Decision Making in Finance: Time Value of Money, Cost of Capital and Dividend Policy

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1 Chapr 11 Dcisio Maig i Fiac: Tim Valu of Moy, Cos of Capial ad Dividd olicy Babia Goyal Ky words: rs valu of a flow, fuur valu of a flow, auiy, doublig priod, compoudig, ffciv irs ra, omial irs ra, rur, ivsm, cos of db, cos of quiy, cos of prfrc soc, wighd cos of capial margial cos of capial Suggsd radigs: 1. Chadra. (1970), Appraisal Implmaio, Taa-McGraw Hill ublishig Compay Limid, Nw Dlhi. 2. Hampo J.J. (1992), Fiacial Dcisio Maig (4 h diio), ric hall of Idia riva Limid 3. Kha M.Y. ad Jai.K. (2004), Fiacial Maagm (4 h diio), Taa-McGraw Hill ublishig Compay Limid. 4. Gupa.K. ad Moha M. (1987), Opraios Rsarch ad Saisical Aalysis, Sula Chad ad Sos, Dlhi. 384

2 11.1 Iroducio Th major objciv of h fiacial dcisio-maig is walh maximizaio. I walh maximizaio, h imigs a which bfis ar rcivd play a impora rol. A fiacial dcisio sprads ovr im horizo, i.., i vurs io h fuur. For xampl, a w pic of quipm isalld oday, will b usful for may yars (usful lif of h quipm) o com. Howvr, h paym for his quipm may also b sprad ovr may yars o com. Th a fiacial dcisio is o b mad o h basis of h cash ouflows (i.. h payms) ad h cash iflows (i.., h bfis) associad wih h dcisio. I such siuaios, i ordr o facilia ffciv ad valid comparisos, i is cssary ha h cash flows durig diffr im priods hav h sam moary valu. From his rquirm origias h cocp of im valu of moy. Moy has im valu. This simply mas ha h valu of moy is diffr a diffr im priods. A rup oday is mor valuabl ha a rup o yar from ow. Worh of moy chags du o h followig rasos. (i) I gral, idividuals prfr prs cosumpio o fuur cosumpio, as fuur is ucrai. (ii) Capial ca b ivsd o gra posiiv rurs, so if r is h aual ra of rur, h o rup ivsd oday would yild Rs. (1+r) o yar hc, so Rs. (1+r) afr o yar will hav h sam worh as o rup oday. So, if w ar irsd i cash flows occurrig a various im pois, as is h cas wih mos of h fiacial problms, w hav o cosidr xplicily h im valu of moy Tim valu of moy I ordr o udrsad h cocp of h im valu of moy, w dfi h followig rms. (i) Fuur valu of a sigl flow Suppos ha w wa o ivs a amou for yars a a ra of irs of i %. Th h fuur valu of amou is dfid as 385

3 S (1 + i) (11.1) Whr S is h fuur valu afr yars. Th facor (1 + i) is calld h compoudig facor or h fuur valu irs facor ( FVIF i, ). If h irs is compoudd coiuously, h h fuur valu of h flow is giv by S i (ii) rs valu of a sigl flow For a sigl flow S (1 + i) (11.2) Th facor 1 (1 + i) is calld h discouig facor or h prs valu irs facor VIF ). Tabls ( i, ar availabl o calcula VIF i, for diffr valus of ad i. If h irs is compoudd coiuously, h h prs valu of h flow is giv by S i Doublig priod Doublig priod of a ivsm is h im dd o doubl ha ivsm. Usig quaio (6.1), w calcula h doublig priod of ivsm as follows: 2 (1 + i) 2 (1 + i) or, log 2 log (1 + i) log 2 log (1 + i) log (1 + i) 386

4 (iii) Fuur valu of a auiy A auiy is a sris of priodic cash flows (payms or rcips) of qual amous. Th cash flows may occur a h bgiig or a h d of a priod. If h cash flows ar occurrig a h bgiig of h priod, h auiy is calld a auiy du ad if h cash flows ar occurrig a h d of h priod, h auiy is calld a rgular or dfrrd auiy. W dfi h fuur valu of a auiy as h amou rcivd i fuur wh a auiy is ivsd a a giv ra of irs. Mahmaically, 1 2 S R(1 + i) + R(1 + i) R (1 + i) 1 R i whr, S Fuur valu of a rgular auiy which has a duraio of priod; R i Cosa priodic flow; Irs ra pr priod; ad Duraio of h auiy. (1 + i) 1 Th facor is calld h fuur valu irs facor for a auiy ) i ( FVIFA. Tabls ar i, availabl o calcula FVIF i, for diffr valus of ad i. If h irs is compoudd coiuously, h h fuur valu of h auiy is giv by i 1 S R i 1 (iv) Siig fud facor Rciprocal of FVIFA ), h siig fud facor is h discouig facor of a fuur flow. So ( i, R i S (1 + i) 1 ad i is calld h siig fud facor. (1 + i) 1 387

5 (v) rs valu of a auiy rs valu of a auiy is is prs worh discoud a a ra qual o h ra of irs. Mahmaically, R + R R 1+ i 1+ i 1+ i (1 + i) 1 R i (1 + i ) whr, rs valu of a rgular auiy which has a duraio of priod; R i Cosa priodic flow; Irs (discou) ra pr priod; ad Duraio of h auiy. Th facor (1 + i) 1 i(1 + i) is h prs valu irs facor for auiy ( VIFAi, ). I ca b s ha VIFA FVIFA VIF i, i, i, Tabls ar availabl o calcula VIFA i, for diffr valus of ad i. Exampl 1: Th paym o a 10 priod auiy of Rs. 5,000 will bgi sv yars from ow. Wha is h prs valu of h auiy a a discou ra of 12%? Sol: Th valu of his auiy o yar prior o is mauriy, i.., six yars from ow, will b Rs.5, 000 VIFA 5, (from abls) 12,10 Rs. 28, 250 rs valu of his amou is Rs. 28,250 VIF 28, (from abls) 12,6 Rs. 14,

6 (vi) Capial rcovry amou Capial rcovry amou, R, is ha amou which ca b wihdraw priodically for a crai lgh of im i rspos o a crai ivsm oday. Mahmaically (1 + i) 1 R i (1 + i ) i(1 + i) R (1 + i) 1 Th facor i(1 + i) is calld h capial rcovry facor. (1 + i) 1 (vii) rs valu of a uv sris Till ow, w hav drivd various xprssios assumig ha cash flows associad wih a auiy ar qual i amou. Howvr, his siuaio may o always b ru ad various cash flows associad wih a auiy ar uqual i amou. For xampl, h dividd sram of a quiy is cosiss of uqual payms. Th prs valu of a uv sris is, h, calculad by cosidrig all h cash flows occurrig a various im pois: V R1 + R R 1+ i 1+ i 1+ i 2 1 R (1 + i) whr, V rs valu of a cash flow sram which has a duraio of priod; R i Cash flow occurrig a h d of h priod ; Irs (discou) ra pr priod; ad Duraio of h cash flow sram. (viii) Shorr compoudig priods Somims h irs is o compoudd aually bu for shorr priods. I his cas h fuur valu of h auiy ca b calculad as follows: S i 1+ m m 389

7 whr, S Fuur valu afr yars; rs amou; i Nomial irs ra pr yar; m Numbr of ims compoudig is do durig a yar; ad Duraio of h compoudig. Th diffrc of h pricipals of h aual compoudig ad h shorr priod compoudig rprss h irs o aual irs. Effciv vrsus omial ra Cosidr h followig offr of a compay. AEO Ld. is offrig 12% irs smi-aually o h ivsms mad o h compay. A prso was o ivs a sum of Rs. 10,000. Calcula h amou, which h will rciv afr o yar. (a) If h compoudig is do smi-aually: (i) Firs six mohs: ricipal a h bgiig Rs.10, Irs of six mohs Rs. 10, Rs ricipal a h d Rs.10, Rs Rs.10, (ii) Scod six mohs: ricipal a h bgiig Rs.10, Irs of six mohs Rs. 10,600 Rs ricipal a h d Rs.10, Rs Rs.11,

8 (b) If h compoudig is do aually: ricipal a h bgiig Rs.10, Irs of six mohs Rs. 10, Rs ricipal a h d Rs.10, Rs Rs.11, Th diffrc bw h wo pricipals, i.., Rs. 36 is h irs o irs of h firs six mohs for h scod six mohs. Thus i h cas of smi-aual compoudig h pricipal is growig ffcivly a a ra of 12.36% aually. Now, w ca diffria bw ffciv ad omial ras of irs: Nomial ra of irs is ha ra which is offrd a a aual basis, irrspciv of h umbr ad siz of h compoudig priods. Effciv ra of irs is ha ra a which h pricipal is acually growig aually if h siz of h compoudig priod is lss ha h siz of h priod for omial ra. I fac his is h ra udr aual compoudig which will l h pricipal grow a h sam ra a which shorr priod compoudig is big do. Thr xiss a mahmaical rlaioship bw ffciv ad omial ras of irs: i m ( m) i 1+ 1 m whr, i Effciv irs ra pr yar; i ( m) Nomial irs ra pr yar;ad m Numbr of ims compoudig is do durig a yar. If d is h discou ra associad wih h prs valu of R.1 h 391

9 d i 1+ i ( m) m d 1 1 m ( m) d Nomial discouig ra pr yar 11.3 Applicaios of prs valu ad fuur valu chiqus Thr ar som siuaios i ral lif whr w hav o compar h cash flows a wo diffr im pois. I such siuaios hs chiqus ca b usd ffcivly o ma maigful comparisos. (1) A aual savig of a crai sum may b rquird o gra a fud which would b dd somim i fuur,.g., o rpay a xisig liabiliy or o rplac a pic of quipm. Th h fud maagr is irsd i owig h siz of h auiy o gra h rquird fud. Exampl 2: A compay has sold 7.5% bods ha will maur afr 8 yars from oday. Now h compay plas o cra a fud for rpaym of bods i which a fixd amou is o b dposid (a h d of) ach yar. If h fuds ar xpcd o ar 7% aual irs, fid h amou of h auiy dd o accumula a sum of Rs. 10, 00,000 a h d of 8 yars. Sol: I his cas w hav o fid h siz of a 5-yar auiy whos fuur valu is Rs. 10, 00,000 FVIFA ,8 10,00,000 Siz of h auiy Rs (2) Wh h loa, which has b borrowd oday, is o b rpaid i fuur, h fud maagr is irsd i owig h siz of h auiy. Exampl 3: A compay has isalld a machi worh Rs. 15, 00,000.h amou has o b rpaid i 5 qual isallms a a irs ra of 12 %. Fid h siz of h auiy. 392

10 Sol: I his cas w hav o fid h siz of a 5-yar auiy whos prs valu is Rs. 15,00,000. VIFA ,5 15,00,000 Siz of h auiy Rs. 4,16, (3) Th mar pric of shars ad scuriis ar sigificaly affcd by h dividds paid by h compay offrig hm. If h growh ra of dividds is highr ha h prvailig irs ra or h growh ra of ohr scuriis, h mar pric of shars will b high. A ivsor may b irsd i drmiig h growh ra of dividds ha h is rcivig. Exampl 4: Giv blow ar h dividds rcivd by Moha from a crai ifrasrucur compay: Yar Tabl 11.1 Dividds (Rs.) Th ra of rur o ohr similar scuriis is 8%. Moha was o ow whhr or o should h dispos off his soc. Wha should h do? Sol: Sic h dividds ar rcivd a h d of h priod (yar), so h abov abl rvals ha h dividds hav grow from Rs. 25 o Rs i fiv yars im. Thus (1 + i) i (1 ) i 10% (From compoudig abls) 393

11 Sic Moha is arig dividd, which has a growh ra highr ha h growh ra of similar scuriis i h mar, h should o sll his soc. Exampl 5: Calcula h valu fiv yars from ow of a dposi of Rs. 20,000 mad oday a h ra of irs (i) 8%, (ii) 10%, (iii) 12%, ad (iv) 15%. Sol: S (1 + i) 20000(1 + i) 5 (i) i 0.08 S (1 + i) 20000(1.360) if 4; 20000(1.587) if 6 S Rs (ii) i 0.10 S Rs (iii) i 0.12 S Rs (iv) i 0.15 S Rs

12 Exampl 6: A ririg prso has b offrd wo alraivs, bw which h has o ma a choic: (a) A aual psio of Rs.30, 000 as log as h livs; ad (b) a lump sum amou of Rs. 2, 00,000. If h xpcd lif of ha prso is 15 yars mor afr rirm ad ha prvailig ra of irs is 15%, which opio is mor lucraiv? Sol: (a) (b) Fuur valu of h auiy afr 15 yars 30, ( ) , Rs.14, 25,000 Fuur valu of h sigl afr 15 yars 2,00,000( ) 15 2,00, Rs.16,27, 400 Scod opio is a br o. Exampl 7: Wha will b h siz of h auiy if Rs. 1,00,000 dposid i a ba a a irs ra of 10% rducs o zro i 30 yars? Sol: R i(1 + i) (1 + i) ,00,000.10(1 +.10) (1.10) ,00, Rs. 10,608 Exampl 8: A firm has isalld a w machi a a dow paym of Rs. 2,50,000 ad will pay Rs. 2,00,000 ad Rs. 1,00,000 rspcivly for firs wo yars ad rs will b paid i 10 qual isallms of Rs. 75,000. If h irs is chargd a ra of 12% pr aum, wha is h prs worh of h machi? 395

13 Sol: Sic h cash flows ar uv, w calcula h prs worh of ach of h ouflow: (i) rs worh of Rs. 2, 00, 000 du i o yar 2, 00, Rs. 1,78,600 (ii) rs worh of Rs. 1, 00, 000 du i wo yars 1, 00, Rs. 79,700 (iii) rs worh of a auiy of siz Rs. 75,000 a h bgiig of yar 3 75, Rs. 3,72,600 rs worh of a sigl flow a h bgiig of yar 3 Rs. 3,72, Rs. 2,96,962.2 Hc h oal cos of h machi is Rs. 2, 50, Rs. 1, 78, Rs Rs. 2, 96, Rs. 8, 05, Exampl 9: A las corac rquirs paym of Rs. 96 pr housad pr moh a h d of vry moh ovr a priod of 12 mohs. Dvlop a rpaym schdul. Sol: Th implid ffciv ra of irs is Rs. 96 VIFA 1000 im,12 VIFA im,12 1, From abls VIFA 2, VIFA 3,

14 i m % Effciv ra of aual irs ( ) % Nomial ra of irs % Tabl 11.2: Loa rpaym schdul (Rs.) Mohs Bgiig amou Isallm Irs (2.25%) Capial Th diffrc is du o roudig off of h valus. 397

15 11.4 Cos of capial Th cos of capial of a firm is h miimum ra ha h firm mus ar o is ivsms i ordr o saisfy h xpcaios of is ivsors who provid h fuds o h firm. Th cos of capial is usd for (i) valuaig h prs valu of h ivsms; ad (ii) drmiig h aracivss of h iral ra of rur. If a firm's ra of rur o is ivsms is mor ha is cos of capial, i rsuls i hacm of h walh of h (quiy) sharholdrs. This is du o h fac ha i his cas h ra of rur ard o h quiy capial afr mig all ohr coss of fiacig, is mor ha h ra of rur rquird by h ivsors. Hc h walh of h sharholdrs will icras. For xampl, cosidr a firm whos cos of quiy ad db ar rspcivly 14% ad 6%ad h firm mploys quiy ad db i qual proporios. Th cos of capial for h firm, which is h wighd avrag cos of capial, is 10%. If h firm ivss Rs. 50 lahs o a projc, which is xpcd o ar 18% ra of rur, h h ra of rur o quiy fuds will b giv by Ra of rur o quiy Toal rur o h projc - Irs o db Equiy fuds % This ra of rur is grar ha ha rquird by h ivsors (14%). Thrfor h mar valu of h quiy capial will icras ad hc h walh of h quiy socholdrs. A firm's cos of capial is h wighd avrag of h cos of various sourcs of fiac usd by i. Hc o calcula h cos of capial for h firm, w d o ow (i) (ii) Th cos of diffr sourcs of fiac; ad Th proporios of diffr sourcs of fiac i h capial srucur of h firm. I ordr o us h avrag cos of capial for appraisig w ivsms, w ma som assumpios: 398

16 (i) Th ris characrizig w ivsms proposals udr cosidraio is sam as h ris characrizig h xisig ivsms of h firm, ad h adopio of h w proposals will o chag h ris srucur of h firm. (ii) Th capial srucur of h firm will o b affcd by h w ivsms, ad h firm will coiu o pursu h sam policis; ad (iii) Each w ivsm is dmd o b fiacd from a pool of fuds i which h various sourcs of log-rm fiacig ar prs i h proporios i which hy ar foud 9 h capial srucur of h firm Cos of diffr sourcs of fiac Th oal cos of a sourc of fiac may b dmd o b cosisig of wo compos: (a) Explici cos; ad (b) Hidd cos. (a) Explici cos Th xplici cos is h ra of discou, which quas h prs valu of h xpcd paym o ha sourc of fiac wih fuds rcivd from ha sourc of fiac. Mahmaically, i is h valu of i 1 C ; (1 + ) whr N fuds rcivd from h sourc; ad C Expcd paym o h sourc a h d of h priod. For calculaig h cos of capial of h firm, w wor wih h xplici cos of diffr sourcs of fiac. (b) Hidd cos hidd cos of a sourc of fiac is h icras i h xplici cos of ohr sourcs of fiac as a rsul of mploym of h sourc of fiac big cosidrd. For xampl, cosidr a firm, which prsly mploys Rs. 50 lah of quiy fuds a a cos of 12%. Now h firm plas o rais addiioal fuds of Rs. 100 lah by issuig dburs havig a xplici 399

17 cos of 6%. Howvr h cos of xisig quiy capial icrass from 12% o 14% as a rsul of mployig dbur capial. This icras is o accou of prcivig grar ris i h compay du o dbur capial. Hc quiy sharholdrs dmad grar rur. This icras i h quiy cos, as a rsul of mployig db capial, is a hidd cos of db. Howvr, hidd coss ar o rad sparaly ad hs ar rflcd fially i h xplici cos. Aohr cos is h implici cos, which is h ra of rur ard o h bs alraiv possibl ivsm o which h fuds of a sourc may b mployd. (c) Cos of db Th xplici cos of db is h discou ra which quas h prs valu of pos-ax irs paym ad pricipal rpayms wih h procds of db issu. Mahmaically, h cos of db is h valu of d i h quaio C(1 T) F + ; (1 + ) (1 + ) 1 d d whr C T F N fuds rcivd from h db; Aual db irs paym ; Tax ra; Rdmpio pric, which is grally h fac valu of h dbur;ad Mauriy priod of h dbur. Th db irs is a ax-dducibl xps, ha is why C is muliplid by (1-T). I ohr words, C is i pr-ax rms ad C (1-T) is i pos-ax rms. C(1 T) F + (1 + ) (1 + ) 1 d d + 1 (1 + d ) 1 C(1 T) + d F (1 + ) d ad 400

18 d F C(1 T) + F + 2 If h diffrc bw F ad is amorizd vly ovr h duraio of db fiacig h d F C(1 T) + (1 T) F + 2 rpual db If h mauriy priod of h db capial is ifii, h db is calld prpual db. For his db, h cos of capial (db) is h valu of d i h quaio 1 C(1 T) (1 + ) d C(1 T) d d C(1 T) Trm loas Trm loas ar h dbs raisd from h fiacial isiuios or bas, which ar rpayabl ormally wihi 8 o 11 yars i qual isallms which ar ihr yarly or half yarly afr a iiial grac priod of o o four yars. Th pos-ax cos of a rm loa is Irs ra(1-ax-ra) If I d sads for oal irs o db ad M d is h oal mar valu of db, h d I d M d ; M d I d d Exampl 10: A firm issus 14% dburs havig fac valu Rs Th amou ralizd pr dbur is Rs. 96, ad h dburs ar rdmabl afr 12 yars. Th ax ra is 40%. Wha is h cos of dburs o h firm? 401

19 Sol: d F C(1 T) + F (1 0.40) Thus h cos of dburs o h firm is approximaly 9%. Exampl 11: A firm is plaig o rais capial hrough issu of 15% dburs a fac valu of Rs Th cos of issu wors ou o b 2%. Th dburs ar rpayabl afr sv yars. Th firm has a ax ra of 40%. If h diffrc bw h par valu ad h amou ralizd ca b amorizd v ly ovr h lif of h dburs, wha is h cos of db o h firm? Sol: N amou ralizd pr dbur Rs d F C(1 T) + (1 T) F (1 0.4) + (1 0.4) % 198 (d) Cos of prfrc capial rfrc capial is ha sourc of fiac, which carris a fixd ra of dividd. Though his dividd is payabl a h discrio of h board of dircors, grally i is paid rgularly. Th cos of prfrc, which is prpual, is h valu of p i h quaio 402

20 D 1 (1 + ) p D d whr D N amou rlizd pr prfrc shar; ad rfrc dividd pr shar payabl aually. p D Rdmabl prfrc soc Th prfrc soc which is o prpual, i.., rdmabl afr yars, is calld h rdmabl prfrc soc. Th cos of such soc is h valu of p i h quaio D F + 1 (1 + ) (1 + ) p p whr F Th rdmpio pric; ad Th, Mauriy priod. p F D + F + 2 If h diffrc bw F ad is amorizd vly ovr h duraio of capial fiacig ad h ax ra for h firm is T, h ( F ) T D + F + 1 (1 + ) (1 + ) p p p F D (1 T) F + 2 Exampl 12: A firm is issuig prfrc shars a a dividd ra of 12%. Th prfrc capial is rpayabl i wo qual isallms a h d of h 10 h ad h 11 h yar rspcivly. Th amou ralizd pr prfrc shar is Rs. 97. Wha is h cos of h prfrc capial? 403

21 Sol: p F F D F (100 97) % () Cos of quiy capial Th cos of quiy capial is h miimum ra rquird o h quiy fuds raisd i ordr o lav h mar pric of h quiy soc uaffcd. To calcula h cos of quiy capial, w mus ow h ra of rur rquird by h quiy socholdrs, which is h adjusd for h floaaio coss wh h firm issus h addiioal quiy soc. Ra of rur rquird by h quiy socholdrs Th dividd sram rcivabl by h quiy soc holdrs is o govrd by ay corac or fixd ruls. Hc masurig h ra of rur rquird by h quiy socholdrs is difficul o ow. Svral approachs hav b suggsd o sima his ra. (i) Dividd forcas approach Th valu of a quiy soc is qual o h sum of h prs valu of dividds associad wih i, i.., 1 D ; (1 + ) whr ric pr shar of quiy soc; D Expcd dividd a h d of h priod ; ad Ra of rur rquird by h quiy soc holdrs. 404

22 If h fuur dividd sram, as xpcd by h quiy soc holdrs ca b forcasd, h giv h curr mar pric pr quiy shar, h ra of rur ca b calculad. If h dividd is xpcd o b cosa aually h D If h quiy socholdrs xpc h dividd o grow aually a a ra of g % forvr, h is giv by h xprssio D D (1 + g) D (1 + g) D (1 + g) (1 ) (1 ) (1 ) D1 1+ (1 + g) < g > 1 + D 1+ g g 1+ D g 1 sic if, prics will d o Thus h cos of quiy capial is qual o h dividd yild plus h aual growh ra of dividd. Exampl 13: Th mar pric pr shar of a compay is Rs ad h dividd xpcd o yar from ow is Rs Th xpcd ra of dividd growh is 6%. Wha is h cos of quiy capial o h compay? Sol: D 1 + g % If D/ raio is 100%, h g 0 405

23 D E 1 1 EN 1 ; N is h umbr of ousadig quiy shars ad N E is h arigs i priod 1. 1 EBIT Id ; M is h oal mar valu of quiy M NI ; NI is h icom availabl o sharholdrs. M M NI Wh h xpcd growh ra of dividd varis ovr im, his variaio has o b a io accou. Suppos ha h xpcd growh ra is g 1 for 1 yars, g 2 for 2 yars ad g 3 forvr afr ha, ad h h quaio for is D (1 + g ) D (1 + g ) D1(1 + g1) (1 + ) 1 (1 + ) 1 (1 + ) Exampl 14: Th mar pric pr shar of a compay is Rs. 150 a prs. Th dividd xpcd o yar from ow is Rs. 20 pr shar, which is xpcd o grow a a ra of 10% pr shar for fiv yars. Thrafr h growh of h dividd is xpcd o dcli o 8% whr i will say forvr. Wha is h cos of quiy o h compay?. Sol: Th cos of quiy o h compay is h valu of i h quaio ( ) 20( ) ( ) + (1 + ) (1 + ) (1.10) 20(1.10) (1.08) (1 ) + (1 + )

24 (ii) Ralizd yild approach Accordig o his approach, h yild ralizd by quiy sharholdrs hisorically is rgardd as a proxy for h ra of rur rquird by hm. Th yild o a quiy soc for h yar is giv by Y D + 1; 1 whr Y D Yild for yar ; Dividd a h d of h priod payabl a h d of h priod; pric pr shar a h d of h priod ; ad pric pr shar a h d of h priod 1,i.. a h bgiig ofh priod. 1 D + 1 is calld h walh ra. Th yild for h -yar priod is D Th basic assumpios of his approach ar (i) Th yild ard by h ivsor ad h xpcaios of h ivsor ar similar; ad (ii) Th ivsors xpcaios i fuur will b similar o hos i h pas. Exampl 15: Th dividd pr shar ad h pric pr shar daa of a quiy soc ar giv blow Tabl 11.3 Yar Dividd pr shar (Rs.) (D ) ric pr shar (Rs.) ( i ) i

25 Obai h yild for h fiv-yar priod o his soc. Sol: W calcula h walh raio as follows Tabl 11.4 Yar D i (Rs.) ( i ) (Rs.) ( i+1 ) (Rs.) W i D i 1 w i i 1 wi Y Thus h rur o h soc is 15.6%. Howvr, h assumpios of his approach, paricularly h scod assumpio is somwha uralisic. Th ivsors xpcaios chag wih h aicipad chag i ra of iflaio ad subsquly chag i h irs ra srucur. Thus if hisorical rur (yild) is o b usd as a proxy for h fuur ra of rur, appropria cauio mus b a. Howvr, h hisorical figur may srv as a sarig poi o obai simas of h fuur Capial ass pricig modl (CAM) As w hav alrady s, CAM ca b usd for pricig of asss ad porfolios. Also w hav usd his modl for h drmiaio of rquird ra of rur. This mhod is basd o h assumpio ha ivsors limia h usysmaic compo of h ris by divrsifyig hir porfolios fficily 408

26 ad ar dd o b compsad for h sysmaic compo of h ris, which is rflcd i h ba coffici. Howvr du o mar imprfcios, usysmaic compo of h ris may crp io h modl for which h ivsor should b approprialy compsad. Bu his faur is missig from h modl. Aohr limiaio of h modl lis i h isabiliy of h ba. This mas h us of hisorical valu of ba somwha usuiabl. I spi of his limiaio his modl is usd widly i maig fiacial dcisios. (i) Earig pric raio approach Accordig o his approach, h ra of rur rquird by h quiy ivsors is whr E E Expcd arigs pr shar for h x yar Curr arigs pr shar(1+growh ra of arigs pr shar) Curr mar pric pr shar. Th approach ca b usd approprialy wh (i) Th arigs pr shar ar xpcd o rmai cosa ad h dividd payou raio is 100%; Th cos of quiy capial i his cas is h valu of i h xprssio D 1 (1 + ) D D (ii) Wh h raid arigs ar xpcd o ar a ra of irs qual o h ra of rur rquird by h ivsors. 409

27 As a simpl cas, l h firm b a all-quiy firm. L h rio ra of h firm is b% i ach priod which is cosa. Sic h rivsd fuds ar a rur qual o %, h arigs, raid arigs ad h dividds ar giv by h followig xprssios Tabl 11.5 Yar Earig Raid arigs Dividds 0 E E b E (1-b) 1 E 0 (1+ b ) E 0 (1+ b ) b E 0 (1+ b ) (1-b) 2 E 0 (1+ b )+ E 0 (1+ b ) b E 0 (1+ b ) 2 E 0 (1+ b ) 2 b E 0 (1+ b ) 2 (1-b) 3 E0 (1+ b ) 3 E 0 (1+ b ) 3 b E 0 (1+ b ) 3 (1-b) M M M M E 0 (1+ b ) E 0 (1+ b ) b E 0 (1+ b ) ( 1-b) Now, 1 D (1 + ) E (1 + b ) (1 b) 1 0 (1 + ) E (1 + b )(1 b) E (1 b) 0 1 E 1 Howvr boh hs siuaios ar difficul o m i pracic. As such his mhod should b usd wih cauio. (ii) Bod yild plus ris prmium approach Accordig o his approach, h ra of rur rquird by h quiy ivsors is giv by 410

28 Yild o h log-rm bods of h firm + ris prmium. Th approach rss o h assumpio ha h quiy ivsors hav a highr dgr of ris ha h bodholdrs ad hc hir rquird ra of rur should iclud a ris prmium i addiio o h rur ard o h log-rm bods. Howvr, hr is o soud horical basis for dfiig h ris prmium ad i is subjciv quaiy basd o opraig ris ad h ris prfrc of h firm. Adjusm for h floaaio cos Th firm should hus ar a ra of rur qual o h ra rquird by h quiy soc holdrs of h firm. Howvr his assrio is ru wh hr is o floaaio cos, for xampl, cos of issuig shars, commissio, brorag c. This will, hus b ru i cas wh h firm obais h quiy fuds from is raid arigs. Howvr, wh a firm raiss fuds by issuig (addiioal) quiy soc, grally floaaio cos is icurrd. I his cas h fuds ralizd by h firm ar lss ha wha has b coribud by h quiy holdrs. I his cas, h firm should ar a ra of rur highr ha h rquird ra of rur by h quiy holdrs o a car of his addiioal cos. Mahmaically, if h floaaio cos is f %, ad h rquird ra of rur is %, h h firm should b abl o ar a ra of rur qual o 1 f % o h quiy fud raisd by i. Wighd avrag cos of capial Oc h cos of diffr sourcs of fiac has b drmid, h firm s ovrall cos of capial is h wighd avrag cos of diffr sourcs of fiac. Mahmaically, a wdd + wpp + wrr + w whr a Ovrall cos of capial; 411

29 d cos of db; w wigh of db; d p cos of prfrrc capial; w p wigh of prfrrc capial; r cos of raid arigs; w r wigh of raid arigs; cos of addiioal quiy; w wigh of addiioal quiy. If h oly sourcs of fiac ar quiy ad db (as i cas of a w compay), h w + w d d Md M d + ; V is h oal valu of h firm. V V M M d d + Md + M Md + M M I M d d d M d d + M + M + NI + M EBIT V EBIT I EBIT Id d + V d M - d V M V d M d d V M d 1 V M + ( d) M M d M d + ( d ) M 412

30 Exampl 16: Cosidr h iformaio availabl abou h four firms A, B, C ad D Tabl 11.6 Firms EBIT (Rs.) I d (Rs.) (%) A 4,00,000 40, B 6,00,000 1,00, C 5,00,000 1,00, D 8,00,000 2,00, Assumig o axs ad h cos of db a 10%, calcula h oal mar valu ad wighd avrag cos of capial of ach firm. Sol: Tabl 11.7 ariculars A B C D EBIT (Rs.) 4,00,000 6,00,000 5,00,000 8,00,000 Lss: Irs (Rs.) 40,000 1,00,000 1,00,000 2, 00,000 NI (Rs.) 3,60,000 5,00, 000 4,00,000 6, 00, M (Rs.) 30,00,000 50,00, ,00,000 40,00,000 I d M d (Rs.) ,00,000 10,00,000 10,00,000 20,00,000 V (Rs.) EBIT (%) V 34,00,000 60,00,000 30,00,000 60,00, Sysm of wighig Assigm of wighs o diffr sourcs of fiac is a impora aspc i drmiai o of h ovrall cos of capial o h firm as variaio is wighs would lad o variaio i h oal cos of 413

31 capial. Svral mhods hav b proposd for drmiaio of wighs. W di scuss hr som of hs mhod. (i) Boo valu mhod I his mhod, h wighs ar assigd accordig o h val us foud i h balac sh of h firm. Th wighs ar h proporio of h boo valu of h sourc of fiac o h oal valu of (log- rm) fiac of h firm. Th boo valu mhods ar simpl o obai ad ar fairly sabl sic boo valus ar o affcd by h mar flucuaios. A ims hs may b h oly availabl wighs.g., h mar valus ar o asily availabl if h firm is o lisd or is shars ar o acivly radd i h mar. Howvr, h mhod suffrs from a umbr of drawbacs. Firs of all, h prs valus of diffr sourcs of fiac may o b much rlad o hir boo valus. Scodly boo valu wighs do o go wih h cocp of h cos of capial, which is h miimum rquird ra of rur o maiai h mar valu of h firm. (ii) Mar valu wighs I his mhod, h wighs ar assigd accordig o h mar valus of h sourcs of fiac of h firm. Th wighs ar h proporio of h mar valu of h sourc of fiac o h oal mar valu of fiac of h firm. Thus hs wighs ar cosis wih h cocp of h cos of capial. Howvr hss wighs may b difficul o obai if h firm is o lisd or is shars ar o acivly radd i h mar. Furhr h spculaiv forcs worig i h mar may disor h wighs. (iii) Fiacig plaig wighs I his mhod of assigig wighs, wighs ar assigd o diffr sourcs of fiac i h proporios i which hss sourcs ar providig fuds o udra prs ad h fuur ivsms. Thus hs wighs ar i acual proporio of h sourcs of fiac ha would corrspod o h mar valu of hs sourcs. Howvr h acual mix of capial dd o fiac fuur ivsms may b difficul o obai. 414

32 Exampl 17: Cosidr h followig daa Capial srucur of h firm As o March 31 s, 2006 Tabl 11.8 Boo valu (Rs. i crors) Mar valu (Rs. i crors) Dburs (8.5% du ) Dburs (11% du ) Log-rm loa (10%) rfrc capial (7%, mar pric pr shar Rs. 50) N worh Equiy dails Tabl 11.9 Valu (Rs.) Earigs pr shar Dividd pr shar Bous 1:12 Adjusd arigs pr shar* Adjusd dividd pr shar* Mar pric** * Adjusd for bous dclaraio i 2001 ** Mar pric is h avrag of high ad low i h moh wh capial srucur has b drmid. Th ffciv ax ra for h compay is 57.75%. Calcula h cos of capial for h firm. Sol: ( i) os ax cos of 8.5% dburs du Ths d burs carry a irs ra of 8.5% ad ar rpayabl i fo ur aual qual isallms sarig from Th mar valu pr Rs. 100 fac valu of h dbur was Rs. 87 i March Th pos ax cos of hs dburs is ha discou ra which would qua h prs valu 415

33 of h pos-ax cash ou flows (irs ad h pricipal rpaym) wih h mar valu, i.., h valu of d i h xprssio ( ) 8.5( ) 8.5( ) 8.5( ) ( 1+ ) ( 1+ ) ( 1+ ) ( 1+ ) d d d d 6.375( ) ( ) ( ) % d ( 1+ ) ( 1+ ) ( 1+ ) d d d (ii) os ax cos of 11% dburs du Ths dburs ar payabl i fiv qual aual isallms. Th pos ax cos of hs dburs is h valu of d i h xprssio 10 11( ) 11( ) ( ) ( 1+ ) ( 1+ ) ( 1+ ) 6.6( ) ( ) ( ) ( 1+ ) ( 1+ ) ( 1+ ) % d d d d d d d (iv) os ax cos of 10% log-rm loa l ra of irs(1-ax ra) 10( ) 4.225% (v) os ax cos of 7% prfrc capial For prpual prfrc capial h cos of capial is giv by p Aual dividd 7 14% Mar pric

34 (vi) os-ax cos of quiy D p g whr g Acual growh ra of dividds ovr h priod (1 + g) 8 g 3% Now, D p % Th w hav Tabl Sourc of capial Wigh (Mar valu) Cos of h sourc Dburs (8.5%) Dburs (11%) Log-rm loa rfrc capial Equiy Cos of capial % 11.7 Margial cos of capial Till ow, w hav b assumig ha h cos of capial rmais h sam irrspciv of h amou of big raisd. Howvr, his is a simplifid assumpio ad usually h cos of capial icrass afr crai amou. This icras i cos whil raisig addiioal fuds for h firm is calld h margial 417

35 cos of capial. To illusra his poi cosidr h followig siuaio wh a firm has h followig capial srucur Tabl Sourc of capial Valu (Rs. i lah) Equiy (mar valu) Db (mar valu) Db-quiy raio Rquird ra of rur by curr quiy holdrs (%) Rquird ra of rur by curr dbors (%) Curr arigs roposd quiy dividd roposd raid arigs Cos of raisig addiioal quiy (%) Cos of db : Nil Tax ra applicabl o h firm 40% Th h margial cos of capial, which h cos of capial a h margi is giv by (1 0.40) % Howvr, a his cos of capial h firm cao rais ulimid fud. As h rquirm for h fud riss, h cos of capial is boud o ris. Th capial schdul ca hav jumps a svral pois wh h cos of capial chags. L h addiioal iformaio i h abov schdul b as follows (i) Th rquird rur o firs 40 lahs of quiy is 15% ad o h x 60 lah is 16%. (ii) Th rquird rur o firs 60 lahs of db is 14% ad o h x 40 lah is 16%. Wha ca b h composiio of h addiioal fuds? To s his, w ca calcula h cos of capial corrspodig of diffr composiio of h addiioal fuds 418

36 Tabl Chu Composiio Avrag cos of capial Firs Rs. 60 lah of raid arigs a cos 15% + Rs. 40 lah of db cosig 14% (1 0.4) 12.36% 5 5 Scod Rs. 30 lah of raid arigs a cos % (icludig 5% issu cos) + Rs. 20 lah of db (1 0.4) 12.81% 5 5 cosig 14% Third Rs. 10 lah of raid arigs a cos 15.75% (icludig 5% issu cos) + Rs lah of db cosig 16% (1 0.4) 13.29% 5 5 Fourh Rs. 50 lah of raid arigs a cos 16.8% (icludig 5% issu cos) + Rs lah of db cosig 16% (1 0.4) 13.92% 5 5 Svral ohr combiaios ar possibl for calculaig h cos of capial Graphically h siuaio is Margial cos of capial (%) Exral quiy a 15% is 14. ha sd % db is xhausd 12. Raid arigs ar xhausd Capial Fig

37 11.8 Margial cos of capial ad capial budgig Whil valuaig capial projcs, h margial cos of capial is a io accou. A projc is worhwhil if i has a posiiv NV discoud a a ra qual o is margial cos of capial. If h margial cos of capial is cosa, h as w hav s, h valuaio of projcs is do wih h xisig cos of capial sic ha will b h margial cos of cap ial also. Howvr if h margial cos of capial is icrasig h w procd as follows. ( i) Drmi all hos projcs, which hav a posiiv NV for ach lvl of fiacig bfor a jump i h margial cos of capial schdul. (ii) Choos h lvl of fiacig ad h corrspodig s of projcs ha has h highs NV. Cosidr h followig simad margial cos of capial schdul for a firm Tabl Lvl of fiacig (Rs. lah) Margial cos of capial (%) For ach lvl of fiacig, h firm firs of all chooss h s of all h projcs wih posiiv NV. L h NV b giv as follows Tabl Lvl of fiacig (Rs. lah) NV (Rs.) Th highs NV is obaid wh h firm raiss Rs. 150 lah of fiacig. 420

38 11.9 Ivsm ad fiacial dcisios Th us of wighd avrag cos of capial is basd o h assumpio ha vry projc is fiacd by h sam db-quiy (or ay ohr proporio of sourcs of fiac) mix. Howvr, h siuaio may o b always so ad diffr projcs may vary for h db capaciy ad ohr faurs li subsidiaris ad ohr rlaxaios. Th impac of fiacig o capial budgig is masurd by h followig wo mhods (i) Adjusd NV mhod Th adjusd NV of a projc is h NV calculad afr maig adjusms for h impac of fiacig o h projc. Adjusd NV Bas cas NV + NV of h fiacig dcisios associad wih h projc whr bas cas NV is h N V of a all-quiy projc. Exampl 18: Cosidr a projc ha ds a ivsm of Rs. 50 lah. I is xpcd o produc a cash flow of Rs. 10 lah pr yar for igh yars. Th rur dd by h quiy holdrs of h projc is 16% ad h cos of issuig h quiy is 4%. Th firms ca rais Rs. 16 lah of h ivsm dd by db a 12% irs ad will b rpaid i igh qual aual isallms ovr igh yars priod, firs isallm du i o yar from ow. Th ax ra applicabl o h firm is 40%. Calcula h adjusd NV of h firm. Sol: Bas cas NV 50,00, ,00,000 (1.15) Rs. 5,13,000 Now, w calcula h adjusm facor 421

39 (i) Adjusm for h issu cos N quiy fiac Rs. (50 Cos of issu 4% 16) lah Rs. 34 lah 34,00,000 Toal quiy soc o b issud Rs. 35,41, Th diffrc of Rs. 1,41,667 is h cos rlad o h issu of h w quiy soc. (i) Adjusm for h ax shild associad wih h db Yar Tabl 11.15: rs valu of ax shild Db ousadig (a h bgiig of h yar) (Rs. lah) Irs (I d ) (Rs. lah) Tax shild (Rs. lah) rs valu of h ax shild (Rs.) Tax shild (1 + r) , , , , , , , , Toal 3,08,571.4 Adjusd NV Bas cas NV NV of h issu cos + NV of h ax shild 5,13,000 1, 41, ,08,571.4 Rs. 3, 46,095.6 Sic h adjusd NV of h projc is gaiv, so i should o b accpd. 422

40 (ii) Adjusd cos of capial mhod Cosidr h followig xampl Exampl 19: Followig ar h fiacial dails of a w projc udr cosidraio ariculars Ivsm dd (Rs. lah) Aual pos-ax savigs (Rs. lah) Lif of h projc (yars) Tabl Valu (Rs.) 50 5 rpual Db capaciy of h projc (Rs. lah) Irs o db (%) Lif of db (yars) Tax ra of h firm (%) Rquird ra of rur (%) rpual Fid whhr h projc is worh accpig. Sol: 5,00,000 Bas cas NV 50, 00, Rs. 8,33, 000 Aual valu of ax-shild 30, 00, Rs.1,20,000 1,20,000 rs valu of ax-shild Rs.12,00, adjusd NV Rs. 8, 33, Rs.12, 00, 000 Rs.3,67,000 Thus h NV of h projc is gaiv wh i is a all-quiy projc. Howvr h projc bcoms accpabl wh i is parly fiacd hrough db. As log as, h adjusd NV of h projc is 423

41 posiiv, i should b accpd. Th adjusd NV is posiiv ill bas cas NV is mor ha Rs. 12,00,000. Calculaio of adjusd cos of capial If h bas cas NV is Rs. 12,00,000, h h aual icom corrspodig o i is aual icom 12,00,000 50,00, aual icom Rs. 4,56,000 Sic h lif of h projc is prpual ad h cash flows ar cosa so h IRR corrspodig o his accpabl icom is IRR Aual cash flow Iiial ivsm 4,56, % 50,00, Dividd policy Dividd rfrs o ha par of a firm s profis, which ar paid o h sharholdrs (quiy holdrs) of h firm. Th dividds ar complmary o h rio of h arigs by h firm. Rio of arigs is a major sourc of fiacig h ivsm rquirms of h firm. So, largr dividds may affc h fiacig of h w ivsm proposals. Thus h wo (alraiv) uss of h arigs of a firm ar compiiv ad coflicig. Th a major dcisio problm of h maagm is o sri a balac bw h wo wih a objciv of h maximizaio of h sharholdrs walh. Thus h profis should b disribud o h sharholdrs if i lads o h maximizaio of h sharholdrs walh. If o, arigs should b raid wih h firm wih a objciv of fiacig h fuur ivsm proposals. Th h problm of h dcisio mar is h appropria allocaio of h arigs io h wo uss of h arigs, viz., h dividds o b paid, ad h arigs o b raid o fiac h fuur projcs. 424

42 11.11 Drmias of h dividd policy Dividd policy is a igral par of h ivsm policy of a firm. Th choic of a appropria dividd policy iflucs h valu of a firm. Howvr, if h dividds ar i xcss of h appropria quaiy, h raid arigs will fall shor of h capial dd o fiac fuur projcs. I such siuaios h firms will hav o rais fuds xrally o fiac h fuur projcs. Thus a balac is dd o b maiaid i payig h dividd ad h rio of h arigs. As such, hr ar svral drmias of h dividd policy. (f) Dividd pay-ou raio (D/ raio) D/ raio is h proporio of h oal arigs o b paid i cash o h sharholdrs (quiy holdrs) of h firm. Mahmaically, Cash dividd pr shar D/ raio 100 Earigs pr shar Accordig o h Walr s modl of dividd policy, h opimal dividd policy of h firm is drmid by h firm s iral ra of rur (r) ad h firm s cos of capial (). Th firm should disribu is arigs amog h sharholdrs if r <, i.., if h rquird ra of rur xcds h iral ra of rur. I his cas, h sharholdrs will b abl o rivs hir arigs o ar a highr rur ha wha could hav b ard if h firm had raid h arigs. Alraivly, if r >, h h firm is abl o ar mor ha wha h sharholdrs could ar if h arigs ar paid o hm i h form of h dividd. Th objciv of h firm i boh h siuaios would rmai h sam, i.., h maximizaio of h sharholdrs walh. To pu h sam argum i a alraiv form, a firm ha has adqua profiabl ivsm opporuiis (a growh firm) should adop a policy of zro dividd payou raio bcaus h rivsm of h raid arigs will maximiz h rur of h firm ad cosquly h mar pric of h shars will b maximizd. If h firm dos o hav suffici profiabl ivsm opporuiis, h a D/ raio of magiud 100 would provid ivsors a opporuiy o ar a highr rur ad as a rsul, h mar pric of h shars will b maximizd. 425

43 For r, h mar pric of h shars will rmai h sam ad hc ay prcag of h arigs (from 0 o 100) could b disribud as dividd ad h firm dos o hav a opimal dividd policy. Udr som assumpio, h rlaio bw h mar pric of h shars ad h dividd o b paid ca b word ou usig Walr s modl Assumpios of h Walr modl 1. Thr ar o xral sourcs of fiac.g., xral db, or w quiy shars. All h fiacig is do hrough raid arigs oly. 2. Th busiss ris of h firm dos o chag wih h w ivsms. I ohr words for w ivsms, h srucur of r ad will rmai h sam as h xisig srucur of r ad. 3. Th y variabls, i.., h arigs pr shar E ad h dividd pr shar D, will rmai h sam. 4. Th firm has prpual or al las vry log lif. Udr hss assumpios, w ow ha h cos of h quiy is giv by D + g (11.4) whr D Cos of h quiy capial; Iiial dividd; ric pr shar; ad g Expcd growh ra of arigs. Sic all h fuur fiacig is o b do from raid arigs oly so g rb (11.5) whr b rio raio E D E 426

44 E D g r E (11.6) Now, g (11.7) r ( E D ) (11.8) ad D + (11.9) Th from (11.7), (11.8) ad (11.9), w hav r D + ( E D) (11.10) Or r D + ( E D) D r 1 + ( E D) (11.11) D + Th facor h facor D of h quaio is h prs valu of all h dividds (h firm has prpual lif) ad is h prs valu of all h capial gais (chags i h prics of h shars). Thus h mar pric of h shars i all-quiy firm is h sum of h prs valu of all h dividds ad h prs valu of all h capial gais. To udrsad h ffc of h dividd policy o h mar pric of shars accordig of h Walr s modl of dividd policy, cosidr h followig xampl 427

45 Exampl 20: Th cos of capial of a firm is 10% ad h arig pr shar is Rs. 20. Wha will b h mar pric of h shars of h firm accordig of h Walr s modl of dividd policy if h ra of rur (r) o h ivsm is (i) 15%; (ii) 10%; ad (iii) 8%? Th D/ raios ar giv o b (i) 0; (ii) 20; (iii) 40; (iv) 50; (v) 60; (vi) 80; ad; (vii) 100. Sol: (i) r 15% (a) D/ raio 0 dividd pr shar (20 0) Rs. 300 (b) D/ raio 20 dividd pr shar Rs. 4 (20% of 20) (20 4) Rs. 280 (c) D/ raio 40 dividd pr shar Rs (20 8) Rs. 260 (d) D/ raio 50 dividd pr shar Rs (20 10) Rs. 250 () D/ raio 60 dividd pr shar Rs (20 12) Rs

46 (f) D/ raio 80 dividd pr shar Rs (20 16) Rs. 220 (g) D/ raio 100 dividd pr shar Rs (20 20) Rs. 200 Similarly, w ca calcula h mar pric of shars for ohr wo ras of rur ad w hav h followig abl D/ raio Tabl Mar pric of shars (R s. ) wh r 15% 10% 8% W ca obsrv h followig pois (i) If r >, h pric of h shars is ivrsly rlad o h dividd payou raio. I his cas, h opimal dividd policy is o pay zro dividds. (ii) If r <, h pric of h shars is dircly rlad o h dividd payou raio. I his cas, h opimal dividd policy is o pay 100 prc dividds. (iii) If r, h pric of h shars is o rlad o h dividd payou raio ad is a cosa. I his cas, hr is o opimal dividd policy. 429

47 Howvr h capial mar is imprfc ad h fuur is ucrai. I hs siuaios, h ivsors would o prfr o forgo prs arigs i h hop of rcivig a br dividd i h fuur. As such 100% rio of h arigs by h firms is a horic cocp. So v if h firms may hav good opporuiis o ivs raid arigs, sill a low D/ raio may caus a dcli i h mar p ric of h shars of h firm. I such siuaios, h provisios of fiacig bcom scodary objcivs of h dividd policy of h firms. (ii) Sabiliy of dividds This is h scod aspc affcig h dividd policy of a firm. Sabiliy of dividd has wo aspcs- rgulariy of dividds ad paym of a miimum crai amou. Thus sabl dividds ar cosis wih rspc o im ad magiud. Nd for sabl dividds A (sabl) dividd policy has a dirc barig up o h mar pric of h shars of h firm. Thr svral rasos ha ca b aribud o his bhavior xhibid by h ivsors. (a) Dsir for a sabl icom Som ivsors prfr rgular curr icom o h highr dividds i fuur. Th popl wih o ohr sourc of rgular icom, for xampl, rird prsos ad sior ciizs, viw dividd as a sourc of fuds o m hir rquirms. If h dividds ar o sabl, h hy migh fid i difficul o m hir rgular xpss i cas dividds dcli. As a rmdy, hy may hav o sll (a par of) hir soc i ordr o m hir rquirms. O h ohr had, if h dividds hy rciv is mor ha hir rquirms, h hy migh rquir rivsig hir addiioal icom. Boh h siuaios may b icovi o hm as i ivolvs a lm of cos (rasporaio cos, commissio, brorag c.) bsids 430

48 physical icovic. Such ivsors prfr sabl icom (dividd) for which hy ar rady o pay highr prics also. (b) Iformaio widow This aspc of sabl dividds is usful from h mar as wll as maagm s poi of viw. Ivsors viw dividd as idicaors of h firm s prformac. If dividds ar sabl, h a chag i h dividds is a idicaor of h log-rm chags i h (xpcd) arigs of h firm. Thus sabl dividds rduc ivsors ris by givig idicaio abou h firm s prformac. O h ohr had, a usabl dividd policy will icras ivsors ris sic hy would o b abl o pp io h firm s fuur prformac. Thus a sabl dividd policy srvs as a iformaio widow for ivsors ad isills h cofidc of mar i h firm. (c) Isiuioal ivsors Isiuioal ivsors li isurac compais or muual fuds c., by viru of hir siz ad h capaciy o ivs, ar a sigifica mar forc i h capial mars. Du o hir rur obligaios, hs isiuioal ivsors ar rquird o ivs hir fuds i hos compais, which hav a rcord of uirrupd ad coiuous sabl dividd policy. Th bul buyig of soc by hs ivsors hacs h mar pric of h shars ad hc h worh of h firm. (d) Capial mar imprfcios By prfc capial mars, w ma a mar whr hr ar o axs, floaaio coss, rasacio coss, ad ohr chargs. As a rsul h ivsors ar idiffr o paym of dividds or h rio of arigs by h firms. Bu his is o h siuaio ad h capial mars ar imprfc. Taxs ar hr ad ar diffr for capial gais ad icom from dividds. Furhr axs ar icrmal. As a rsul, h ivsors from h lowr ax bracs dm paym of dividds a br opio ha h rio of arigs by h firms. 431

49 Form of sabl dividds Sabl dividds ca b i o of h followig forms (i) Cosa dividd pr shar I his form of dividd policy, a crai fixd sum is paid as dividds ach yar. For xampl, dividd may b a crai prcag of h fac valu of h shar. Th, h sam amou will b paid vry yar irrspciv of whhr or o h firm has ard profis. Ev if hr ar flucuaios i h arigs of h firm, dividd sram will rmai sabl. If h dividd icrass, h icras will b maiaid for somim bfor h x icras. ES DS (Rs.) ES DS Yars Fig As is vid from h figur, dividds rmai sabl v if h arigs of h firm flucua. I such siuaios, h firm will hav o ma provisios for dividd o b paid i hos yars wh h arigs ar o suffici o pay h dividd. Th balac sadig i such a fud is calld h rsrv for h dividd qualizaio. This fud ca b ivsd i hos asss, which ca asily b liquidad. This form of dividd policy is cosidrd o b h bs by h ivsors sic hy ar gig assurd dividds for hir ivsms. Thr is o lm of irrgulariy ad ucraiy i rcivig of h icom. 432

50 (ii) Sabl dividd payou raio This is h scod form of sabl dividds. I his policy, h firms pay a cosa or fixd prcag of h arigs as dividds. Howvr, if h arigs ar o sabl, h udr his policy, h dividds will also flucua. If a som poi of im h arigs ar vry low or hr ar losss, h dividdss will pracically b il. This siuaio is good from h maagm s poi of viw sic hy would o hav o pay dividd if h arigs ar low ad if h arigs ar good, hy will hav suffici fuds o rai for fuur ivsms. Howvr his siuaio is o good from h ivsors poi of viw sic hr is o assurd dividd (rur) for hir ivsms. Thus h lm of ucraiy crps i. (iii) Sabl rup dividd plus xra dividd I his form of sab l dividds, h firm pays a miimum crai sum o h sharholdrs. I addiio if h arigs o f h firm ar abov ormal, alog wih rgular dividd som addiioal dividd is paid. Wh h firm ars ormal icom, i will gai ur ovr h ormal dividd. From h ivsors poi of viw, his siuaio is o cosidrd as good sic i his cas ivsors ow ha h icom ha hy ar rcivig is o prma ad hir rur will dcli if h arigs of h firm bcom ormal. Agai hr is a lm of ucraiy. Th d for a sabl dividd policy is suppord by Gordo s modl also. Gordo s modl for dividd policy Th modl is basd o h assumpio ha h ivsors ar ris avrs popl. As a rsul, hy would pu a prmium o h curr icom. Th curr icom limias h lm of ris, which is h ucraiy i rms of im ad amou of rurs. Th firms rai arigs so ha a highr dividd ca b paid i fuur. Bu h fuur is ucrai so a ris avrs ivsor would prfr curr icom o h fuur icom. Thus h raid arigs would hav a highr discou ra ad cosquly 433

51 h mar pric of h shars of a firm, which has highr raid arigs, would dcli. I ordr o avoid ucraiy, h ivsors ar willig o pay a highr amou hus icrasig h valu of h firm. Assumpio of h modl 1. Th firm is a all-quiy firm. This mas ha hr is o ohr sourc of fiac ad all h ivsms ar fiacd by raid arigs oly. 2. Th cos of quiy ad h ra of rur o h firm s ivsms r ar cosa. 3. Th lif of h firm is (pracically) prpual. 4. Th rio raio b is cosa. As a rsul, h growh ra g ( rb) is also cosa. 5. Th cos of quiy is grar ha h growh ra, i.., > g ( rb). Graphically h argum ca b prsd as follows Discou ra Rio ra Fig Mahmaically, udr h assumpios of h modl h pric of a shar is giv by 1 D (1 + br) 1 E(1 b) (1 + br), E is h arigs pr shar E(1 b), as h lif of h firm is prpual. br To udrsad h implicaios of his formula, cosidr h followig xampl 434

52 Exampl 21: Th cos of (quiy) capial of a firm is 20% ad h arig pr shar is Rs. 20. Wha will b h mar pric of h shars of h firm accordig of h Gordo s modl of dividd policy if h ra of rur (r) o h ivsm is (i) 15%; (ii) 10%; ad (iii) 8%? Th D/ raios ar giv o b (i) 0; (ii) 20; (iii) 40; (iv) 50; (v) 60; (vi) 80; ad; (vii) 100. Sol: Hr E Rs. 20 pr shar 20% Th w hav Tabl D/ raio (1 - b) Rio raio (b) Mar pric of shars (Rs.) wh r 15% 10% 8% g ( rb) E(1 b) br g g Thus h dividd policy affcs h mar valu of h firm. Lir s modl of dividd policy A auorgrssiv modl, Lir s modl of dividd policy is basd o h assumpio ha dividds ar afr ffcs of h arigs ad hc lag bhid h arigs for o or mor priods. Mos of h 435

53 firms hav wo compos of dividd policy a sabl rup amou of dividds ad h (logrm) arg pay ou raio. Th priod-o-priod dividds may o b sam as h arg pay ou raio, which h firms aim a. I ordr o avoid ay coflic bw h payou policy ad h arigs wh h arigs ar la, h firms rais h dividds gradually. Dividds, accordig o his modl, ar fucios of arigs of ha yar, xisig dividd ra, h arg pay ou raio, ad a muliplir rprsig h spd of adjusm (parial adjusm modl). Th chag i h dividds i h coscuiv im priods is giv by D D a + α * 1 0 ( D D 1) (11.12) whr h D Dividd paid i T im priod; T, -1 T a Cosa ( 0 0) D * Targ pay-ou raio ( r) r α Dividd pay-ou raio rofi afr axs Spd of adjusm. R.H.S. of (11.12) ca b rwri as D D + a + α( r D ) 1 0 a + αr + (1 α) D a + α( r D ) 0 1 a + β + β D whr β αr is h shor-rm propsiy o pay dividds; ad 1 β 2 (1 α) is h log-rm propsiy o pay dividds. 436

54 11.12 Cosrais of dividd policy Till ow, w hav b discussig h miimum dividds ha ar o b paid. Howvr h firms cao pay ulimid dividd or a amou a hir wish oly. Thr ar crai cosrais ha pu a cilig o h amou of dividd o b paid. Th dividds ar rsricd by svral facors. (i) Lgal cosrais aym of dividds is o a lgal compulsio or v rquirm. Howvr law dircs h codiios udr which dividds ar o b paid. (a) Capial impairm Accordig o lgal sipulaios, firms cao pay dividds mor ha hir curr icom ad h accumulad pas raid arigs. Th implicaio of his rsricio is ha worig capial of h firm cao b usd for paym of dividds ad h claims of ldrs ad crdiors ar procd sic hy rlid upo h quiy bas of h firm whil xdig crdi o h firm. Thus udr law, h impairm of h capial is illgal. (b) Isolvcy A firm is said o b isolv if is liabiliis bcom largr ha is asss or h firm is o i a posiio o pay is bills. A isolv firm cao pay dividds. Th raso for his rsricio is ha h dividds ar h rsuls of h firm arigs ad h primary liabiliy of h firm is o rir db firs, ad oly h dividds ca b paid. (iii) Coracual rsrais Somims, xral crdiors also impos rsricios o h dividds o b paid. Th rsricios may b o h prcag of arigs o b paid as dividds, h absolu amou o b paid as dividds or o dividd a all ill a crai lvl of arigs is rach d. This rsricio ariss from h fac ha lowr dividds ma highr raid arigs ad hc low db/quiy raio. A low db/quiy raio lads o a largr margi of safy for h ldrs. 437