3. Cost of equity. Cost of Debt. WACC.

Transcription

1 Corporae Fiace [ ] 3. Cos o equiy. Cos o Deb. WACC. Cash lows Forecass Cash lows or equiyholders ad debors Cash lows or equiyholders Ecoomic Value Value o capial (equiy ad deb) - radiioal approach FCFF V = (+ R CV(FCFF) + R ) = A ) (+ A Value o equiy (or equiy holders) V E = FCFE CV(FCFE) R ) + = (+ R E ) (+ E Required Rae o Reur Weighed Avarage Cos o Capial Cos o Equiy Ieres Rae (Cos o Deb) CREDIT RISK RISING ODES Deaul robabiliy odels Sharpe's odel CA AT odel CAITA ASSETS RICING ODES Credi Risk remium odels (e.g. ero odel) BARRA ad oher models

2 Corporae Fiace [ ]. Cos o equiy The cos o equiy is equal o he reur expeced by sockholders. The cos o equiy ca be compued usig he capial asse pricig model (CA) or he arbirage pricig heory (AT) model... Basic Reur ad Risk Coceps Reur Simple rae o reur The relaive reur, or perce reur, or he same period (HY, holdig period yield) is () p p r = p + d p + d p- + = p = p d Two diere ypes o reurs mus be disiguished. A ex ae reur is he ucerai reur ha a ivesor expecs o ge rom a ivesme. The ex pos or realized reur is he cerai reur ha a ivesor acually obais rom a ivesme. Ivesors make decisios o he beeis hey expec rom a ivesme. The acual oucomes may o mach heir expecaios. The equivale aualized rae is equal o 365 () i = ( + r ) The log price chage (coiuously compouded reur) o a securiy is deied o be he aural logarihm o is gross reur: * () r = l( + r ) = l = l( p + d ) l( p ) p + d p The expeced reur rom a ivesme is he average reur rom he ivesme ad may be calculaed as he probabiliy-weighed sum o all possible reurs: () E ( ri ) = k i= p r i i I his deiiio p is he probabiliy o a paricular reur. Equaio requires ha each reur be muliplied by is probabiliy o occurrece ad he all hese producs be added ogeher. The expeced reur o a porolio is 0 (3) E ( r ) = = wr + wr + + wr (4) E(r p ) = w r = 0 where w is he proporio (weigh) ivesed i securiy, ad r is he expeced reur o securiy. The expeced reur rom a wo-asse porolio, is give as E r = w r + w (5) ( ) r

3 Corporae Fiace [ ] Risk The mos popular ad radiioal measure o risk is he variace or he sadard deviaio o a disribuio. The variace ( ) o reurs rom a ivesme is he sum o he probabiliy-weighed squared deviaios o reurs rom he mea: k (3) [ ( )] = p r E r I i= i i I Variace is calculaed by idig he expeced reur, idig he dierece bewee each possible reur ad he expeced reur, squarig his value, muliplyig i by he probabiliy o ha occurrece, ad summig his resulig value over all possible occurreces. The variace o a wo asse porolio is calculaed as (6) = w + w + wwρ The variace o a asse porolio is calculaed as (7) = w T Vw = [ w w... w ] or (8) = u T Ru = [ w w... w ] ρ ρ ρ ρ O w w w ρ ρ w w w The sadard deviaio () o reurs is he square roo o he variace o he disribuio. O (4) = robabiliy Disribuios A probabiliy disribuio is a collecio o he diere possible oucomes rom a ucerai variable ogeher wih he probabiliy o each possible oucome. robabiliy disribuios o reurs are esimaed usig acual hisorical daa. The iormaio coaied i he disribuio may be summarized i wo simple measures:. expeced reur rom a ivesme,. riskiess (or variabiliy) o hese reurs. 3

4 Corporae Fiace [ ] Diversiicaio ad orolio Risk Diversiicaio is he process o reducig risks by ormig a porolio o imperecly correlaed securiies. Ivesors ca lower heir risks by ormig porolios o ge he beeis o diversiicaio. Naure o he Risk Compoes I is coveie o divide oal risk (variace risk) io wo disic compoes: udiversiiable risks (he covariace risk) ad diversiiable risk (he remaiig risk i he porolio). Udiversiiable risks are marke risks, also kow as sysemaic risks (bea risks). arke risks represe ha compoe o oal risk ha are sysemaically depede o he vagaries o he U.S. ecoomy. Uique (diversiiable) risks are risks ha are speciic o a compay. These are risks ha ca be diversiied away by ormig a large porolio... CA arkowiz porolio heory The basic arkowiz model shows he relaio bewee expeced reur ad expeced risk measured as he sadard deviaio o expeced rae o reur. The las depeds o correlaio bewee reurs o asses. A ivesme is cosidered o be eicie i o oher ivesme oers higher expeced reur wih he same (or lower) level o risk, or lower risk wih he same (or higher) expeced reur. The eicie roier represes he se o porolios ha has maximum rae o reur or every give level o risk, or he miimum risk or every level o reur. The uiliy ucio deermies which paricular porolio o he eicie roier gives he highes value or a ivesor. The opimal porolio is he eicie porolio ha has he highes uiliy. There are diere uiliy ucios or coservaive ad aggressive ivesors. Rae U U uiliy ucios o B Reur eicie roier r B A r A C (o eecive ivesme) A B Risk E() 4

5 Corporae Fiace [ ] Capial arke ie The maor acor ha allowed porolio heory o develop io capial marke heory is he cocep o risk-ree asse. I is a asse wih zero variace ad zero correlaio wih oher asses. Risk-ree asse provides he risk-ree rae o reur (R ). The sadard deviaio o a porolio ha combies he risk-ree asse wih risky asses is he liear ucio o he sadard deviaio o he risky asses porolio. A ivesor may wa o achieve higher reur ha is available a poi accepig higher risk. She may borrow a he risk ree rae ad ives i he risky asse porolio. Boh reur ad risk icrease liearly beyod poi. A ivesor may also wa o achieve lower reur ad lower risk. This ime she should ives par o her moey i he risk-ree asse. The porolio () ha icludes all risky asses is reerred o as he marke porolio. I is a compleely diversiied. Oly sysemaic risk remais i he marke porolio. C becomes he eicie roier o porolios. Ivesors may selec ay poi o he C. Tobi called his divisio o he ivesme decisio rom he iacig decisio he separaio heorem. Ivesor iiially decides o ives i he marke porolio (ivesme decisio). The based o her risk preereces, she has o led or borrow (iacig decisio) o aai he preerred poi o he C. Rae o Reur r B edig B Borrowig C R A A B Risk E() CA ad S ricig model delivers discou rae used i valuaios, especially i pricig shares. CA delivers discou rae (RRR, required rae o reur or equiy holders, which is equal o he cos o equiy or a compay). Because all ivesors wa o be o he C, a asse s covariace wih he marke porolio appeared o be he releva measure o risk. This sep akes us io he capial asse pricig model (CA) ad he securiy marke lie (S). Bea is a sadardized measure o sysemaic risk (covariace wih he marke porolio is divided by he variace o he marke porolio): (9) β = = ρ m m m m 5

6 Corporae Fiace [ ] The Securiy arke ie represes he relaio bewee rae o reur ad risk measured by he bea coeicie. The Securiy arke ie relecs he risk-reur combiaios available or all risky asses i he capial marke a a give ime. Ivesors choose ivesmes ha are cosise wih heir risk preereces; some preer oly low-risk ivesmes ad ohers selec high-risk ivesmes. Rae o coservaive porolio marke porolio aggressive porolio Reur uderpriced securiies S V>0, NV>0 overpriced securiies R R - R β(r - R ) R V<0, NV<0 0,3 Risk (bea) Expeced Rae o Reur ad Risk (CA) The expeced (required rae o reur or shareholders, RRR, equal o he cos o equiy or a compay) is (0) R = R + β [ R R ] β is he bea coeicie o sock i, ad measures he volailiy o he sock s reurs relaive o he marke s reurs R m is he expeced reur o he marke porolio (S& 500, WIG) R is he risk -ree ieres rae. The erm [ R R ] i he CA is called he marke risk premium or bearig oe ui o marke risk. Capial asse pricig model (CA) idicaes wha should be expeced or required raes o reur (RRR) o he risky asses (which is equal o cos o equiy, discouig rae used o value equiy, ad ivesme proecs). I also shows how o creae aggressive ad coservaive porolios. I aswers he quesio, which asses should be seleced o achieve posiive ecoomic prois (value added, wealh creaed, goodwill, NV). I is used o deermie wheher he asse is udervalued, properly valued or overvalued. We ca ow see why CA is called a pricig model. Give he expeced cash lows rom a ivesme (FCFE), he value o he asse is he prese value o hese expeced cash lows, calculaed a he discouig rae provided by he CA (cos o equiy). A asse is priced airly i he marke price is equal o he equilibrium price provided by CA. Wheever a sock is overvalued, i alls below he securiy marke lie (S); wheever i is udervalued, i alls above he S. 6

7 Corporae Fiace [ ]..3 Arbirage ricig Theory The arbirage pricig heory assumes ha he reurs o a securiy are aeced by several acors ha aec he ecoomy. The sesiiviy o sock i s reur o a acor, is he acor bea, β i. I a o-arbirage ecoomy, he ollowig relaioship should hold: () R = R + β [ R R ] + β [ R R ] β [ R R ] F F F F I he AT ramework, a asse ca have as may beas as here are releva acors. The oal risk premium is he sum o risk premiums associaed wih each acor. I appears ha he AT is a simple exesio o he oe-acor CA, i which he marke porolio is he oly releva acor.. Cos o Deb Cos o deb is o a coupo rae or he saed rae i he loa agreeme bewee a compay ad he bak. Whe a compay issues bods, he iacial iermediary (ivesme bak) charges ees, called loaio coss, a he ime he bods are issued. To id he e proceeds o a compay rom issuig bods, we subrac he loaio coss rom he price o he bods. Whe a compay akes a loa, he bak charges provisios. The e proceeds o a compay are equal o he omial loa value less provisios. To id he RRR or he bodholders or baks ad i he same ime he cos o deb or a compay i is ecessary o id he ieral rae o reur o uure cash lows (ieres ad repaymes) ad he acual e proceeds o a compay (wih egaive sig). There is always some risk ha he irm will deaul. I is possible o use oe o wo approaches: adus cash lows wih probabiliies o deaul ad discou hem wih risk ree raes o reur, or discou omial cash lows wih ieres raes which are equal o risk ree raes adused or credi risk premiums ha are depede o he raig o he compay (raigs may be assumed o chage - upgrades ad dowgrades). I is a misake o adus cash lows ad i he same ime use ieres raes ha explicily ivolve credi risk. The described procedures give us he preax required rae o reur or bodholders or baks (cos o deb or a compay). I radiioal approach we may have oe ieres rae (cos o deb), bu i is also possible o derive he erm srucure o cos o deb or a compay. To derive he erm srucure o cos o deb we may use he risk-ree rae erm srucure adused or credi risk premium. The las may be depede o he geeral ecoomic siuaio orecass ad be depede o recovery raes ad also subecive assumpios o upgrades or dowgrades. Sice ieres paymes o corporae deb are ax deducible, deb provides a ax shield. All we eed o do o id aer-ax cos o deb is muliple he preax cos by mius he ax rae. F F 7

8 Corporae Fiace [ ].3 WACC The weighed average cos o capial is a discou rae used i radiioal (FCFF) mehods i capial budgeig proecs. erhaps he mos basic iuiio uderlyig ivesme decisios is ha he reur o ivesme (e asses) mus exceed he cos o capial WACC (sockholders ad bodholders capial) used o iace he ivesme. The WACC is compued i wo simple seps:. Compue he coss o idividual sources o capial - ha is, equiy ad all sources o deb.. Compue he weighed average o hese idividual coss, wih he weighs depedig o he proporio o each compoe i he irm s capial srucure. The bes approach is o use marke values i deermiig he capial srucure. WACC = u k+ uk u k u weigh o iacial source, k cos o iacial source (required rae o reur or ivesors providig capial). We have show ha i is possible o calculae erm srucure or cos o equiy ad cos o deb. So he resul is obvious, we ca also easily calculae he varyig weighed average cos o capial or all uure ime seps. This leads us o o-arbirage approach i calculaig WACC. Quesios:. Aalyze he cos o equiy usig he CA.. Describe he AT heory. 3. Aalyze cos o deb usig YT approach. 4. Explai he reame o loaaio coss or provisios i calculaig cos o deb. 5. Describe he role o axes i cos o capial. 6. Describe he mehods o calculaig he weighs i WACC. 8