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==Chapter:2 COST OF CAPITAL A company may raise long term finance from various sources such as : Long term debts, Equity share capital, preference share capital and retained earnings. Capital is a ascarce source, hence raising the funds from various sources. But the cost of capital depends upon the risk incidence born by the provider of finance. Specific Cost Of Capital The cost of each component of long term finance is termed as specific or component cost of capital. Cost is denoted as K. 1. C o s t o f D e b t ( K d ) 2. C o s t o f p r e f e r e n c e s h a r e s ( K p ) 3. C o s t o f e q u i t y ( K e ) 4. C o s t o f r e t a i n e d E a r n i n g s ( K r e ) C o s t o f D e b t, c o s t o f p r e f e r e n c e s h a r e s a n d c o s t o f e q u i t y a r e c a l l e d e x t e r n a l f i n a n c e o r e xp l i c i t c o s t. c o s t o f r e t a i n e d e a r n i n g s i s c a l l e d i n t e r n a l f i n a n c e o r i mp l i c i t c o s t. Explicit Cost This is the cost associated with raising of external finance. The external finance cash inflows are received by a firm on which it pays cash outflows. The Explicit cost is related to extra cash flows that result from the raising of such external finance. Implicit Cost It is the implied cost of the opportunity cost of investors shareholders that they are required to incur or lose on account of the company/firms retaining the earnings and not distributed it as dividends amongst the shareholders 1. Cost of Debt(Kd) A company may raise debt funds by taking loans or issuing debentures or bonds or accepting public deposits, etc. The providers of debt funds expect to receive/earn interest on the amount loaned by them. This interest is their income and cost for the company pays them. There is a need of computing an effective rate of debt cost to the company on annual basis. The computation of cost of debts depends upon the fact that the debt is the redeemable or irredeemable. The basic principle of computing effective post tax Kd (in case income tax is applicable) is the same. The annual cost to the company is the numerator and the funds to be utilized by the company over its lifetime in denominatior. A. Cost of Irredemable/perpetual debt = I(1- t)/NP Q. 1 ) C omp u t e K d f o r x l t d i f i t i s i s s u i n g 1 2% d e b e n t u r e s o f R s . 1 0 0 e a c h 1 0 0 0 0 0 i n n umb e r s . i g n o r e I n c ome T a x . S o l n : K d = I / P I = amo u n t o f a n n u a l i n t e r e s t P = p r i c e o f d e b t i n s t r ume n t 1 0 0 0 0 0 * 1 0 0 = 1 0 0 0 0 0 0 0 ( 1 2 0 0 0 0 0 / 1 0 0 0 0 0 0 0 ) * 1 0 0 = 1 2% Q . 2 ) P r e s um i n g i n Q. 1, t h e d e b e n t u r e s a r e i s s u e d a t a d i s c o u n t o f 1 0%. S o l n : 1 0 0 0 0 0 * 9 0 = 9 0 0 0 0 0 0 ( 1 2 0 0 0 0 0 / 9 0 0 0 0 0 0 ) = 1 3. 3 3% Q. 3 ) P r emu n e i n Q . 1, t h e d e b e n t u r e s a r e i s s u e d a t a d i s c o u n t o f 5% a n d f l o a t a i o n c o s t o f i s s u e i s 4% o f i s s u e p r i c e . S o l n : K d = I / P = 1 2 0 0 0 0 0 / ( 9 5 0 0 0 0 0 - 3 8 0 0 0 0 ) = 1 3 . 5% Floatation Cost It is the cost associated with the floating/making the issue of securities and includes expenses such as :- printing cost of prospectus and application forms, advertisement cost, brokerage, legal fees in regard to making the issue, underwriting commissing, etc. No t e s : I n c a s e p e r c e n t a g e o f f l o a t a t i o n c o s t i s g i v e n a n d d i t i s n o t me n t i o n e d a s t o t h i s p e r c e n t a g e i s t o b e a p p l i e d o n i s s u e p r i c e o r f a c e v a l u e , t h e n g i v e a n o t e t h a t t h e p e r c e n t a g e o f f l o a t a t i o n c o s t i s b e i n g a p p l i e d t o i s s u e p r i c e. Q. 4 ) Y l t d i s i s s u i n g d e b e n t u r e s o f c o u p o n r a t e ( r a t e o f i n t e r e s t ) 1 3 . 5% . Numb e r s o f d e b e n t u r e s b e i n g i s s u e d i s 2 0 0 0 0 0 . F a c e v a l u e o f d e b e n t u r e s i s r s . 1 0 0 . T h e d e b e n t u r e s a r e b e i n g i s s u e d a t a p r em i um o f 5%, t h e f l o a t a t i o n c o s t i s r s . 5 0 0 0 0 0 . C omp u t e K d . S o l n : K d = I / N T = 1 3 . 5 / 1 0 5 - 2 . 5 = 2 7 0 0 0 0 0 / ( 2 1 0 0 0 0 0 0 - 5 0 0 0 0 0 ) = 1 3 . 1 7% Role of Income Tax computation of Kd Interst is a tax deductable expense. interest is allowed as an expense and after deducting interest expense, the remaining income will be chargeable to income tax. Hence, it can be said that interest expense saves tax. While computing effective cost of debt, this feature of tax savings on interest will be taken to consideration. The cost of irredeemable/ perpetual debt can be said to be post tax annual interest expense in relation to net proceeds on the amount which is to be utilized by the firm/ company in perpetuity or forever. K e = I ( 1 - t ) / N P wh e r e, I = amo u n t o f i n t e r e s t e xp e n s e. t = c o r p o r a t e i n c ome t a x r a t e N P = n e t p r o c e e d s o r i s s u e p r i c e n e t o f f l o a t a t i o n c o s t B. cost of Redeemable debt T h e e q u a t i o n u s e d f o r c omp u t i n g c o s t o f r e d e ema b l e d e b t i s d i f f e r e n t f r om t h e e q u a t i o n s u s e d f o r c omp u t i n g c o s t o f i r r e d e ema b l e d e b t, t h e f a c t t h a t t h e p r i n c i p l e amo u n t i s t o b e r e p a i d a t t h e e n d o f a f i x e d p r e d e f i n e d ma t u r i t y a f f e c t s t h e a n n u a l c o s t o f d e b t s. K d = [ I ( 1 - t ) + ( R V - N P / n ) ] / [ ( N P + R V ) / 2 ] wh e r e, R V= R e d e ema b l e V a l u e N P = N e t P r o c e e d s n = n umb e r o f y e a r s Q. 1 ) P l t s i s i s s u i n g r s . 5 0 0 0 0 0 0 0 wo r t h d e b e n t u r e s ( 5 0 0 0 0 0 d e b t s o f r s. 1 0 0 e a c h ) a t p a r . T h e i r d e b e n t u r e s a r e r e d e ema b l e a t t h e e n d o f 1 0 y e a r s a t p a r . T h e c o u p o n r a t e p a y a b l e i s 1 2 5 0 b a s i s p o i n t s, t h e c omp a n y i s i n a n i n c ome t a x b r a k e t o f 4 0% . C omp u t e p o s t t a x K d . S o l n : K d = I ( 1 - t ) / N P = 1 2 . 5 ( 1 - 0. 4 ) / 1 0 0 = 7 . 5% Q . G l t d i s i s s u i n g R s . 1 0 0 d e b e n t u r e s ; 4 0 0 0 0 0 i n n umb e r a t a p r em i um o f 4%, t h e d e b e n t u r e s a c o u p o n r a t e o f 1 1 0 0 b a s i s p o i n t s . F l o a t a t i o n c o s t i s 2% o f i s s u e p r i c e . T h e c omp a n y i s i n a t a x b r a c k e t o f 3 0% . c omp u t e K d . S o l n : K d = I ( 1 - t ) / N P = 1 1 ( 1 - 0. 3 ) / 1 0 4 - 2 . 0 8 = 7 . 7 / 1 0 1 . 9 2 = 7 . 5 5% Q . 7 1 ) C h a p l t d. i s s u e s 1 2% d e b e n t u r e s o f f a c e v a l u e R s. 1 0 0 e a c h a n d r e a l i s e R s. 9 5 p e r d e b e n t u r e. T h e d e b e n t u r e a r e r e d e ema b l e a f t e r 1 0 y e a r s a t a p r em i um o f 1 0%. C a l c u l a t e t h e c o s t o f c a p i t a l p r e s um i n g i n c ome t a x r a t e i s 5 0%. S o l n : K d = [ I ( 1 - t ) + ( R V - N P ) / n ] / [ ( N P + R V ) / 2 ] = [ 1 2 ( 1 - 0 . 5 ) + ( 1 1 0 - 9 5 ) / 1 0 ] / [ ( 9 5 + 1 1 0 ) / 2 ] = ( 6 + 1 . 5 ) / 1 0 2. 5 = 7 . 3 2% Optimal Choice of Debt If a firm can obtain debt funds from more than 1 debt providers, then chose the one having least effective post tax Kd. 2. Cost of preference Shares P r e f e r e n c e s h a r e s c a r r y a f i x r a t e o f d i v i d e n d s wh i c h a r e n o t t a x d e d u c t i b l e. T h e c o s t o f p r e f e r e n c e s h a r e s ( K p ) a r e c omp u t e d i n t h e s ame ma n n e r a s c omp u t a t i o n o f c o s t o f d e b t w i t h a n e x c e p t i o n t h a t i n t e r e s t o n d e b t i s a t a x d e d u c t i b l e e xp e n s e, wh e r e a s p r e f e r e n c e d i v i d e n d s a r e n o t. A. Cost of irredeemable preference shares I n i n d i a i s s u e o f i r r e d e ema b l e p r e f e r e n c e s h a r e s i s p r o h i b i t e d b u t i n t e r n a t i o n a l l y, i n mo s t o f t h e we s t e r n c o u n t r i e s i s s u e o f p e r p e t u a l p r e f e r e n c e s h a r e i s a l l owe d b y l aw. T h e c o s t o f i r r e d e ema b l e p r e f e r e n c e s h a r e i s c omp u t e d a s f o l l ows : - K p = D / N P D = amo u n t o f a n n u a l p r e f e r e n c e d i v i d e n d s N P = n e t p r o c e e d s o r i s s u e p r i c e n e t o f f l o a t a t i o n c o s t s. B. Cost of redeemable preference shares T h e c o s t o f r e d e ema b l e p r e f e r e n c e s h a r e s i s a l s o c omp u t e d i n t h e s ame ma n n e r a s c omp u t a t i o n o f c o s t o f d e b t s w i t h a n e x c e p t i o n t h a t p r e f e r e n c e s h a r e s a r e p a y a b l e i n s t e a d o f i n t e r e s t a n d s u c h d i v i d e n d s a r e n o t t a x d e d u c t a b l e. K p = [ D + ( R V+ N P ) / n ] / [ ( N P + R V ) / 2 ] wh e r e, D = Amo u n t o f p r e f e r e n c e d i v i d e n d s R V = R e d e ema b l e V a l u e N P = N e t P r o c e e d s n = n umb e r o f y e a r s t o ma t u r i t y 3. Cost of Equity(Ke) U n l i l e d e b t a n d p r e f e r e n c e s h a r e c a p i t a l, e q u i t y s h a r e s d o n o t r e q u i r e a n y f i x e d p a yme n t s t o b e ma d e t o e q u i t y s h a r e h o l d e r s. T h u s t h e r e i s n o s i n g l e mo d e l a c c e p t a b l e b y a l l a n a l y s t s a s t o c omp u t a t i o n o f c o s t o f e q u t i y. E q u i t y s h a r e h o l d e r s a r e t h e own e r s o f t h e c omp a n y a n d t h e e q u i t y c a p i t a l i s t h e p e r ma n e n t s o u r c e o f l o n g t e r m f u n d s. T h e b a s i c o b j e c t i v e o f f i n a n c i a l ma n a g eme n t i s ma x i m i s a t i o n i f we a l t h o f e q u i t y s h a r h o l d e r s. T h e r e a r e s e v e r a l me t h o d s / mo d e l s o f d e t e r m i n i n g t h e r e q u i r e d r a t e o f r e t u r n o f e q u i t y s h a r e h o l d e r s. T h e s e a r e : 1. D i v i d e n d s P r i c e Mo d e l / D i v i d e n d s Y i e l d Mo d e l 2. E a r n i n g P r i c e Mo d e l / E a r n i n g s Y i e l d Mo d e l 3. D i v i d e n d s G r ow t h Mo d e l / D i v i d e n d s D i s c o u n t Mo d e l / G o r d o n Mo d e l 4. E a r n i n g s G r ow t h Mo d e l 5. C a p i t a l A s s e t s P r i c i n g Mo d e l 6. R e a l i s e d Y i e l d Mo d e l 1. Dividends Price Model A c c o r d i n g t o t h i s mo d e l, t h e e q u i t y s h a r e h o l d e r s e xp e c t t o e a r n d i v i d e n d s e a c h y e a r ( a f i x e d amo u n t ) i n r e l a t i o n t o t h e ma r k e t v a l u e o f t h e e q u i t y s h a r e. T h i s mo d e l c o n s i d e r t h e b a s i c p r i n c i p l e o f r e t u r n o n i n v e s t me n t f r om t h e p o i n t o f v i ew o f a n e q u i t y i n v e s t o r. T h e ma r k e t p r i c e p e r s h a r e i s i n v e s t e d b y a n i n v e s t o r t o e a r n d i v i d e n d s r e t u r n. i. e. k e = D P S / M P S Assumptions T h i s mo d e l a s s ume s t h a t D P S ( D i v i d e n d s P e r S h a r e ) a n d M P S ( M a r k e t p r i c e P e r S h a r e ) w i l l r ema i n c o n s t a n t f o r e v e r. Q. Numb e r o f e q u i t y s h a r e s = 1 0 0 0 0 0 0 F a c e v a l u e o f E q u i t y s h a r e s = R s. 1 0 M P S = R s. 2 5 T o t a l E q u i t y D i v i d e n d s = R s. 5 0 0 0 0 0 0 C omp u t e K e u s i n g d i v i d e n d s p r i c e mo d e. S o l n : K e = D P S / M P S = 5 / 2 5 = 2 0% D P S = 5 0 0 0 0 0 0 / 1 0 0 0 0 0 0 = R s. 5 2. Earnings Price Model A c c o r d i n g t o t h i s mo d e l, a n e q u i t y s h a r e h o l d e r e xp e c t s t h e e n t i r e e a r n i n g s a v a i l a b l e f o r e q u i t y s h a r e h o l d e r wh e t h e r d i s t r i b u t e d o r n o t. T h e d e s i r e d r e t u r n s o f e q u i t y s h a r e h o l d e r s i s t h e r a t e o f E P S i n r e l a t i o n t o M P S. K e = E P S / M P S Assumption T h o s mo d e l a s s ume s t h a t t h e b u s i n e s s r i s k o f a f i r m r ema i n s c o n s t a n t a n d h e n c e t h e r e l a t i o n s h i p b e t we e n E P S a n d M P S r ema i n s c o n s t a n t. 3. Dividends Growth Model/Gordon Model A c c o r d i n g t o M y r o n G o r d o n, t h e l o n g t e r m e q u i t y i n v e s t o r s e xp e c t t o r e c e i v e d i v i d e n d s e v e r y y e a r. T h e s e d i v i d e n d s s h o u l d g r ow a n n u a l l y a s t h e s ame r a t e a s t h e g r ow t h r a t e i n e a r r n i n g s o f t h e c omp a n y. F u r t h e r t h e e q u i t y s h a r e h o l d e r s e xp e c t a c a p i t a l g r ow t h o r g r ow t h i n t h e ma r k e t v a l u e o f e q u i t y s h a r e s. T h e e xp e c t a t i o n o f e q u i t y s h a r e h o l d e r s o r e q u i t y c a p i t a l i s a t i o n r a t e ( K e ) i s h e n c e t h e s um o f a n n u a l d i v i d e n d s y i e l d a n d c a p i t a l g r ow t h. K e = ( D 1 / P 0 ) + gwh e r e, D 1 = D i v i d e n d s t o b e p a i d a t t h e e n d o f t h e y e a r / N e x t e xp e c t e d d i v i d e n d s / D i v i d e n d s p a y a b l e a t t h e e n d o f t h e y e a r 1 / D i v i d e n d s p a y a b l e a t t h e e n d o f c u r r e n t y e a r / D i v i d e n d s p a y a b l e a t t h e b e g i n n i n g o f t h e n e x t y e a r / D i v i d e n d s p a y a b l e o u t o f c u r r e n t y e a r ' s e xp e c t e d e a r n i n g s. P 0 = M a r k e t p r i c e P e r S h a r e n ow o r a t t h e b e g i n n i n g o f c u r r e n t y e a r o r t o d a y o r a t 0 p e r i o d. g = G r ow t h r a t e o f c omp a n y / G r ow t h r a t e i n E a r n i n g s o f c omp a n y / G r ow t h r a t e i n D i v i d e n d s o f a c omp a n y / c a p i t a l G r ow t h r a t e / G r ow t h r a t e o f ma r k e t p r o i c e o f E q u i t y S h a r e. D 1 = E ( 1 - b ) wh e r e ; E = E xp e c t e d e a r n i n g s f o r c u r r e n t y e a r. b = r e t e n t i o n r a t i o n o r 1 0 0 - d i v i d e n d s p a y o u t r a t i o / p r o p o r t i o n o f e a r n i n g s d e s i r e d t o b e r e t a i n e d b y t h e c omp a n y f o r ma k i n g n ew i n v e s t me n t s. D 1 = D 0 ( 1 + g ) wh e r e ; D 0 = d i v i d e n d s a t 0 p e r i o d / D i v i d e n d s n ow/ D i v i d e n d s J u s t p a i d / D i v i d e n d s p a i d a t t h e b e g i n n i n g o f c u r r e n t y e a r / D i v i d e n d s p a i d a t t h e e n d o f p r e v i o u s y e a r / D i v i d e n d s p a i d o u t o f p r e v i o u s y e a r ' s e a r n i n g s. Assumptions 1. T h a t t h e f i r m h a s i n f i n i t e l i f e. 2 . T h a t t h e b u s i n e s s r i s k c omp l e x i o n o f t h e f i r m r ema i n s c o n s t a n t. I n o t h e r wo r d s, t h e r a t e o f r e t u r n o n i n v e s t me n t f o r e q u i t y ( r ) a n d e q u i t y c a p i t a l i s a t i o n r a t e ( K e ) r ema i n s c o n s t a n t e v e n a f t e r ma k i n g f r e s h i n v e s t me n t s. 3 . T h a t t h e g r ow t h r a t e o f a f i r m i s t h e p r o d u c t o f r e t e n t i o n r a t i o n ( b ) a n d r a t e o f r e t u r n o n I n v e s t me n t f o r e q u i t y ( r ). g = b * r 4. T h a t t h e r e a r e n o e x t e r n a l s o u r c e s o f f i n a n c e a v a i l a b l e f o r n ew i n v e s t me n t s t o b e ma d e b y t h e f i r m a n d o n l y i n t e r n a l l y g e n e r a t e d f u n d s o r r e t a i n e d e a r n i n g s a r e a v a i l a b l e f o r e xp l o i t i n g t h e n ew i n v e s t me n t o p p o r t u n i t y. 5 . T h a t t h e e q u i t y c a p i t a l i s a t i o n r a t e o r K e i s mo r e t h a n t h e g r ow t h r a t e o f t h e f i r m o r g. K e > g Determination of annual growth rate using data of part earnings/dividends/market price:- Q. 1 ) Y e a r s 2 0 1 0 2 0 1 1 E P S 2 0 2 2 S o l n : g [ ( 2 2 - 2 0 ) / 2 0 ] = 1 0% Q . 2 ) Y e a r s 2 0 0 5 2 0 0 7 E P S 1 0 1 2. 1 S o l n : D P S ( 1 + g ) ^ 2 = D P S 1 0 ( 1 + g ) = 1 2. 1 g = 1 0% Q. 3 ) Y e a r s 2 0 0 1 2 0 0 4 D P S 2 6 3 0 S o l n : D P S ( 1 + g ) ^ 3 = D P S 2 6 ( 1 + g ) ^ 3 = 3 0 ( 1 + g ) ^ 3 = 1 . 1 5 R e f e r e n c e t o t a b l e C ( c omp o u n d v a l u e o f R s. 1 t a b l e ) f o r y e a r 3 g i v e s u s : G r ow t h R a t e C omp o u n d V a l u e 4% 1 . 1 2 5 7, 0 . 0 2 9 5% 1 . 1 5 8 7 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1% 0 . 0 3 3 g = 4% + [ 1% * ( 0. 0 2 9 / 0 . 0 3 3 ] = 4 . 8 7 8% 4. Earnings Growth Model A c c o r d i n g t o t h i s mo d e l, t h e e xp e c t a t i o n o f E q u i t y s h a r e h o l d e r s i s t h e s um o f e a r n i n g s t i e l d a n d c a p i t a l g r ow t h. T h e e q u i t y s h a r e h o l d e r s a r e e xp e c t i n g t h e e n t i r e e a r n i n g s wh e t h e r d i s t r i b u t e d o r n o t. Ap a r t f r om t h i s, t h e y d e s i r e c a p i t a l g r ow t h a l s o. K e = ( E P S / M P S ) + g Wh e r e ; E P S = E xp e c t e d E a r n i n g s P e r S h a r e f o r c u r r e n t Y e a r. M P S = M a r k e t P r i c e P e r S h a r e a t t h e b e g i n n i n g o f t h e y e a r g = c a p i t a l g r ow t h Assumptions 1. T h a t t h e f i r m h a s i n f i n i t e l i f e. 2 . T h a t t h e r e a r e n o e x t e r n a l s o u r c e s o f f i n a n c e a v a i l a b l e f o r ma k i n g n ew i n v e s t me n t s o n l y r e t a i n e d e a r n i n g s w i l l f i n a n c e n ew i n v e s t me n t s. 3 . T h a t t h e b u s i n e s s r i s e c omp l e x i o n r ema i n s c o n s t a n t e v e n a f t e r ma k i n g n ew i n v e s t me n t s ( r a n d K e r ema i n c o n t a n t ). 4 . T h a t t h e g r ow t h i s t h e p r o d u c t o f r t e n t i o n r a t i o ( b ) a n d t h e r a t e o f R e t u r n O n E q u i t y ( r ). g = b * r Capital Asset Pricing Model(CAPM) CAPM was primarily developed by William Sharpe.However, Jan Morrin and John Linter also made their independent contribution towards the development of CAPM in 1990, William Sharpe, Hardy markowitz and Merton Miller shared the Nobel Prize of Economics for their contribution towards the development of CAPM. According to CAPM, the risk associated with capital assets/securities can be related in a Linear manner with the required rate of return of the investors. CAPM categories risk into 2 types: 1. SYSTEMATIC RISK It is the risk associated with the entire stock market and hence is non diversible. Each security listed in the stock market is affected by the changes in factors such as : change in general state of econony (BOOM, recession; normal), changes in political conditions of the country etc. However, the levek of effect on each company may differ some companies may be more sensitive to market changes and some of them may be less sensitive. 2. Unsystematic Risk It is the company/industry. Specific risk does not affect the entire stock market, unsystematic risk can be reduced through diversification as we add more stocks into our portfolio ( investment), the unsystematic risk gets reduced. Factors which may affect the company/ industry only losing of legal suit in court, fire in factory, strike, ill health of key persons of company, ban on use of some products, ban on issuing of license, etc. CAPM EQUATION R e q u i r e d R e t u r n o f I n v e s t o r s ( K e ) T i me v a l u e o f mo n e y + R i s k P r em i um o n A s s e t R i s k F r e e + ß ( e xp e c t e d r e t u r n o f M a r k e t R i s k f r e e r e t u r n ) K e = R ƒ + ß [ E R ( M ) - R ƒ ] Determination of required Rate Of Return or Ke with the help of CAPM According to CAPM, the required rate of return of equity investors depends upon the level of systematic risk of the underlying capital asset. Higher the systematic risk, higher the rate of Return. CAPM requires the investors desired rate of Return to be consisting of 2 parts. 1. Risk free Rate of Return(Rƒ) This is the rate of interest on RBI/central bank's treasury bills. The investors desire to be compensated for parting with their money spent to purchase the share at the beginning of any year. The risk free rate of interest represents the compensation to investors on account of time value of money. 2. Risk Premium on account of systematic risk incidence on the portfolio of their assets/ Portfolio or capital Assets Risk Premium::: ß [ER(M) - Rƒ] Beta is a measure of systematic risk. It is computed in times. ß = 2 implies that the risk or sensitivity or movement or deviation of an asset is twice of the risk or sensitivity or movement or deviation in relation to the market movement. ß = 0.5 implies that the movement of the capital asset is half in relation to the market movement. ß = 1 implies that the movement of the asset is equal in relation to the market movement ß of a risk free asset is 0. An investor desores risk premium on his capital asset (in addition to risk free return), in accordance with the level of systematic risk (ß) of his underlying asset. The risk premium on his asset is the product of Beta coefficient of his asset and the market risk premium. K e = R ƒ + ß [ E R ( M ) - R ƒ ] wh e r e ; R ƒ = R i s k F r e e r a t e o f R e t u r n / R i s k o f i n t e r e s t o n T r e a s u r y B i l l s. ß = B e t a c o e f f i c i e n t o r R i s k I n d e x o r s y s t ema t i c r i s k o r s e n s i t i v i t y o f a s s e t i n r e l a t i o n t o s e n s i t i v i t y o f ma r k e t. E R ( M ) = E xp e c t e d r e t u r n o f M a r k e t o r M e a n R e t u r n o n M a r k e t. [ E R ( M ) - R ƒ ] = M a r k e t R i s k P r em i um Security Market Line(SML) The graphical representation of CAPM equation is termed as SML. Beta coefficient (ß) is plotted on the horizontal (x- axis) and rate of return (Ke) is plotted on the vertical (y-axis). Higher the ß, higer the Ke. Ke is a linear function of Beta and this straigt line showing relationship between ß and Ke is SML. The starting point of SML is risk free rate of Return. Determination of Rƒ, ER(M) and ß Rƒ = It is the mean risk free return. It is usually computed by averaging past annual risk free rate of return for a number of years. ER(M) = It is the mean of market rate of return. It is usually computed by averaging past annual market rate of return for a number of years. ß ( a s s e t ) = [ ( σ ( a s s e t ) * γ ( a s s e t *ma r k e t ) ] / σ ( ma r k e t ) σ ( a s s e t *ma r k e t ) = c o e f f i c i e n t o f c o r r e l a t i o n b e t we e n a s s e t a n d ma r k e t . Computation of Return on Investment in a Share R ( i ) = [ ( P 1 - P 0 ) + D 1 ] / P 0 Computation of Mean Returns from Expost data _ Χ = [ ( X 1 + X 2 + X 3 +. . . . . . . . . . + X n ) / n ] Computation of Standard Deviation and Variance with the help of expost data _ _ _ _ V a r i a n c e o f X = [ ( x1 - x ) ² + ( x2 - x ) ² + . . . . . + ( xn - x ) ² ] ÷ n σ x = ( V a r i a n c e ) ½ Computation of Covariance of X and Y Covariance of xy = [(x1-x)(y1-ӯ) +....+ (xn-x) (yn-ӯ)]/n Computation of correlation between x and y γ x = [ C o v a r i a n c e o f x y / σ x * σ y ] Computation of Beta of a company as a whole where the company carries out more that one type of business having its own beta Beta of company as a whole is the weighted average where weights are determined on the basis of amount of equity investments in each business. Weighted Avegare Cost of Capital (WACC) / Overall cost of Capital (Ko) A c omp a n y r a i s e s f u n d s f r om v a r i o u s s o u r c e s, s u c h a s : d e b t , p r e f e r e n c e c a p i t a l a n d e q u i t y c a p i t a l. T h e s p e c i f i c / c omp o n e n t c o s t o f c a p i t a l o f e a c h s o u r c e i s c omp u t e d s e p a r a t e l y a n d i s d e p e n d e n t u p o n r i s k i n c i d e n c e o f e a c h s o u r c e. T h e c omb i n e d / O v e r a l l / a v e r a g e c o s t o f c a p i t a l o f O v e r a l l / T o t a l f u n d s i s WA C C. If any instrument are to be made, the investment will be made out of the pool of funds. The weights to be taken for computing WACC are the proportion of funds of each source of finance in the total/overall capital employed. Steps for Computing WACC 1. Compute specific cost of capital of each source of finance (i.e., compute Kd, Kp, Ke, Kre). 2. Determine the weight/proportion of funds raised from each source of finance. 3. Compute the overall cost of capital as follows:- S o u r c e - o f - F i n a n c e Amo u n t we i g h t C o s t - o f - C a p i t a l WA C C E q u i t y 5 0 L 0. 5 1 6% 8% P r e f e r e n c e C a p i t a l 3 0 L 0. 3 1 2 . 5% 3 . 7 5% D e b t. 2 0 L 0. 2 9% 1 . 8 0% O R K o = ( K e *WE ) + ( K p *WP ) + ( K d *WD ) = ( 1 6% * 5 0 / 1 0 0 ) + ( 1 2 . 5 * 3 0 / 1 0 0 ) + ( 9% * 2 0 / 1 0 0 ) = 1 3. 5 5% Use of Ke for computing Ko Usually Dividends Growth Model and CAPM are preferred to be used for computation of Ke. In case information of any one of these models is given, then use this model for determining Ke and finally computation of Ko. However, if information of both models (ie. CAPM and Dividends growth model) is given and no single model is preffered in the question specifically, then use average Ke, computed with the help of both these models for computation of Ko. Optimal Capital Structure The basic objective of financial management is maximisation of wealth of equity shareholders. A capital structure is said to be optimal if it helps in fulfillment of this objective. An optimal capital structure is one which minimises the overall cost of capital or Ko and maximises the market value of equity shares. Cost of Debt If the term cost of debt is given in the problem, then assume it to be pretax cost or interest rate. If post tax or effective cost of debt is given, then the computation of tax saving on debt is not required to be made. Computation of Cost of Equity when Net Proceeds(NP) are known The expectation of equity shareholder is in accordance with the market price payable by him/her, but the cost to the company is in accordance with Net Proceeds receivable by it. N e t P r o c e e d s = I s s u e P r i c e o r s a l e p r i c e n e t o f floatation cost today/now. Cost of Retained Earnings(Kre) Usually the companies retain a part of their earnings and reinvent them for future expansion of business, diversification and growth. Often, people believe that retained earnings being internally generated funds or being the profits retained have no cost. However, this being a misconception. When a company retains earnings, these earnings basically belongs to the equity shareholders who expects to reinvest this money themselves if it were not retained and were distributed amongst the shareholders. Also, the company shall be required to raise funds from outside if these earnings were not retained. Thus there is an implicit cost or implied cost of earnings retained by the company which is equal to the opportunity cost or required rate of return of equity shareholders. NOTE : Always remember that Kre will be either to Ke or less than Ke as it does not involve any incurrence of floatation costs. The Kre is computed with the help of same model as are used for computation of Ke. Earnings Price/Yield Model K r e = E P S / M P S Dividends Price/yield model K r e = D P S / M P S Dividends growth/discount Model K r e = D 1 / P 0 + g Earnings Growth Model K r e = E P S / M P S + g CAPM K r e = R ƒ + β [ E R ( M ) - R ƒ ] Impacts of Dividends Distribution Tax(DDT) / Corporate Dividend Tax(CDT) on consumption of Kp, Ke and Kre As per section 115 - 0 of Income Tax Act,1961, a company shall be required to pay DDT on the amount of dividends to be distributed by it among its shareholders (both equity dividends and preference dividends) at the rate prescribed in the said act. Impact on Cost of Irredeemable Preference Shares K p = [ D ( 1 + C D T r a t e ) ] ÷ N P / M P S Impact on cost of Redeemable Preference Shares K p = [ D ( 1 + C D T r a t e ) + ( R V - N P ) / n ] ÷ [ ( N P + R V ) / 2 ] Impact on Computation of Ke Dividends Yield Model K e = [ D P S ( 1 + C D T r a t e ) ] ÷ ( N P / M P S ) Dividends Growth Model K e = [ D 1 ( 1 + C D T r a t e ) g ] ÷ ( N P / P o ) Impact on Computation of Kre Dividend Yield Model K r e = [ D P S ( 1 + D D T r a t e ) ] ÷ M P S Dividends Growth Model K r e = [ D 1 ( 1 + D D T r a t e ) ÷ P o ] + g Market Price to be taken into consideration while computing Kp, Kd, Ke (when NP is not known) and Kre The appropriate market price to be taken into consideration is Ex-Interest/Ex-Dividends Market Price. in case the problem under consideration takes into account (i.e gives the cum Interet/cum Dividend Market Price, then reduce the Interest) dividends amount therefrom in order to determine ex-Interest/ex- dividends Market Price. Choice of weigts to be used for computation of overall cost of capital Usually, after computation of specific cost of capital of each source of finance(i.e, Kd, Kp, Ke, Kre), the next step is to determine the proportion or weight of each source of finance in relation to the overall/total finance. There are two methods of determining the weights to be taken into consideration:- Book value weights/Accounting Value Weights/Balance Sheet value weights This method takes into consideration the information from balancesheet of the company. Book value are easily computed with reference to latest drawn BalanceSheet. However, the use of Book Value weights should be made only when the market value data all sources of finance is under unavailable or unrealisable or ineffective. Market Value Weigts The book Values are not related to the present economic value of each component/source of finance. The market value are consistent with the concept of the wealth (i.e, market value of the company). The market values are the present economic values of various source of finance which can be arranged from the stock exchange where the security of the company are listed. Market values show the present expectation of investors. However, such weigts cannot be calculated in case of private limited company and unlisted public ltd company. Also market value is used should be avoided if the market value of all sources of finance is not given in the problems (unless it is specifically mentioned in the problem to use market value weights).