l y i n l i g h t of the l a r g e amounts of p o t e n t i a l tax savings i n v o l v e d . The d i s e q u i l i b r i u m i n t e r p r e t a t i o n i s a l s o c o n s i s t e n t w i t h the f i n d i n g t h a t the p r o b a b i l i t y of the c o r -porate form i n c r e a s e s w i t h the amount of p o t e n t i a l tax s a v i n g s , s i n c e one would expect t h a t the f i r s t farmers to adopt the co r p o r a t e form would be the ones who have the most to g a i n from i t . I f i t i s t r u e t h a t the c u r r e n t p a t t e r n of o r g a n i z a t i o n a l forms among Saskatchewan farmers i s a d i s e q u i l i b r i u m phenomenon, then tax c o l l e c t i o n a u t h o r i t i e s have reason to f e a r the attainment of an e q u i l i b r i u m . On the b a s i s of the sample, i t i s p r e d i c t e d t h a t the t o t a l amount of income tax p a i d by Saskatchewan farmers would d e c l i n e by 26% i f every farmer 54 adopted the tax-minimizing o r g a n i z a t i o n a l form. Although the e x i s t e n c e of a d i s e q u i l i b r i u m does appear to be the most p l a u s i b l e i n t e r p r e t a t i o n of the r e s u l t s , some c a u t i o n i s necessary because the tax savings v a r i a b l e c o u l d be b i a s e d upwards f o r some farmers. The l a c k of a r o l l o v e r f o r c o r p o r a t e farms on the t r a n s f e r of farming a s s e t s to a 14 5 c h i l d of the farmer i s one tax c o s t of i n c o r p o r a t i o n t h a t c o u l d not be q u a n t i f i e d . Another i s the a v a i l a b i l i t y o f income-averaging annuity c o n t r a c t s and f i v e - y e a r b l o c k a v e r a g i n g o n l y to u n i n c o r p o r a t e d farmers. A study i n v o l v i n g i n t e r v i e w s w i t h farmers and t h e i r a d v i s o r s on the reasons f o r not i n c o r p o r a t i n g c o u l d shed l i g h t on t h i s q u e s t i o n . The estimated p r o b i t c o e f f i c i e n t s may a l s o be used t o p r e d i c t the e f f e c t of tax changes on the p r o p o r t i o n of Saskat-chewan farms which are i n c o r p o r a t e d . Two r e c e n t tax changes which might be expected to a f f e c t t h i s are the 1978 r e d u c t i o n i n the p e r s o n a l income tax burden on d i v i d e n d s and the 19 80 e x t e n s i o n to u n i n c o r p o r a t e d b u s i n e s s e s of the r i g h t to deduct s a l a r i e s p a i d to owners' spouses. The f i r s t change may be expected to i n c r e a s e the p r o p o r t i o n of farms which are i n c o r -porated, w h i l e the second may be expected to reduce i t . The 19 7 8 change i n the tax treatment of d i v i d e n d s , which r a i s e d the gross-up f a c t o r from 4/3 to 3/2 and r a i s e d the tax c r e d i t from 4/15 t o 3/8, r e s u l t e d i n a s i g n i f i c a n t over-i n t e g r a t i o n of corpora t e income s u b j e c t to the s m a l l b u s i n e s s tax r a t e . 5 5 T h i s i s r e f l e c t e d i n a 23% ($375) i n c r e a s e i n the average tax s a v i n g from i n c o r p o r a t i o n f o r Saskatchewan farmers, r e l a t i v e to the tax savings f o r 19 78 i f the change i n the 5 6 t a x a t i o n o f d i v i d e n d s had not been made. The c a l c u l a t i o n s assume t h a t farmers a l t e r t h e i r mixture of s a l a r y and d i v i d e n d payments to take advantage of the c h a n g e . 5 7 I t i s p r e d i c t e d t h a t t h i s w i l l i n c r e a s e the p r o p o r t i o n of Saskatchewan farmers 146 who are i n c o r p o r a t e d h a r d l y a t a l l , as might be expected i n view of the low s e n s i t i v i t y to tax savings e v i d e n t i n Table A s i m i l a r simulation, o f the e f f e c t o f g r a n t i n g u n i n c o r -porated b u s i n e s s owners the r i g h t to pay s a l a r i e s t o t h e i r spouses shows t h a t the average tax savings from i n c o r p o r a t i o n f o r 1980 f o r Saskatchewan farmers d e c l i n e d by 18% ($271) as a r e s u l t , r e l a t i v e t o what the tax savings would have been 5 9 f o r t h a t year without the change. T h i s assumes t h a t un-i n c o r p o r a t e d farmers respond t o the tax change by paying t h e i r spouses the amount of s a l a r y which minimizes the t o t a l tax burden of husband and w i f e , s u b j e c t to the reasonableness requirement o f c o n s t r a i n t ( 4 5 ) . 6 0 T h i s c a l c u l a t i o n may under-s t a t e the d e c l i n e i n tax savings from i n c o r p o r a t i o n because the maximum reasonable spousal s a l a r y i n (45) i s determined on the b a s i s o f the r e p o r t e d number of hours the spouse worked on the farm i n 1977, which was bef o r e the tax change was made and hence b e f o r e there was an i n c e n t i v e to exaggerate the hours worked. In the survey, 36% of the farmers r e p o r t e d t h a t t h e i r spouses d i d no work on the farm, while the spouses who d i d work on the form worked an average of 1,427 hours. Assuming t h a t the d e c l i n e i n average tax savings from i n c o r p o r a t i o n o f 18% i s approximately c o r r e c t , t h i s change w i l l cause only a very sm a l l d e c l i n e i n the percentage o f farms which are i n c o r -p o r a t e d . 6 1 Even a much l a r g e r d e c l i n e i n average tax savings - 14 7 from adopting the c o r p o r a t e form would not l i k e l y cause many d i s i n c o r p o r a t i o n s , due to the l a r g e c o s t s , but i t might slow down the pace of new i n c o r p o r a t i o n s . 5.4 CONCLUSION In summary, most Saskatchewan farmers have chosen the o r g a n i z a t i o n a l form which i s b e s t f o r them f i n a n c i a l l y — t h e non-corporate form. However, there i s a s i z e a b l e m i n o r i t y of farmers who c o u l d shave thousands of d o l l a r s o f f t h e i r annual tax b i l l s by i n c o r p o r a t i n g , but who have not y e t done so. The problem seems to be one of a l a c k of i n f o r m a t i o n and r e s i s t a n c e to change, s i n c e the l e v e l o f e d u c a t i o n of the farmer i s an important i n f l u e n c e on h i s p r o b a b i l i t y of i n c o r -p o r a t i o n f o r any l e v e l of tax s a v i n g s . T h i s suggests t h a t tax i n c e n t i v e s f o r s m a l l b u s i n e s s which apply o n l y to corpo-r a t i o n s are not r e a c h i n g a l l of the t a r g e t p o p u l a t i o n and perhaps should be r e c o n s i d e r e d . Such i n c e n t i v e s i n c l u d e the s m a l l business deduction, s i m i l a r p r o v i n c i a l r a t e r e d u c t i o n s , 6 2 and O n t a r i o Small Business Development C o r p o r a t i o n s . Another f i n d i n g i s t h a t r e c e n t changes i n the tax laws a f f e c t i n g farmers have had a s i g n i f i c a n t impact on the r e l a t i v e tax burdens of c o r p o r a t e and non-corporate forms of business o r g a n i z a t i o n . For Saskatchewan farmers, the r e d u c t i o n i n the tax burden on d i v i d e n d s i n c r e a s e d the average tax s a v i n g from i n c o r p o r a t i o n by 2 3% i n 19 78, and e x t e n s i o n of d e d u c t i b i l i t y o f s a l a r i e s of owners' spouses to u n i n c o r p o r a t e d businesses 148 reduced the average tax sa v i n g by 18% i n 1980. N e i t h e r of these changes i s l i k e l y t o cause many farmers to change o r g a n i z a t i o n a l forms, s i n c e the e s t i m a t i o n r e s u l t s suggest t h a t t h i s d e c i s i o n i s not very s e n s i t i v e t o changes i n r e l a t i v e tax burdens. D i f f u s i o n o f knowledge about tax savings from i n c o r p o r a -t i o n may be expected to i n c r e a s e over time the number of farm c o r p o r a t i o n s . T h i s c o u l d r e i n f o r c e the c u r r e n t t r e n d toward l a r g e - s c a l e farms s i n c e the tax laws a s s i s t c o r p o r a t i o n s more i n accumulating the c a p i t a l r e q u i r e d t o purchase new, s i z e -i n c r e a s i n g t e c h n o l o g y . 6 3 N O T E S 1. Corporate farms i n Saskatchewan have been s t u d i e d by Brown, Elmgren and Minogue (1973). 2. See Grover and I a c o b u c c i (1980), pp. 29-42. 3. See P r i e h a r d (197 8), Appendix D. 4. See Taube (1978), chapter 10. 5. Shead (1975), Winslade (1978), P u r i c h (1982). 6. The survey used i s the J u l y 1978 A g r i c u l t u r e Enumerative Survey ( p u b l i c r e l e a s e v e r s i o n ) of S t a t i s t i c s Canada. 7. S t a t i s t i c s Canada catalogue 96-701 ( J u l y 1973) and 96-800 (March 1978). The f i g u r e s are f o r census farms, the d e f i n i t i o n o f which changed between 1971 and 1976. The 1976 f i g u r e f o r a l l a g r i c u l t u r a l h o l d i n g s , which may be a b e t t e r comparison, i s 4.1%. 8. Unpublished S t a t i s t i c s Canada estimates based on AES-FES data, January 22, 1981. 9. S t a t i s t i c s Canada catalogue 96-800 (March 1978). 10. Johnston (1982), p. 69. 11. King (1977), pp. 112-115 uses t h i s approach. 12. T h i s i s based on f i n a n c i a l data i n Saskatchewan Department of A g r i c u l t u r e (1978) f o r the average 600-1,200 acre g r a i n farm i n the b l a c k s o i l zone. Of the $35,000, $19,000 i s c o r -porate tax and $16,000 i s p e r s o n a l tax on the deemed d i v i d e n d . 13. Meyerhoff (1978). 14. Fuke (1974), Shead (1975). 15. See B a r c l a y (1979), B i r d (1974), and Brown, Elmgren and Minogue (19 73). 16. P u r i c h (1982). 1-49 .150" 17. See C a r s w e l l (1955). 18. S t a t i s t i c s on r e a l i z e d net income of Saskatchewan farmers show t h a t the year covered by the survey (1977) was not an e s p e c i a l l y bad or good year, although i t was worse than the very good years o f 1974-6. See S t a t i s t i c s Canada catalogue 21-201. 19. In some cases i t i s onl y an assumption t h a t the farmer has a spouse, s i n c e none of the survey q u e s t i o n s ask t h i s d i r e c t l y . 20. The r i g h t to use the cash b a s i s of accounting i s the most important o f the s p e c i a l tax b e n e f i t s a v a i l a b l e t o farmers. See Brinkman (1981) and Johnston (1982) . 21. I n t e r e s t expense i s c a l c u l a t e d from the amounts of loans o u t s t a n d i n g and r e p o r t e d r a t e s of i n t e r e s t i n J u l y 1978. 22. From the wording of the q u e s t i o n i t appears t h a t s a l a r i e s p a i d to spouses are excluded, as they should be i n c a l -c u l a t i n g the income o f an un i n c o r p o r a t e d farm. 23. Lime i s excluded but Saskatchewan s o i l s need l i t t l e l ime. 24. T h i s i s the method S t a t i s t i c s Canada uses to estimate farm machinery and equipment d e p r e c i a t i o n ( S t a t i s t i c s Canada catalogue 21-202P). The CCA estimate i s probably low because CCA on b u i l d i n g s i s not i n c l u d e d . 25. A few farms r e p o r t e d p o s i t i v e p a r t n e r ' s hours w i t h the farm o p e r a t o r ' s own hours r e p o r t e d as zero. These farms had to be excluded from the sample as there was no way to estimate the o p e r a t o r ' s share of the farm net income. 26. S i n c e i n the survey some s o l e p r o p r i e t o r s and co r p o r a t e farm o p e r a t o r s r e p o r t e d p o s i t i v e p a r t n e r ' s hours, i t appears t h a t survey respondents i n t e r p r e t e d " p a r t n e r s " t o i n c l u d e persons i n a bu s i n e s s agreement and s h a r e h o l d e r s . 27. At the time, Revenue Canada made i t very d i f f i c u l t to have husband-wife p a r t n e r s h i p s r e c o g n i z e d f o r tax purposes. 28. T h i s assumes complete d e d u c t i b i l i t y of farm l o s s e s . There i s no d e d u c t i b i l i t y a t a l l i f the farm does not have a reasonable e x p e c t a t i o n o f p r o f i t , and i n a "hobby farm" s i t u a t i o n d e d u c t i b i l i t y i s l i m i t e d t o $5,000. Ther e f o r e f o r some farms the a t t r a c t i v e n e s s of the non-corporate form i s o v e r s t a t e d . 151 29. The importance of an op t i m a l s a l a r y - d i v i d e n d c h o i c e i s s t r e s s e d by Eddy (1978) and Novis and Lazarus (1980). 30. Thi s assumes t h a t the c o r p o r a t i o n a l s o uses the cash method of accounting, which seems l i k e l y as a l l of the i n c o r p o r a t e d farms surveyed by Brown, Elmgren and Minogue (1973) d i d so. 31. I d e a l l y , t h i s f r a c t i o n should be made endogenous and farm-specific." as there i s probably c o n s i d e r a b l e v a r i a t i o n among farms. Brown, Elmgren and Minogue (19 73) found t h a t 20% of t h e i r sample of i n c o r p o r a t e d farms p a i d out no income a t a l l to s h a r e h o l d e r s . 32. C h e n h a l l (1980). 33. Brown, Elmgren and Minogue (1973) found t h a t j o i n t husband-wife shareholding, was common among i n c o r p o r a t e d Saskatchewan farmers; i n j u s t over o n e - t h i r d of t h e i r sample, the only shareholders'were husband and w i f e . 34. I f the respondent has p a r t n e r s ( i . e . , other s h a r e h o l d e r s ) , one would expect t h a t the amount of d i v i d e n d s p a i d would a l s o depend on t h e i r p r e f e r e n c e s and t h e i r tax s i t u a t i o n s . T h i s i s not co n s i d e r e d i n t h i s model. 35. For a review of the use of c o r p o r a t i o n s i n i n c o m e - s p l i t t i n g , see Dart (1980). 36. I t i s assumed t h a t the c o r p o r a t i o n ' s t a x a t i o n year i s the same as t h a t of the s h a r e h o l d e r s , i . e . , the calendar year. 37. T h i s would not be c o r r e c t f o r a farm c o r p o r a t i o n with a cumulative deduction account over $600,000, but very few farm c o r p o r a t i o n s would be t h a t l a r g e . 38. Another i n t e r p r e t a t i o n of the problem i s t h a t i t i n v o l v e s four mutually e x c l u s i v e s e t s o f l i n e a r c o n s t r a i n t s , and t h e r e f o r e i t c o u l d be s o l v e d by mixed i n t e g e r programming. 39. I f the husband i s over 65, there i s a l s o an age exemption of $1,420. 40. For example, (e.) and (f) w i l l have no s o l u t i o n i f the w i f e ' s non-farm income exceeds $2,370. 41. The tax sav i n g from a p p l y i n g the l o s s t o the c o r p o r a t i o n ' s income'in other years ( i f there i s any) i s not co n s i d e r e d . 15-2 42. See Eddy (19 7 8). 43. P a r t i a l d e d u c t i b i l i t y of a spousal s a l a r y i n a p a r t n e r -s h i p was p o s s i b l e b e f o r e 1980. 44. See fo o t n o t e 2 8 above. 45. As noted i n the t e x t , the tax s a v i n g i s reduced by the respondent's share o f the estimated $800 annual e x t r a expense a s s o c i a t e d w i t h the c o r p o r a t e form. 46. A v a r i a b l e f o r farm type ( l i v e s t o c k , g r a i n or mixed) was co n s i d e r e d as a proxy f o r d i f f e r e n c e s i n r i s k , but there was no s a t i s f a c t o r y way of making the c l a s s i f i c a t i o n . 47. Or d i n a r y l e a s t squares i s not a p p r o p r i a t e , although i n t h i s p a r t i c u l a r a p p l i c a t i o n the r e s u l t s happen to be q u a l i t a t i v e l y almost i d e n t i c a l . On e s t i m a t i o n w i t h d i s -c r e t e dependent v a r i a b l e s , see Pindyck and R u b i n f e l d (1981) and Amemiya (19 81). 48. I d e a l l y , t h i s should be estimated as two simultaneous equations, w i t h the second equation e x p l a i n i n g tax savings as a f u n c t i o n of o r g a n i z a t i o n a l form and other f a c t o r s . The argument i s t h a t c o r p o r a t e farms can more e a s i l y accumulate r e t a i n e d e a r n i n g s , which i n c r e a s e s p r o f i t s and i n c r e a s e s tax savings from i n c o r p o r a t i o n . However, Heckman (19 78) shows i t i s not p o s s i b l e to estimate a model of t h i s type. 49. Of the 149, 45 are i n c o r p o r a t e d . Another d i f f e r e n c e i s t h a t there i s grouping i n the responses to many quest i o n s on the p u b l i c r e l e a s e tape. 50. The c a t e g o r i e s are: 0-5 ye a r s , 6-15 y e a r s , and over 15 ye a r s . 51. The r i g h t - t a i l p r o p o r t i o n s a r e : $2,500-$5,000, 8.2%; $5,000-$15,000, 8.9%; $15,000-$25,000, 1.3%; over $25,000, 1.4%. 52. See Huffman (1977), S c h u l t z (1975) and Welch (1978). On Canadian farmers, see B a r i c h e l l o (1979). 53. On the r e l a t i o n s h i p between i n f o r m a t i o n and farm s c a l e , see Welch (1978). 15 3 54. Survey weights are used to p r o j e c t from the sample to the p o p u l a t i o n . 55. See Eddy (1978). 56. In both s i m u l a t i o n s , the change i n tax savings i s r e p o r t e d i n 1977 d o l l a r s f o r c o m p a r a b i l i t y w i t h o t h e r f i g u r e s . 57. To estimate the 197 8 tax savings from i n c o r p o r a t i o n , the parameters of the l i n e a r programming problems were changed to r e f l e c t the changes i n tax laws, the new minimum wage, and changes i n non-farm and net farm income. The net farm income of each farmer was i n c r e a s e d by the average growth of r e a l i z e d net income of a l l Saskatchewan farmers between 1977 and 1978, as estimated by S t a t i s t i c s Canada i n catalogue 21-202P. The 1978 tax savings o b t a i n e d from s o l v i n g the tax m i n i m i z a t i o n problem were converted to 1977 d o l l a r s u s i n g the consumer p r i c e index b e f o r e they were used f o r p r e d i c t i o n purposes. One problem wi t h t h i s s i m u l a t i o n i s t h a t the survey asked the farmer's o r g a n i z a t i o n a l form as of J u l y 197 8, and so some farmers may a l r e a d y have responded to the change i n d i v i d e n d t a x a t i o n by i n c o r p o r a t i n g . 58. Using the survey weights to p r o j e c t from the sample to the p o p u l a t i o n , the tax change i n c r e a s e d the p r e d i c t i o n of the p r o p o r t i o n o f farms t h a t are i n c o r p o r a t e d from 2.64% to 2.80%. Although the change i n t h i s v a r i a b l e should be meaningful, the l e v e l may be i n e r r o r due to the e x c l u s i o n s which reduced the usable sample to 3,017 farms. 59. The r e a l i z e d net income of Saskatchewan farmers i n 1980 was estimated by the author to be $900 m i l l i o n . The S t a t i s t i c s Canada estimate was not a v a i l a b l e at the time of w r i t i n g . 60. T h i s problem was s o l v e d by a sequence of l i n e a r programming problems, u s i n g a model s i m i l a r to t h a t presented f o r the c o r p o r a t e farm. The m o d i f i c a t i o n s * were the d e l e t i o n of c o n s t r a i n t s (43), (44), (46) and (47), the d e l e t i o n of. v a r i a b l e s D, , D , Y and Y, , and the replacement of S, by v _ c h' w' s 1 * h -* . b w 61. The d e c l i n e i n the p r e d i c t e d percentage i n c o r p o r a t e d i s from 2.59% t o 2.48%:. 62. Lahey (1979) p r o v i d e s f u r t h e r arguments why s m a l l business tax i n c e n t i v e s should not be r e s t r i c t e d to c o r p o r a t i o n s , and a l s o d i s c u s s e s the t e c h n i c a l problems i n v o l v e d . 63. See Reimund (1979). CHAPTER 6 CONCLUSION T h i s chapter summarizes the f i n d i n g s of the t h e s i s and d i s c u s s e s some p o l i c y i m p l i c a t i o n s . 6.1 SUMMARY OF FINDINGS In Chapter 2, a model i s c o n s t r u c t e d of the f i n a n c i a l p o l i c y of a Canadian c l o s e l y - h e l d c o r p o r a t i o n w i t h a s i n g l e owner. T h i s model takes i n t o account both the s p e c i a l economic c h a r a c t e r i s t i c s of c l o s e l y - h e l d c o r p o r a t i o n s and t h e i r s p e c i a l tax regime. S o l u t i o n of the model by the Kuhn-Tucker method r e v e a l s t h a t i n an o p t i m a l f i n a n c i a l p o l i c y i t w i l l not be p o s s i b l e to decrease t o t a l taxes by a f e a s i b l e i n c r e a s e i n one form of owner's remuneration and a f e a s i b l e decrease i n another. The r e l e v a n t forms of owner's remuneration are s a l a r y , t a x a b l e d i v i d e n d s , c a p i t a l d i v i d e n d s , and the repayment of loans from s h a r e h o l d e r s . I t i s a l s o shown t h a t u t i l i t y maximization by the owner-manager i m p l i e s t h a t tax e f f e c t s w i l l be taken i n t o account i n choosing h i s consumption bundle of t a x a b l e b e n e f i t s , non-taxable b e n e f i t s , and other goods. 1 T h i s i s done through the use of p r i c e s which are a d j u s t e d f o r the tax change which purchase of the r e l e v a n t goods w i l l cause. The necessary c o n d i t i o n s f o r an optimum were used to develop algorithms and graphs f o r the o p t i m a l choice among forms of owner's remuneration f o r a c l o s e l y - h e l d c o r p o r a t i o n o p e r a t i n g i n B r i t i s h Columbia i n 19 80. I t i s found t h a t the o p t i m a l c h o i c e v a r i e s g r e a t l y , depending on the amount of the 154 155 c o r p o r a t i o n ' s a c t i v e business income before deducting the owner's s a l a r y ("gross c o r p o r a t e income"). For fi r m s having l e s s than $150,000 i n gross c o r p o r a t e income, Which w i l l i n c l u d e most s m a l l b u s i n e s s e s , the op t i m a l choice i s u s u a l l y the maximum amount of c a p i t a l d i v i d e n d s and repayment of share h o l d e r ' s l o a n s , a l a r g e amount of d i v i d e n d s , and a small or zero amount of s a l a r y . Chapter 3 i s devoted t o s i m u l a t i o n w i t h the model u s i n g l i n e a r programming. E f f e c t i v e p r i c e s of i n - k i n d b e n e f i t s are found to vary s i g n i f i c a n t l y w i t h the amount of gross c o r p o r a t e income, the f r a c t i o n d i s t r i b u t e d , and the type o f c o r p o r a t i o n . The tax expenditure from the sm a l l business d e d u c t i o n i s found to be s u b s t a n t i a l l y over-estimated by c o n v e n t i o n a l methods which ignore changes i n f i n a n c i a l p o l i c y . The tax s a v i n g from r e g i s -t e r e d r e t i r e m e n t savings p l a n c o n t r i b u t i o n s i s found to be small f o r many owners of s m a l l e r c o r p o r a t i o n s and i t i s shown t h a t a combination o f c o n t r i b u t i o n s t o r e g i s t e r e d r e t i r e m e n t savings plans and d e f e r r e d p r o f i t s h a r i n g plans o f t e n o f f e r s h i g h e r tax > sa v i n g s . The income of s m a l l e r c o r p o r a t i o n s i s found to be s u p e r - i n t e g r a t e d , r e s u l t i n g i n l a r g e annual tax savings from i n c o r p o r a t i o n . The e x i s t e n c e o f a tax b e n e f i t from i n c o r p o r a t i o n r e i n f o r c e s o t h e r b i a s e s i n the tax system f a v o u r i n g self-employ-2 ment over s a l a r i e d work. I t a l s o suggests a d i f f e r e n t view of -15.6 the i n c i d e n c e of the c o r p o r a t e income tax, along the l i n e s suggested by F e l d s t e i n and Slemrod (1980). The key assumptions of the t h e o r e t i c a l model are examined i n Chapter 4. I t i s shown t h a t the model can be g e n e r a l i z e d to a l l o w m u l t i p l e owners by assuming t h a t an o p t i m a l f i n a n c i a l p o l i c y i s P a r e t o - e f f i c i e n t f o r the s h a r e h o l d e r s , although there i s some d i f f i c u l t y i n determining the c o n s t r a i n t s . The model can a l s o be made dynamic i n order to e x p l a i n the time path of the cumulative deduction account balance, r e a l i n v e s t -ment, borrowing: and l e n d i n g , the use o f r e t i r e m e n t income p l a n s , and the amount of owner's s a l a r i e s accrued i n one year but p a i d i n another year. The c h i e f problem i s s p e c i f y i n g how the value of a f i r m ' s shares v a r i e s w i t h i t s tax and f i n a n c i a l charac-t e r i s t i c s . In Chapter 5, a multi-owner v e r s i o n o f the model presen-te d i n Chapter 2 i s used to c a l c u l a t e the tax savings from i n c o r p o r a t i o n f o r each of 3,000 farms sampled i n 1978. Tax savings from i n c o r p o r a t i o n i s one of the v a r i a b l e s used i n a p r o b i t a n a l y s i s of the c h o i c e between c o r p o r a t e and non-corporate o r g a n i z a t i o n a l forms. The main r e s u l t i s t h a t , as expected, the h i g h e r . t h e farmer's e d u c a t i o n and the g r e a t e r the p o t e n t i a l tax savings from i n c o r p o r a t i o n , the h i g h e r i s the p r o b a b i l i t y t h a t a farm w i l l be i n c o r p o r a t e d . However, the p r o b a b i l i t y of i n c o r p o r a t i o n i s s u r p r i s i n g l y unresponsive to the p o t e n t i a l .157 tax s a v i n g s . As a r e s u l t , i t i s p r e d i c t e d t h a t two subsequent tax changes which s i g n i f i c a n t l y change the tax savings from i n c o r p o r a t i o n w i l l not have a s i g n i f i c a n t e f f e c t on the per-centage of farms t h a t are i n c o r p o r a t e d . T h i s f i n d i n g lends some e m p i r i c a l support to the assumption i n the l i t e r a t u r e on c o r p o r a t e tax i n c i d e n c e t h a t f i r m s do not switch between the c o r p o r a t e and non-corporate s e c t o r s i n response to changes i n 3 r e l a t i v e tax burdens. However, c l o s e l y - h e l d c o r p o r a t i o n s can achieve much the same e f f e c t as s w i t c h i n g s e c t o r s by a l t e r i n g t h e i r f i n a n c i a l p o l i c i e s . S w itching owners 1 remuneration from d i v i d e n d s to s a l a r y e l i m i n a t e s any e x t r a burden imposed by a c o r p o r a t e income tax on d i s t r i b u t e d e a r n i n g s . Since the November 12, 19 81 f e d e r a l budget made a l a r g e number of s i g n i f i c a n t tax changes, i t i s u s e f u l to i n d i c a t e how the r e s u l t s of t h i s work are a f f e c t e d . Many of the changes are j u s t changes i n tax parameters and thus have no e f f e c t on the t h e o r e t i c a l model. Some of these a r e : the r e d u c t i o n i n the d i v i d e n d tax c r e d i t from 37.5% of t a x a b l e d i v i d e n d s to 34%; the r e d u c t i o n i n the top marginal tax r a t e f o r i n d i v i d u a l s ; exempting income taxed at the s m a l l business r a t e from the surtax; r a i s i n g the f r a c t i o n of c o r p o r a t e expenditure on t a x a b l e b e n e f i t goods which i s a t a x a b l e b e n e f i t to employees; and r a i s i n g the l i m i t s t o the s m a l l business d e d u c t i o n . O n t a r i o ' s two-year suspension of the p r o v i n c i a l c o r p o r a t e income tax on income s u b j e c t to the s m a l l b u s i n e s s r a t e a l s o f a l l s i n t o t h i s .15.8 category. Some other tax changes do r e q u i r e m o d i f i c a t i o n s to the t h e o r e t i c a l model. These are: the 12.5% d i s t r i b u t i o n s tax on taxable d i v i d e n d s p a i d out of income taxed a t the s m a l l b u s i n e s s r a t e , e f f e c t i v e January 1, 1983; the dropping of the c e i l i n g of the f e d e r a l tax r e d u c t i o n from $500 to $200; and the end to r e d u c t i o n of the cumulative deduction account balance by payment of t a x a b l e d i v i d e n d s . A l s o , the new r u l e s on r e s t r i c t e d i n t e r e s t expense c r e a t e a new reason to pay out t a x a b l e d i v i d e n d s , s i n c e d e d u c t i b i l i t y of i n t e r e s t i s to be l i m i t e d to investment income and t a x a b l e d i v i d e n d s i n c r e a s e 4 investment income. The s o l u t i o n a l g o r i t h m s i n Chapter 2 and the s i m u l a t i o n i n Chapter 3 are more a f f e c t e d than the theore-t i c a l model because of the key r o l e t h a t the values of tax parameters p l a y i n t h i s work. A l s o , the DPSP s i m u l a t i o n i s no longer r e l e v a n t s i n c e a company can no longer c l a i m a deduc-t i o n f o r c o n t r i b u t i o n s to a DPSP f o r a s i g n i f i c a n t shareholder or f a m i l y member. 6.2 POLICY IMPLICATIONS One p o l i c y i m p l i c a t i o n of the model presented i n Chapter 2 r e l a t e s t o loans from s h a r e h o l d e r s and the cumulative deduction account. The o b j e c t i v e of i n t r o d u c i n g the cumulative deduction account i n 19 72 appears to have been to p l a c e a l i m i t on the amount of r e t a i n e d earnings which c o r p o r a t i o n s e l i g i b l e f o r the s m a l l b u s i n e s s deduction can have. The problem r e v e a l e d by the model i n Chapter 2 i s t h a t the l i m i t can be evaded by 159 paper t r a n s a c t i o n s i n v o l v i n g i n c r e a s e s i n loans from share-h o l d e r s . Amounts can be p a i d out as t a x a b l e d i v i d e n d s and owner's s a l a r y and then can be immediately loaned back to the company, thus r e d u c i n g the cumulative deduction account w i t h -out changing the amount of earnings t h a t i s " r e t a i n e d " i n the economic sense. Such d i s t r i b u t i o n s normally do i n v o l v e a tax c o s t , so there i s some l i m i t to. the e x t e n t to which t h i s can be done. The November 12, 19 81 budget made r e f e r e n c e to the loaning-back of d i v i d e n d s i n the e x p l a n a t i o n f o r the ending of the a b i l i t y t o reduce the cumulative d e d u c t i o n account through the payment o f d i v i d e n d s . However, the measure i s f a u l t y i n t h a t owner's s a l a r y can s t i l l be p a i d out and loaned back to the company. The budget's o t h e r argument f o r e l i m i n a -t i n g d i v i d e n d s from the computation of the cumulative deduction account i s to t a r g e t the s m a l l business i n c e n t i v e to growing s m a l l b u s i n e s s e s and businesses i n the s t a r t - u p phase. T h i s le a d s to the c o n c l u s i o n t h a t s a l a r y p a i d to p r i n c i p a l share-h o l d e r s a l s o should not reduce the cumulative deduction account, s i n c e both s a l a r y and d i v i d e n d s are methods of withdrawing funds from the company f o r p e r s o n a l use. A r e l a t e d f i n d i n g based on the s p e c i f i c a t i o n of the model i n Chapter 2 i s t h a t the tax system f o r c l o s e l y - h e l d c o r p o r a t i o n s i s not b i a s e d i n favour of debt r a t h e r than e q u i t y f i n a n c e . The t r a d i t i o n a l view i n the l i t e r a t u r e i s t h a t the c o r p o r a t e income tax encourages f i r m s to be f i n a n c e d by debt r a t h e r than e q u i t y because i n t e r e s t payments are a d e d u c t i b l e expense and d i v i d e n d s are n o t . 5 T h i s does not apply to c l o s e l y - h e l d c o r p o r a t i o n s because the owners normally i n v e s t the v a s t bulk of t h e i r funds through s h a r e h o l d e r s ' loans r a t h e r than purchase of shares. The owners can choose between r e c e i v i n g i n t e r e s t payments and d i v i d e n d s as a r e t u r n on t h e i r " e q u i t y " investment. A l s o , even i f the investment i s by purchase of shares, owners' remuneration can take the form of s a l a r y and d i r e c t o r s ' fees i n order to be a d e d u c t i b l e expense to the c o r p o r a t i o n . Perhaps the most important p o l i c y i m p l i c a t i o n of t h i s study i s t h a t i t may be unwise to s u b j e c t r e l a t i v e l y unsophis-t i c a t e d taxpayers to a complicated system of tax r u l e s which p r o v i d e s s u b s t a n t i a l r e t u r n s to tax p l a n n i n g . I f the taxpayers a f f e c t e d were a few dozen l a r g e m u l t i n a t i o n a l c o r p o r a t i o n s r a t h e r than thousands of s m a l l b u s i n e s s e s , there might not be any problems. For example, the r u l e s governing i n t e r n a t i o n a l t r a n s a c t i o n s are not known to cause s i g n i f i c a n t economic d i s t o r t i o n s or high p u b l i c or p r i v a t e c o s t s , even though these r u l e s are also- complex and p r o v i d e scope f o r tax p l a n n i n g . For c l o s e l y - h e l d f i r m s , which are t y p i c a l l y s m a l l i n s i z e and o f t e n do not purchase p r o f e s s i o n a l tax p l a n n i n g a d v i c e , the p r e s e n t system produces a waste of resources and h o r i z o n t a l i n e q u i t y . 161 The waste of resources i s p a r t l y the r e s u l t of d i s t o r t i o n o f p r o d u c t i o n and consumption c h o i c e s , but i t i s a l s o due t o the expenditure of r e s o u r c e s on tax p l a n n i n g . Since such expenditures are a d e d u c t i b l e b u s i n e s s expense, i t i s worth-w h i l e t o spend up to $ l / ( l - u ) t o save $1 i n taxes, where u i s the c o r p o r a t e tax r a t e . For example, wi t h a 50% c o r p o r a t e tax r a t e , i t i s worth spending up to $2 to save $1 i n taxes. The d e d u c t i b i l i t y of the $2 expenditure on tax p l a n n i n g r e t u r n s the other $1. Some taxpayers may even spend more than i s j u s t i f i e d by t h i s c r i t e r i o n . One tax a d v i s o r has commented on the tax regime f o r s m a l l businesses t h a t "...the r u l e s are c o m p l e x — s o much so, t h a t some even q u e s t i o n whether the b e n e f i t i s a l l t h a t i m p r e s s i v e , given the time and e f f o r t r e q u i r e d of the owner and the c o s t of p r o f e s s i o n a l a d v i c e . " 6 The o t h e r u n f o r t u n a t e r e s u l t of the p r e s e n t tax system f o r c l o s e l y - h e l d f i r m s i s h o r i z o n t a l i n e q u i t y . Business owners i n the same economic s i t u a t i o n w i l l be paying d i f f e r e n t amounts of tax j u s t because one i s i n c o r p o r a t e d and the other i s not, or because one i s u s i n g a d i f f e r e n t s a l a r y - d i v i d e n d mix than the o t h e r . The i n e q u i t y i s probably s y s t e m a t i c a l l y r e l a t e d t o the p r o x i m i t y t o major c e n t r e s , e d u c a t i o n and o c c u p a t i o n of the owner. Business owners who are d i s t a n t from major ce n t r e s are l e s s l i k e l y to get t o p - q u a l i t y a d v i c e , i n p a r t because t h e i r a d v i s o r s w i l l not have access to the resources of the n a t i o n a l 16-2 a c c o u n t i n g f i r m s . 7 The more h i g h l y educated business owners are more l i k e l y to seek out and f o l l o w tax p l a n n i n g a d v i c e . T h i s i s the f i n d i n g o f Chapter 5 w i t h r e s p e c t t o the p r o b a b i -l i t y o f i n c o r p o r a t i o n among farmers. There i s a l s o some evidence o f an o c c u p a t i o n a l d i f f e r e n c e i n a t t i t u d e s toward tax p l a n n i n g , although t h i s may simply be a product of d i f f e r e n c e s i n e d u c a t i o n a l and income l e v e l s . Doctors and d e n t i s t s have a r e p u t a t i o n among a t l e a s t some tax p r a c t i t i o n e r s f o r being e s p e c i a l l y keen on m i n i m i z i n g taxes, and do not seem to mind very much the i n c r e a s e d complexity i n business o p e r a t i o n s which r e s u l t s from u s i n g management or p e r s o n a l s e r v i c e c o r p o r a t i o n s f o r tax p l a n n i n g . I t has a l s o been s a i d t h a t farmers are unusual i n r e f u s i n g t o use a l l l e g a l means to a v o i d taxes, the m o t i v a t i o n b e i n g t h a t t h e r e i s something "not q u i t e n i c e " i n doi n g so. T h i s r e l u c t a n c e i s evidenced by the s m a l l number o f farmers who h i r e q u a l i f i e d accountants f o r tax p l a n n i n g o r s p l i t g income through s a l a r i e s p a i d t o spouses and c h i l d r e n . P a r t of the cause of these problems i s the hig h frequency of changes i n the tax r u l e s . As S c h u l t z (1975) has argued, economic a c t o r s are l i k e l y t o be c l o s e r t o an economic optimum i f the r u l e s governing t h e i r a c t i o n s have been r e l a t i v e l y cons-t a n t f o r some time. In the d i s e q u i l i b r i u m c r e a t e d by frequent tax changes, h o r i z o n t a l i n e q u i t i e s i n tax burdens are l i k e l y t o be more common. T h i s o b s e r v a t i o n i s e s p e c i a l l y t r u e o f sm a l l b u s i n e s s e s because o f the many and v a r i e d demands on t h e i r owners' time. 163 The r o o t o f the problems of resource waste and h o r i z o n t a l i n e q u i t y l i e i n the l a r g e v a r i a t i o n i n tax burdens which i s p o s s i b l e g i v e n d i f f e r e n t o r g a n i z a t i o n a l forms and f i n a n c i a l p o l i c i e s , so perhaps the b e s t s o l u t i o n may be to change the tax r u l e s t o minimize the p o s s i b l e v a r i a t i o n s . Recent moves i n t h i s d i r e c t i o n i n c l u d e : the e x t e n s i o n t o u n i n c o r p o r a t e d businesses of d e d u c t i b i l i t y of spousal s a l a r i e s and e l i g i b i l i t y f o r Small Business Bonds; the r e d u c t i o n of the maximum RRSP c o n t r i b u t i o n f o r i n d i v i d u a l s who are members of DPSPs to $3,500; and the 1981 budget p r o p o s a l o f a 12.5% d i s t r i b u t i o n s tax on ta x a b l e d i v i d e n d s p a i d out of income taxed a t the s m a l l business r a t e . The d i s t r i b u t i o n s tax p r o p o s a l i s p a r t i c u l a r l y s i g n i f i c a n t because i t removes much o f the d i f f e r e n t i a l i n tax burdens between d i v i d e n d and s a l a r y payments as w e l l as r e d u c i n g the tax b e n e f i t s from i n c o r p o r a t i o n . The O n t a r i o Small Business Development C o r p o r a t i o n program i s a change i n the opp o s i t e d i r e c t i o n because SBDCs can i n v e s t o n l y i n i n c o r p o r a t e d s m a l l b u s i n e s s e s . One tax change which would f u r t h e r reduce the d i f f e r e n c e i n tax burdens between i n c o r p o r a t e d and un i n c o r p o r a t e d b u s i -nesses i s to f i n d a means of a p p l y i n g l o s s e s i n c l o s e l y - h e l d c o r p o r a t i o n s a g a i n s t p e r s o n a l income, perhaps l i k e the Sub-chapter S e l e c t i o n i n the U.S. At pr e s e n t , l o s s e s i n a c o r -p o r a t i o n cannot be used t o reduce the p e r s o n a l income o f share-h o l d e r s . A l o s s i s allowed o n l y on the d i s p o s i t i o n of the shares or debt a t a l o s s , although a t t h a t time the r u l e s f o r l o s s a p p l i c a t i o n are q u i t e generous. T h i s makes the d e c i s i o n whether to i n c o r p o r a t e a s m a l l business very d i f f i c u l t i f there i s much chance o f f u t u r e l o s s e s . Another tax change which would help i n t h i s s i t u a t i o n i s a t a x - f r e e r o l l o v e r f o r d i s i n c o r p o r a -t i n g . At p r e s e n t there i s a r o l l o v e r f o r i n c o r p o r a t i o n but subsequently dropping c o r p o r a t e s t a t u s can t r i g g e r t a x a b l e c a p i t a l g ains and ot h e r income i n the c o r p o r a t i o n and a deemed d i v i d e n d on the d i s t r i b u t i o n o f a s s e t s to s h a r e h o l d e r s . On the o t h e r hand, these changes would have the e f f e c t o f i n c r e a s i n g the tax advantages to i n c o r p o r a t i o n , which perhaps are a l r e a d y too g r e a t . The two tax changes suggested above have major p o l i c y i m p l i c a t i o n s and may be t e c h n i c a l l y d i f f i c u l t . However, brie simple measure which would help t o e q u a l i z e the tax burdens between i n c o r p o r a t e d and u n i n c o r p o r a t e d businesses would be t o t i g h t e n the r u l e s on accrued but unpaid amounts due to share-h o l d e r s . The p r e s e n t time l a g s o f two to three years between the time of a c c r u a l and the payment of the p e r s o n a l w i t h h o l d i n g tax, as d i s c u s s e d a t the end o f Chapter 4 , are f a r too l o n g . The U.S. r e q u i r e s t h a t amounts due to shareholders a t the end o f a f i s c a l year must be p a i d w i t h i n two and a h a l f months o r the deduction to the c o r p o r a t i o n i s disallowed."'" 0 165 The c o n c l u s i o n of t h i s study of the tax regime f o r Canadian c l o s e l y - h e l d c o r p o r a t i o n s i s t h a t k n o t t y problems remain. Small b u s i n e s s e s j u s t i f i a b l y f a u l t the system f o r i t s complexity and p i t f a l l s , w h i l e the government cannot be p l e a s e d w i t h the p o s s i b i l i t i e s f o r tax m i n i m i z a t i o n . Unfor-t u n a t e l y , the way ahead i s u n c l e a r . C l o s e l y - h e l d c o r p o r a t i o n s have been taxed i n many d i f f e r e n t ways i n v a r i o u s c o u n t r i e s and time p e r i o d s and a consensus as to the b e s t system has not y e t been reached. N O T E S 1. See Long and S c o t t (1982) f o r e m p i r i c a l evidence t h a t employees choose f r i n g e b e n e f i t s on t h i s b a s i s . A l s o , C l o t f e l t e r (1979) d e r i v e s a s i m i l a r t h e o r e t i c a l r e s u l t f o r owners of u n i n c o r p o r a t e d b u s i n e s s e s . 2. See Long (19 82). 3. T h i s assumption i s made e x p l i c i t l y by Shoven and Whalley (1972) . 4. Drache (19 82). 5. 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(19 52), E f f e c t s of Taxation: Corporate Fi n a n c i a l Policy, Boston: Harvard University Graduate School of Business Administration. Sommerfeld, R. (1978), Federal Taxes and Management.Decisions (revised e d i t i o n ) , Homewood, 111.: Irwin-Dorsey. S t i g l i t z , J . (1973), Taxation, 'Corporate F i n a n c i a l Policy, and the Cost of Cap i t a l , Journal of Public Economics, 2:1-34. Taube, S. (1978), Estate and Tax Planning, Toronto: Carswell. Welch, F. (1978)., The Role of Investments i n Human Capital i n Agriculture, i n T. Schultz (ed.) Distortions of A g r i c u l t u r a l Incentives, Bloomington, Indiana: Indiana University Press. Williamson, O.E. (1964), The Economics of Discretionary Behavior, Englewood C l i f f s , N.J.: Prentice-Hall. Winslade, R. (1978), The Role of the Government and Farm Organi-zations, i n Law Society of Upper Canada, Advising the Farmer, Toronto: Dept. of Continuing Education, Law Society of Upper Canada. Zimmer, Henry (1980), Income Tax Problems with Detailed Solutions, Sudbury, Ontario: Clarence Byrd. APPENDIX SOLUTION OF THE NON-LINEAR PROGRAMMING PROBLEM IN CHAPTER 2 Providing I>0, th i s variable can be eliminated from the the problem using the personal budget constraint. The Lagrangian becomes: (S, Dr, D1^, DK, L, Xf, XP, Zf, ZP, Y P to Y P 3, B± to B 4 , Y^ , Y^ , X^, *•* 1^9^ = U ( i j - ( S + Dr + D*^ + D K + L - 4 B ± (1+p) + B 1 P P P 1 = 1 + 0.09B - p X X P - p Z Z P ), X f + XP, Z f + ZP) f + X 1 {S + D^+D™ + DK + L + p X X f + p Z f Z f +" u ¥ + uV" - Dr/4 - M} + A 2 {Y33 - S - p ^ X f - p ^ Z f - Y*5 - } + A 3 D1^ (Dr - Dr) + X 4 (200 - B^ + \ (2,022 - B 2 ) + X g (3,334 - Bg) + X ? (2,022 - B2) B 3 + X 4 1 3 P 8 { E B , - E t.YT , 3 , r . ^nr> } i=l 1 i=l 1 1 IT ( D + D + 1 2 X • ( Y P - Y P ) E A 9 i v i i ; i=l + A10 { E 3 - S - 4 (Dr + D3^) - r p ^ X^ + A } i=l 1 Z 17 3 174 + A n {S + r p ^ / - S^} + X 1 2 ( x f -+ A 1 3 (Z f - Zf) + A 1 4 (Y3 - V s ) + A 1 5 {n - 7 s - Y1, + 'icF} + A l g (5r - Dr) + A 1 7 ( D K - DK) + A l g (L - L) + A 1 9 ( L - L 1 1 ^ ) The Kuhn-Tucker conditions for th i s problem are the following conditions, where a £ 0 <_ b i s used to denote a <_ 0, b > 0, and a • b = 0: U I I + X l " X2 " A10 + A l l 1 ° 1 S P ^ + A x + A 3 (Dr - Dr) + | A 8 - | A 1 Q + * A 1 5 < 0 < Ux. K ~T + X l ~ X17 - ° - ° P U I P = + A, - A , 0 + A . n = 0 (since L may be negative) £=- U + U < 0 < "X* X X j\ —- . 175 f •£ f f U x + A-L.p^ - A 2p - A ^ r p ^ + A i : L r p X - \ 2 < 0 < Xf Z P - p U T + U„ < 0 < Z P ~~T~ Z ~ P U z + A ^ - - A 1 3 < 0 < Z f - t . A g - A g i + A 1 Q < 0 < Y p i = 1,2,...12 ~ H XB + X10 < 0 1 Y i 1 = 1 3 U.. " - T P " X4 + X8 < 0 1 B l P' ~ U I — (1 + p) - A 5 - A ? B 3 + Ag < 0 < B 2 P ~ U I — (1 + p - 0.09) - A g + A 7 (2,022 - B 2) + A g < 0 <_ B 3 P ^ - (1 + p) + Ag < 0 < B 4 u S A x - A 2 - A ^ - A 1 5 < 0 < Y 5 u L A 1 - A 2 - A 1 5 < 0 < Y 1 The r e s t o f t h e K u h n - T u c k e r c o n d i t i o n s a r e : t h e c o n s t r a i n t s (3) t o ( 2 1 ) ; n o n - n e g a t i v i t y c o n s t r a i n t s on L a g r a n g e m u l t i p l i e r s c o r r e s p o n d i n g t o i n e q u a l i t y c o n s t r a i n t s ; and a c o n d i t i o n f o r e a c h i n e q u a l i t y c o n s t r a i n t t h a t , i f t h e c o n s t r a i n t i s n o t b i n d i n g , t h e a s s o c i a t e d L a g r a n g e m u l t i p l i e r e q u a l s z e r o . 176 These c o n d i t i o n s are e q u i v a l e n t t o the c o n d i t i o n s below, where the d e f i n i t i o n s of u , u + , c , c + , d , d + , b , b + , t and t + are g i v e n i n Chapter 2. The main changes are t h a t the c o n d i -t i o n s f o r p o s i t i v e versus zero v a l u e s of the v a r i a b l e s have been separated, and a l l Lagrange m u l t i p l i e r s which appear i n the c o n d i t i o n f o r only one v a r i a b l e have been e l i m i n a t e d . ^ + x _ x2 _ h Q + h i < o (Al) P uT -y + \ - X2 - X 1 0 + X1± :_> 0 unless S = 0 (A2) V + d ~ & + | *8 " ! X10 " C " X15> 1 0 ( A 3 ) P h + d + l ^ + | l g - | A 1 Q - c + X } :* 0 (A4) P unless D r + lPr = 0 (combining the D r and conditions) A, <_ - ^1 unless D K + L = D K + L (A5) I P *1 > " ^ unless D K + L = L™" n (A6) P (ocmbining the D and L conditions) 177 Hx (A7) U T — I I P u x p = 2 _ unless X P = 0 (A8) I P U„ + X f {X, - X - - X.rtr + X,,r} < 0 unless / = ^ (A9) X p 1 2 10 11 — U x + { X x - X 2 - X 1 Q r + ^ r } >_ 0 unless ^ = 0 (A10) U 7 Z p - ? - < £ — (All) u • - I I p _?_ = £ _ unless Z p = 0 (A12) I P Z f f - f U z + p { X x - X 2 } < 0 unless Z 1 = z"" (A13) T T ^ Z f ( X , - X 0 } > 0 unless Z f = 0 (A14) U z + p 1 2 -X 1 Q < t " X 8 (A15) t + X 8 < X 1 Q (A16) (combining the Y? conditions) 178 -X8 - b % .. (A17) I P b + - i :< .-Xg (A18) P (ccnfoining the conditions) i f A 1 - X 1 5 < X 2 (A19) X„ < u + X , - X i r - unless Y 3 + Y 1 = 0 (A20) 2 — 1 lb (canbining the Y 3 and conditions) X l l ' X15 - 0 ( A 2 1 ) The c o n d i t i o n s d e s c r i b e d i n Chapter 2 may be obtained from (Al) to (A21) p l u s the c o n s t r a i n t s (3) to (21). The e a s i e s t t o o b t a i n are c o n d i t i o n s (23), which r e l a t e t o the c h o i c e of X P and Z P. They are j u s t a minor rearrangement of (A7), (A8), ( A l l ) and (A12). For the other c o n d i t i o n s , the approach used i s to combine t h e . i n e q u a l i t y r e l a t i n g to the v a r i a b l e being i n c r e a s e d w i t h the i n e q u a l i t y f o r the v a r i a b l e being decreased, together w i t h other i n e q u a l i t i e s needed to e l i m i n a t e the Lagrange m u l t i p l i e r s . To b e g i n , c o n d i t i o n (27a) r e l a t e s to an i n c r e a s e i n t a x a b l e b e n e f i t s and a decrease i n repayment of s h a r e h o l d e r ' s l o a n s . I n e q u a l i t y (A9) r e l a t e s to an i n c r e a s e i n t a x a b l e b e n e f i t s , s i n c e the 179 i n e q u a l i t y does not h o l d i f X f = X^, i n which case t a x a b l e b e n e f i t s cannot be i n c r e a s e d . S i m i l a r l y , i n e q u a l i t y (A6) r e l a t e s to a decrease i n repayment of shareholder's l o a n s , s i n c e i t does not h o l d i f such a change i s not p o s s i b l e . From (A9) and (A20) , X f + °X + P { A 1 ( 1 ~ u > " A 1 0 r } - 0 u n l e s s X f = X f o r Y S + Y L = 0 Combining t h i s w i t h (A6) to e l i m i n a t e \^ y i e l d s : X f + U T U x + p A {(-1 + u +) -± - A 1 Q r } < 0 u n l e s s D K + L = L m i n => U x + p {(-1 + u ) _ r t - X q } < o by (A15) =^> ^X < p X {1 - u + + r t " b~} by (A17) and because U > 0 u i P 1 T h e r e f o r e , the r e s u l t i s : U X^ ^ 1 L {1 + T X L } u n l e s s X f = X f or Y S + Y L = 0 I P rr or L + D = L , XL _ _l_ where T = r t b - u 180 Condition (27b) may be derived s i m i l a r l y using (A10) and (A19): UX + P { A 1 ( 1 " u ) + X i 5 _ \or + Xnr} 1 0 unless X f = 0 X f = > U x + p A { A 1 ( l - u ) - A 1 ( )r} > 0 unless Y S + Y L - |DNR = n or S + r p x f X f = S m i n ==> U x + {(-1+ u") ^1 - A 1 Qr} > 0 by (A5) P 1 unless DK + L = DK + L ^ U x +• p ^ {(-1 + u") h - r t + Ag} > 0 by (A16) P Uj - 2 j - {1 - u + r t b } by (A18) and because V > 0 P u x^ * ' ' ^ > 2 = - U - T^} unless L + DK = L + DK or X f = 0 I P S + r p x f X f = Y 5 + Y 1 - | D111 = n, where = u - r t b Relations (A4) and (A5) may be combined to produce condition (22c) d+ { l A8 " I A10 " C + A l 5 } + ( d + " 1 ] ^ - 0 P 1 unless DR + DF = 0 or DK + L = DK + L 181 =» d + { | X 8 " ! X10} + ( d + " 1 } -± ± 0 P unless {V s + - ^ EF" = nandN L D = - c + d + > 0 } ==i -d + (|t+ - |) Ag + (d + - 1)^1 > 0 by (A16) and because d + > 0 P 1 T> _d+ (|t+ _ | ) bLD + D + _ -L , 0 L b" i f -d + (|t+ - |) > 0, where b = { b otherwise since UJ > 0 and (A17) and (A18) imply that P T 1 , 0 > 0 unless L + DK = DK + L or DR + D™7 = 0 or (iP > 0 and V s + Y1, - |DF = n), where = -d + (|t+ - + d + - 1 S i m i l a r l y , r e l a t i o n s (A3) and (A6) i n combination produce (22d): => -d" {| Ag - | \ } - (d~ - 1) > 0 unless DK + L = L 1 ^ P 1 => d~ ; (|t~ - | ) Ag - (d~ - 1)^1 > 0 by (A15) and because d" > 0 P 1 => d~ (|t~ - | ) b D L - (d" - 1) > 0 182 where b D L = b i f d (|t~ - f) > 0, { + 2 8 " b otherwise s i n c e TJ^ > 0 and (A17) and (A18) imply t h a t ~ r a " <K - f > » D L > a " <K - !> \ P J*. T D L > 0 un l e s s L + D K = L m i n , where T D L =. d" (§t~ - | ) b D L - (d~ - 1) The d e r i v a t i o n of c o n d i t i o n (26a) begins w i t h the e l i m i n a t i o n of A 2 from (A9) through the use of (A20): X f + U X + p { A 1 ( 1 " u > + X15 " A 1 0 r } - 0 u n l e s s X f = x f or Y S + Y L = 0 U x + p X {-(r - |(1 - u +) d +) X 1 Q - d + (1 - u +) ft + | X8) P 1 - \ (-1 - (1 - u +) c + d +)} < 0 by (A4) u n l e s s D r + D n r = 0 =3> U x - p x f {(r - | (1 - u +) d +) X 1 Q + d + (1 - u +) ft + | Xg) } < 0 P 1 u n l e s s {Y3 + Y^ - ^ P30 =• n and = -1 - (1 - u +) c + d + > 0} 183 "x-Alrt™- -|) d - u + ) d + ) X 8 ==> A - L V J - i - \2 8 + d + (1 - u +)^l} < 0 I P where t X D E t i f r - | (1 - u + ) d + > 0, t + otherwise s i n c e (A15) and (A16) imply t h a t (r - | (1 - u + ) d + ) t X D X 8 > ( r - | (1 - u + ) d + ) X 1 Q < | / {1 + r t X D b X D - ( | t X D - |) (1 - u + ) b X D d + U I P 1 + ( d + - 1) (1 - u +) - u +} where b E b i f r t - (-^ t - g-) (1 - u )d >_ 0, { b otherwise s i n c e > 0 and (A17) and (A18) imply t h a t ( r t X D _ (3tXD _ 3, ( 1 _ u + ) d + ) U, bXD > P 1 - .XD /3.XD 3v ,, \ ( r t - (^t - Q) ( l - u ) d ) A g < p x f {1 + T*0} unl e s s X f = X f o r Y S + Y L = 0 U I P 1 or D r + D1^ = 0 o r { N X D > 0 a n d Y S + Y 1 - 3 b n r = n}, , _XD _• ^XD^XD /3.XD 3, ,-, +.,XD^+ where T = r t b (-^ t ~ ~Q> (1 - u )b d + ( d + - 1) (1 - u +) - u + S i m i l a r l y , (26b) may be d e r i v e d by u s i n g (A19) t o e l i m i n a t e from ( A 1 0 ) : x f U X + p { X 1 ( 1 " u } + A15 " X 1 0 r + X l l r } - 0 u n l e s s X f = 0 = > ( U x + p ^ {(f (1 - u~)d - r) A 1 Q - d" (1 - u ) ft + | A8) P 1 + A r + Alf. (1 + (1 - u") c~ d~) } _> 0 by (A3) =J U x + p X {(|(1 - u~)d~ - r) A 1 Q - d" (1 - u~) ^1 + | Ag) } > 0 P 1 unless (Vs + - ^P* = n and N ° X E 1 + (1 - u~) c~ d" > 0) or S + r p x f X f = S m i n => U x + p x f {(§t D X -§•) (1 - u")d" - r t D X ) Ag - d" (1 - u ~ f t } > 0 P 1 where t A = t i f f (1 - u")d" - r > 0, ^ t + otherwise s i n c e (A15) and (A16) imply t h a t ( f (1 - u~)d" - r ) t D X Ag > (| ( i - U - ) D - _ R ) A I Q 185 * ^ > E_L" t l + r t D X b D X - (|t D X - §) (1 - u")b D Xd-U I P 1 + (d - 1) (1 - u ) - u"} where b D X •= b" i f ( | t D X - §) (1 - u _ ) d _ - r t D X > 0, b + otherwise s i n c e > 0 and (A17) and (A18) imply t h a t ( ( | t D X - f) (1 - u")d" - r t D X ) ^ I b D X > P 1 ( ( | t D X - |) (1 - u")d" - r t D X ) A 8 f f •'• ^£ > PlL t l - T D X } u n l e s s X f = 0 or S + r p X xf= S m i n U I P 1 or ( N D X > 0 and Y S + Y L - | D n r = n ) , , mDX _ J^DX 3,,DX t l , DX, DX where T = (-^ t " " g ) 1 3 ( l - u ) d - r t b - (d~ - 1) (1 - u~) + u" Corresponding t o c o n d i t i o n s (26) and (27) f o r t a x a b l e b e n e f i t s are an e q u i v a l e n t s e t of c o n d i t i o n s f o r non-taxable b e n e f i t s . A comparison o f (A9) and (A10) w i t h (A13) and (A14) shows t h a t the p r o o f s of the l a t t e r s e t of c o n d i t i o n s may be f f obt a i n e d simply by s e t t i n g r = 0 and r e p l a c i n g X w i t h Z and X w i t h Z. The onl y d i f f e r e n c e i s t h a t A ^ does not appear i n (A13) and (A14) and so i n the p r o o f o f the e q u i v a l e n t c o n d i t i o n s 186 to (26b) and (27b) the q u a l i f i c a t i o n that S + r p X X f j£ S m i n i s omitted. Also corresponding to conditions (26) and (27) are an equivalent set of conditions for salary — (22a), (22b), (22e) and (22f). The close relationship i s due to conditions (Al) and (A2) being a spe c i a l case of (A4) and (A10) i n which y f j _.c r = l / U x = U I , p = p , and x = 0 0. The proofs for the salary conditions are therefore p a r a l l e l to the proofs of (26) and (27) . The only conditions l e f t to be derived are those r e l a t i n g to the choice among salary, taxable benefits and non-taxable benefits. Condition (25a) may be derived by combining (A2) and (A9): °X + {~^- + X10 ( 1 " r ) ~ X l l ( 1 " r ) } - 0 P 1 unless S = 0 or X f =- X f => U x + p x f {-^ 1 + X 1 Q (1 - r)} < 0 P 1 , _ , X ^ v f „min unless S + rp X1- = S => ^X < p ^ {1 - t + b + (1 - r) } U r I I p since > 0 and (A16) and (A18) imply that : 187 p < p^_ {1 + T X S} unless S = 0 or X f = X f or S + rp X = S , where T X S = - t + b + (1 - r) S i m i l a r l y , (Al) and (A10) may be combined to produce condition (25b): U x + p x f {-^l + X 1 Q (1 - r) - X u (1 - r)} > 0 P 1 unless = 0 UX X f _ > :u~ - L { 1 - t~.b" (1 - r)} P since * 0, .\J > 0, and (A15) and (A17) imply that A 1 Q < t " b " ^1 P •"• 1 Pf_. t l - T S X} unless X f = 0. U T I where T S X = t~ b~ (1 - r) The analogous conditions to (25) for non-taxable benefits rather than taxable benefits may be derived using (A13) and (A14) instead of (A9) and (AlO). The results are i d e n t i c a l except that r = 0 and X^ and X are replaced by and Z. 188 The l a s t c o n d i t i o n s r e l a t e t o the choice between ta x a b l e and non-taxable b e n e f i t s . To d e r i v e c o n d i t i o n (24a), s u b s t i t u t e f o r X 1 - X 2 from (A14) i n t o (A9): U X + p X *~ U g ~ A i o r ^ - 0 u n l e s s x f = X f o r Z f = 0 => n + {- U Z - r t ~ b~ U I } < 0 X " T f ~T ~ Z p p F s i n c e (A15) and (A17) imply t h a t A10 1 t _ b ~ — = > "x. < p ^ {1 + r t b }-because U z > 0 and \JJ > 0 U z z f ^Z p ^ P u i z f < p^__ {1 + T X Z } u n l e s s X f = X f or Z f = 0, U Z Z f P where T XZ r t b U„ I Z p 189 C o n d i t i o n (24b) may be d e r i v e d s i m i l a r l y from (A10), (A13), (A16) and (A18). The above p r o o f s show t h a t the Kuhn-Tucker c o n d i t i o n s imply (22) to (27) and r e l a t e d c o n d i t i o n s , but i s the converse a l s o t r u e ? In o t h e r words, do t h e r e e x i s t any other i m p l i c a t i o n s of the Kuhn-Tucker c o n d i t i o n s t h a t are not themselves i m p l i e d by the c o n d i t i o n s s p e c i f i e d i n Chapter 2? The answer seems to be no. The p r o o f s above have u t i l i z e d every p a i r of r e l a t i o n s (Al) to (A14) which can be combined w i t h the e l i m i n a t i o n of one or more Lagrange m u l t i p l i e r s , and the remaining c o n d i t i o n s have been used to e l i m i n a t e the o t h e r Lagrange m u l t i p l i e r s . Combi-n a t i o n s of more than two of (Al) to (A14) appear to generate r e s u l t s which are i m p l i c a t i o n s of the c o n d i t i o n s s p e c i f i e d i n Chapter 2. Even i f other c o n d i t i o n s do e x i s t , the f a c t remains t h a t the c o n d i t i o n s s p e c i f i e d i n Chapter 2 are necessary c o n d i -t i o n s f o r an optimum, assuming t h a t the c o n s t r a i n t q u a l i f i c a t i o n i s s a t i s f i e d .
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Economics
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Taxation and the financial policy of Canadian closely-held corporations
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