4. Levered and Unlevered Cost of Capital. Tax Shield. Capital Structure

Transcription

1 4. Levered ad levered Cos Capial. ax hield. Capial rucure. Levered ad levered Cos Capial Levered compay ad CAP he cos equiy is equal o he reur expeced by sockholders. he cos equiy ca be compued usi he capial asse prici model (CAP, he arbirae prici heory (AP or some oher mehods. Accordi o he CAP, he expeced reur o sock a levered compay is ( ( where is he expeced rae reur o sock a levered compay (levered cos equiy capial, is he riskfree reur, is he bea coefficie sock a levered compay, ad measures he volailiy he sock s reurs relaive o he marke s reurs (sysemaic risk, i is called levered bea, is he expeced reur o he marke porfolio, ( is he marke risk premium for beari oe ui marke risk. levered compay ad CAP equired rae reur for he sockholders a ulevered compay (a compay wihou deb ca be also expressed as a fucio risk freerae reur ad marke premium risk. his ime ulevered bea coefficie is used: (2 ( where: is he expeced rae reur o sock a ulevered compay (ulevered cos capial, is he bea coefficie for a ulevered compay (ulevered equiy bea, allequiy bea..2 Projec Bea aaers e assume ha he cash flows from he projec uder cosideraio will be as risky as he cash flows from he exisi operaios he firm (scaleehaci projecs. his approach is sricly valid for scaleehaci projecs. Whe a firm akes o a projec wih cash flows ha do o have he same characerisics as he firm s exisi asses, i should use he appropriae cos equiy for specific projecs ad o cos equiy for he whole compay. he for a ivesme should be projec specific ad o compay specific. he opporuiy cos for a paricular projec depeds o he projec s risk ad should be deermied by he marke. A projec s releva risk ( proj should be measured i erms he relaioship bewee he reurs eeraed by he projec ad he reurs o he marke porfolio. hus a projec bea measures he sesiiviy chaes i a projec s reurs o chaes i he marke reur.

2 A projec s bea may be esimaed usi hisorical iformaio whe i is available. Whe i is o available he followi procedure may be used:. id a publicly raded compay whose busiess is as similar as possible o your projec. he compay hus ideified is called a pureplay compay. I is beer o work wih idusry beas. 2. eermie he equiy bea,, for he pureplay firm s sock. 3. Calculae he pure play s ulevered equiy bea (asse bea,, from is, by explicily adjusi he for he pure play s fiacial leverae. 4. Calculae he projec s bea proj from is ulevered equiy bea, by explicily adjusi he for he projec s fiacial leverae. 5. id he for your projec, usi he projec s bea proj from ep 4. si amodara s relaioship bewee levered bea ad ulevered bea he he followi formulas are used: ( (ep 3 comp comp ( (2 ( comp proj proj proj (ep 4 proj where comp ad comp represe he marke values he pureplay compay s deb ad equiy, ad comp is he pure play s ax rae. proj ad proj represe he marke values he compay s deb ad equiy used o fiace he projec, ad proj is is ax rae. he equiy risk icreases as he deb equiy raio icreases. Accordi o CAP, he projec s wih a sysemaic risk level proxied by proj (ep 5 is (3 ( proj proj

3 .3 Capial rucure ad irm Value he proporio each compoe capial used by a firm deermies he firm s capial srucure. he compay s capial srucure is e measured by debequiy raio, also called leverae raio. A compay ha has o deb is called a ulevered firm; a compay ha has deb i is capial srucure is a levered firm. How levered should he firm be? Is i possible o deermie opimal capial srucure? Opimal capial srucure is he debequiy raio, ha maximizes he firm s value. heoreically i is easy o esablish he opimal srucure. I pracice his problem is difficul o solve..3. Opimal Capial rucure Wihou axes odiliai ad iller (& hypohesis. Wih riskless deb ad he absece axes, capial srucure is irreleva. he mehod fiaci has o impac o firm s value. As lo as reur o asses is o affeced, he firm s value is idepede is capial srucure. he mos impora assumpios for his irrelevace resul is ha capial markes have o imperfecios such as axes, brokerae fees, ad bakrupcy coss..3.2 Opimal Capial rucure Wih axes odiliai ad iller (& hypohesis 2. Whe a compay pays corporae ax, i should be oally deb fiaced. his is because deb provides valuable ax shields (ax savis..3.3 ax hield Oeperiod ax shield (ax savis for a levered compay is equal o: (3 ax shield * I where is icome ax rae I is he ieres paymes (I is he marke value loerm deb Accordi o & he prese value fuure ax savis ca be foud wih a simple formula: (4 ( I is assumed ha ieres rae is equal o risk free rae ad ha appropriae discou rae is he required rae reur o deb is also equal o risk free rae. I is assumed furher a cosa level deb ( ad a series equal ax savis o ifiiy. Accordi o & heory value ax shields is equal o: (5 he value levered firm is reaer ha he value a ulevered by he prese value ax shields: (6 A

4 .3.4 iacial isress iacial isress ad efaul Cosideraios As he debequiy raio icreases, he probabiliy ha a firm will be uable o mee is fiacial obliaios also icreases. If he credi risk is hih, fiacial disress or defaul may happe. he coss associaed wih defaul are e referred o as bakrupcy coss. here are wo ypes bakrupcy coss: direc ad idirec. irec coss are leal ad accoui fees, reoraizaio coss, ad oher admiisraive expeses. Idirec coss are more difficul o measure. xamples idirec are los sales, los pris, hiher ieres raes (cos deb, ad i he ed he iabiliy o ives i priable projecs because exeral fiaci sources become uavailable. I he case possible defaul, a levered firm s value is lower by he prese value expeced bakrupcy coss. Value levered firm Value ulevered firm Prese value ax shields Prese value bakrupcy coss Value wihou ax wih ax wih bakrupcy coss bakrupcy coss ax shield V / op /.3.5 Aecy Coss Aecy Coss Cosideraios aaers are expeced o ac i he bes ieres owers, bu someimes maaers ac i heir ow ieres. he clic bewee hese ieress is called aecy coss. Aecy coss arise from he clic bewee he ieress he maaers ad he owers a compay. Aecy coss i a levered compay I is supposed ha as a firm icreases is debequiy raio, is aecy coss rise ad, as a resul, he value a levered compay is lower. Bu oher viewpois sues ha aecy coss ca decrease wih deb. ice i is difficul o measure aecy coss, i is ucerai o wha exe hey ifluece he marke value a levered compay.

5 Value value wih ax shield I III II bakrupcy coss aecy coss V / op /.4 Levered Bea ad ax hield elecio he relaio bewee levered bea ad ulevered bea or aleraively he appropriae way calculai he value ax shield is esseial. I is a misake for example o use amodara s formula for levered bea ad i he same ime iller ad odiliai formula for a ax shield. he precise relaioship bewee levered bea ad ulevered bea deermies cos equiy capial ad i he same ime uiquely deermies he value ax shield. he chose relaioship or ierdepede paricular ax shield defiiio iflueces he value a asse or NPV i capial budei. iffere ax shield defiiios are preseed by: odiliai i iller, 2 yers 2, 3 iller 3, 4 iles ad zzel 4, 5 Harris ad Prile 5, 6 amodara 6, 7 eradez praciioers mehod 7. 8 eradez ocosleverae, 9 eradez wihcosleverae, 0 arciiak decomposiio mehod 8.. odiliai,. iller (963, Corporae Icome axes ad he Cos Capial: A Correcio, America coomic eview, Jue 963, s C. yers,.c., Ieracios Corporae iaci ad Ivesme ecisios Implicaios for Capial Budei, Joural iace, arch 974, s iller, eb ad axes, Joural iace, ay 977, s J.A. iles, J.. zzell, he Weihed Averae Cos Capial, Perfec Capial arkes ad Projec Life: A Clarificaio, Joural iacial ad Quaiaive Aalysis, epember ad iles, J.A. ad J.. zzell, eequaioi ax hield Valuaio: A Noe, Joural iace Vol XL, 5, ecember 985, s Harris i J.J. Prile, iskadjused iscou aes xesios form he Averae isk Case, Joural iacial esearch, 985, s A. amodara, A (994, amodara o Valuaio, Joh Wiley ad os, 994, New York. 7 P.eradez, Valui Compaies by Cashflow iscoui: e ehods ad Nie heories, ebruary 2002

6 he relaioship bewee levered bea ad ulevered bea ad i he same ime uiquely deermied ax shield are show i he followi able able. Levered Bea ad ax hield No Auhor Levered Bea ax hield. & ( 2. yers ( ( 3. iller 0 4. iles ad zzel ( u ( 5. Harris ad Prile ( ( 6. amodara ( ( ( ( 7. eradez praciioers mehod ( ( 8. eradez wihcosleverae ( [ ] ( ( 9. eradez ocosleverae ( ( ( 0. arciiak B C C ( B 8 Z.arciiak, Value ad isk aaeme usi erivaives, Oficya GH. Warszawa, ecember 200.

7 where is ulevered bea is levered bea is deb bea is ulevered cos capial is levered cos equiy is riskfree reur C is coupo rae is ieres rae (yield, is marke rae reur ( is marke risk premium, is icome ax rae is equiy icludi ax shield is loerm deb B is book value deb is ax shield is rowh ax shield.