Corporate Finance, Berk, Jonathan and Demarzo, Peter, 4 th Edition Chapter 18: Capital Budgeting and Valuation with Leverage

Transcription

1 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage opoae Finance, Bek, Jonahan an emazo, Pee, 4 h iion hape 18: apial Bugeing an aluaion wih eveage Key Poins: Fomulas fo he Weighe Aveage os of apial iscuss he WA meho, AP meho an F meho iscuss pojec base WA iscuss which meho o use fo iffeen leveage policies 18.1 Oveview of Key onceps hee ae hee mehos iscusse in his chape o value a fim: he WA Meho, he AP Meho an he F Meho. You shoul become familia wih he hee mehos an in wha cicumsances i is bes o use each meho he Weighe Aveage os of apial Meho (WA he WA meho akes he inees ax shiel concep ino accoun by using he afe ax cos of capial as he iscoun ae. ( 1 WA Make alue of quiy Make alue of eb (ne of cash Maginal copoae ax ae quiy os of apial eb os of apial If we assume a consan eb-o-quiy aio an ha he WA emains consan, we can calculae he evee alue of a fim. Memoizaion: efiniion evee alue of an Invesmen: Pesen value of a fim s fuue fee cash flow using he fim s WA. he invesmen s iniial levee value sing he WA o alue a Pojec: 0 is: FF1 1 FF (1 FF ( WA WA WA One can use he Fee ash Flows an he WA o calculae he evee alue of a Fim.... XP Acuaial Founaions of opoae Finance an RM xam 1

2 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage xample: A fim has a pojec ha equies a $24M upfon invesmen an $6.67M of upfon makeing expenses. he pojec pouces he following Incemenal anings foecas fo he nex 4 yeas an esuling balance shee: Yea ales os of Goos ol - (25.00 (25.00 (25.00 (25.00 Goss Pofi Opeaing xpenses (6.67 (9.00 (9.00 (9.00 (9.00 epeciaion - (6.00 (6.00 (6.00 (6.00 BI ( Income ax (40% 2.67 (8.00 (8.00 (8.00 (8.00 nlevee Ne Income ( Fee ash Flow Plus: epeciaion ess: apial (24.00 xpeniues ess: Incease in NW Fee ash Flow ( Asses iabiliies & quiy os of apial ash 20 eb 320 eb 6% xising Asses 600 quiy 300 quiy 10% oal Asses 620 oal 620 alculae he pojecs evee alue an eemine if he fim shoul ake he pojec. oluion: alculae he fims WA using he balance shee above. Noe: fis you mus calculae he fim s ne eb amoun. Ne eb = eb ash = = 300 WA ( 1 10% 6%(1 40% 6.8% You can eemine he pojecs evee alue by iscouning he pojecs Fee ash Flows wih he calculae WA $61.25 he pojec coss $24M in upfon invesmen plus $6.67M in makeing expenses. Howeve, we save axes on he $6.67M of $2.67M. heefoe, he ue cos a ime 0 is $24M + $4M = $28M. heefoe, since he pojec geneaes $61.25M i has an NP of $33.25M (= XP Acuaial Founaions of opoae Finance an RM xam 2

3 ummay of he WA Meho: opoae Finance - hape 18: apial Bugeing an aluaion wih eveage he mos commonly use meho in pacice fo capial bugeing puposes. he fim can use he WA as he companywie cos of capial fo new invesmens ha ae compaable o he es of he fim an ha will no ale he fim s eb-o-equiy aio. Memoizaion: oncep he WA Meho: 1. eemine he Fee ash Flow of he invesmen 2. ompue he WA 3. ompue he value of he invesmen, incluing he ax benefi of leveage, by iscouning he Fee ash Flow of he invesmen using he WA. Implemening a onsan eb-quiy Raio: By aking he pojec above, he fim has incease is asses by 0 $61. 25M, in oe o mainain he fim s consan eb-o-alue aio of 50%, he fim mus a 50% x 61.25M = $30.625M in new eb. Insea of boowing he full M, he fim uses $20M of cash an boows he emaining $10.625M. he fim s balance shee woul look like his afe he pojec: Asses iabiliies & quiy ash - eb 320 uen Asses 600 New eb RFX Pojec quiy 300 New quiy oal oal he cos of he pojec is only $28M bu he fim has ae $30.625M in eb an cash. o he fim pays he iffeence o shaeholes $2.625M ( = as a ivien. o he oal value ha he shaeholes ge is he incease in equiy of $30.625M an he ivien of $2.625M fo a oal of $33.25M, which is he NP we calculae peviously. Memoizaion: efiniion eb apaciy: he amoun of eb a ae ha is equie o mainain he fim s age eb-ovalue aio,. whee is he pojec s levee value of Fee ash Flow afe ime FF 1 1 WA 1 XP Acuaial Founaions of opoae Finance an RM xam 3

4 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage xample: Assume we use he above Fee ash Flow an WA (6.8%, we can eemine he pojec s levee value a ime an he esuling eb apaciy. Yea Fee ash Flow ( evee alue eb apaciy he evee alue a ime 0 is $61.25M (as calculae above an he eb apaciy wih a consan eb-o-alue ( aio of 50% is $30.62M. he WA above was 6.8%. o calculae he evee alue a ime 1 use he fomula above: FF % WA hen he eb apaciy is: 18.3 Ajuse Pesen alue (AP % he Ajuse Pesen alue (AP meho splis he levee value of a fim ino he unlevee value of a fim an he pesen value of inees ax shiels. AP P ( Inees _ ax _ hiel he nlevee alue of a Pojec: o calculae he unlevee value of a fim you fis nee o calculae he Pe-ax WA. Pe-ax WA = Noe: he ax shiel will have he same isk as he fim if he fim mainains a age leveage aio. Memoizaion: efiniion age eveage Raio: a fim ajuss is eb popoionally o he pojec s value o is cash flows. XP Acuaial Founaions of opoae Finance an RM xam 4

5 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage Fo he fim above, we ha a eb-o-alue aio of 50%, an quiy os of apial of 10% an a eb os of apial of 6%. heefoe, he unlevee cos of capial is: % % 8.0% hen he unlevee value of he pojec is: aluing he Inees ax hiel: We have calculae he unlevee value of he pojec an now we nee o compue he pesen value of he inees ax shiels. o o his we will nee o fis compue he inees pai in each yea. Inees pai in yea = 1 Inees ax hiel in yea = Inees pai in yea x Yea eb apaciy Inees Pai ( =6% Inees ax hiel (c=40% Memoizaion: oncep When he fim mainains a age leveage aio, is fuue inees ax shiels have simila isk o he pojec s cash flows, so hey shoul be iscoune a he pojec s unlevee cos of capial P(Inees ax hiel = heefoe, he evee alue of he fim using he AP meho is: P ( In _ ax _ hiel ummay of he AP Meho: 1. eemine he invesmen s value wihou leveage, by iscouning i s fee cash flows a he unlevee cos of capial,. Wih a consan eb-o-equiy aio, may be esimae using he Pe-ax WA. 2. eemine he pesen value of he inees ax shiel. XP Acuaial Founaions of opoae Finance an RM xam 5

6 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage a. eemine he expece inees ax shiel: Given he expece eb on ae, he inees ax shiel on ae +1 is. c b. iscoun he inees ax shiel, if a consan eb-o-equiy aio is mainaine, using is appopiae. 3. A he unlevee value, o he pesen value of he inees ax shiel o eemine he value of he invesmen wih leveage,. Memoizaion: Avanages/isavanages Avanages of AP: - asie o apply when a fim oes no hol is eb-o-quiy aio consan - Povies you wih a sepaae numbe fo he inees ax shiel. isavanages of AP: - Moe complicae han WA as hee ae wo pieces o calculae - We nee he pojecs eb capaciy a each ime, which equies he pojecs value a each ime. - Nee o calculae he pojec s eb an value simulaneously he Flow o quiy Meho (F he Flow o quiy meho calculaes he fee cash flow available o equiy holes afe aking ino accoun all paymens o an fom eb holes. he cash flows ae hen iscoune using he equiy cos of capial. alculaing he Fee ash Flow o quiy (FF: he Fee ash Flow o quiy (FF is he fee cash flow ha emains afe ajusing fo inees paymens, eb issuance, an eb epaymen. FF FF ( 1 ( Inees _ Paymens ( Ne _ Boowing FF = ales OG Opeaing xpenses epeciaion Inees xpense Income ax + epeciaion apx Incease in NW + Ne Boowing Ne Boowing a ae = 1 Fom he inees ax shiel able above we have he eb in each ime peio in each peio. Yea eb apaciy Inees Pai ( =6% an he inees pai XP Acuaial Founaions of opoae Finance an RM xam 6

7 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage he Ne Boowing a =0 is = ( he Ne Boowing a =1 is = (using he above fomula. his is coninue fo = 2 o 4. he able below summaizes he cash flows: xample: Yea ales os of Goos ol - (25.00 (25.00 (25.00 (25.00 Goss Pofi Opeaing xpenses (6.67 (9.00 (9.00 (9.00 (9.00 epeciaion - (6.00 (6.00 (6.00 (6.00 BI ( Inees xpense - (1.84 (1.42 (0.98 (0.51 Peax Income ( Income ax (40% 2.67 (7.27 (7.43 (7.61 (7.80 Ne Income ( Fee ash Flow o quiy Plus: epeciaion ess: apial xpeniues (24.00 ess: Incease in NW ess: Ne Boowing (6.92 (7.39 (7.89 (8.43 Fee ash Flow o quiy Noe: he FF a ime 0, is he same amoun ha we calculae peviously as he ivien pai o shaeholes $2.62 = $ $ aluing he quiy ash Flows: he value of he iscoune FF epesens he gain o shaeholes fom he pojec. ummay of Flow-o-quiy-Meho: NP( FF FF NP FF FF ( ( 2 4 $ eemine he fee cash flow o equiy of he invesmen 2. eemine he equiy cos of capial 3. ompue he conibuion o equiy value,, by iscouning he fee cash flow o equiy using he equiy cos of capial. sing he Fee ash Flow o quiy fomula above: FF FF ( 1 ( Inees _ Paymens ( Ne _ Boowing XP Acuaial Founaions of opoae Finance an RM xam 7

8 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage he fee cash flow o equiy can be calculae wih he Fee ash Flow, he Inees Paymen an he Ne Boowing fom each peio. Yea Fee ash Flow ( Afe-ax Inees xpense - (1.10 (0.85 (0.59 (0.30 Ne Boowing (6.92 (7.39 (7.89 (8.43 Fee ash Flow o quiy sing he F Meho equies ha he pojec s isk an leveage mach he fims, an ha he fims equiy cos of capial is hel consan. his is only ue if he fim mainains a consan eb-o-equiy aio. If he eb-o-equiy aio changes ove ime, hen he equiy cos of capial will change ove ime. Memoizaion: Avanages/isavanages Avanages of F Meho: - Allows fo calculaion of value of equiy fo he enie fim when capial sucue is complex - Moe anspaen meho fo shaeholes isavanages of F Meho: - Nee o compue he pojec s eb capaciy o eemine he inees an ne boowing 18.5 Pojec Base oss of apial simae he nlevee os of apial: When a pojec iffes fom he fim as a whole an i is no appopiae o use he fims unlevee cos of capial, you can esimae he unlevee cos of capial using aa fom simila fims in he make place. Fo example, if hee ae wo fims ha manufacue he same pouc as you pojec an hey have he following chaaceisics: Fim quiy os of apial eb os of apial eb-o-alue (/+ A 12.0% 6.0% 40% B 10.7% 5.5% 25% Fim A: % % 9.6% Fim B: % % 9.4% o eemine he fim s you coul simply ake he aveage of he wo compaable fims. = 9.5%. Wih his ae we can use he AP meho o calculae he value of he invesmen. XP Acuaial Founaions of opoae Finance an RM xam 8

9 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage XP Acuaial Founaions of opoae Finance an RM xam 9 Pojec eveage an he quiy os of apial: uppose we have a iffeen age leveage aio fo a pojec han he fim as a whole. We can calculae as follows: ( he pojec s epens on he i s unlevee cos of capial,, an he eb-equiy aio of he iniviual pojec. Once we have he we can hen calculae he WA using he fomula: 1 ( WA We can evelop a new Pojec Base WA if we efine o be he aio of eb-o-alue o /+. Pojec-Base WA = WA Poof: c WA ( ( (1 (1 ( ( (1 ( (1 (1 (1

10 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage xample: A fim cuenly has an equiy cos of capial of 12.7%, a boowing cos of 6% an has mainaine a eb-o-value aio of 40%. uppose he fim enes a new pojec ha is iffeen han he fim as a whole. he fim has suveye compaable fims an he unlevee cos of capial fo hose fims is 15%. Also suppose ha he fim will finance his pojec wih 10% eb an hol he eb-o-value aio consan. he eb will have a 6% cos associae wih i an he copoae ax ae will be 35%. alculae he fims unlevee cos of capial, an he pojec s equiy cos of capial an pojec base WA? oluion: he fim s cuen is 12.7% an he eb-o-value is 40%. WA % 0.406% (1 35% 9.2% % 0.406% 10.0% he fims unlevee cos of capial is 10.0%. he pojec has an unlevee cos of capial of 15% base on compaable companies. We can esimae he using he following fomula: s. ( s % (15% 6% 16% 0.90 We can hen esimae he pojec base WA using he following: Pojec WA 15% 0.106% 35% 14.8% XP Acuaial Founaions of opoae Finance an RM xam 10

11 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage ommon Misake: uens ofen make a misake wih he following quesion (on pevious OA exams! Given a fims equiy cos of capial, eb cos of capial an a eb-o-value, he suen is ol ha he fim inceases is cuen eb-o-value aio an hen aske o eemine he new WA fo he fim. Fo example, he fim s cuen equiy cos of capial is 12% an he eb cos of capial is 6.67%. he fim cuenly has a eb-o-value of 25% (ax ae = 40%. Assume ha he fim inceases is eb-ovalue o 50%. Wha is he new WA? I is emping o jus use he WA fomula: % %( % howeve, his is incoec. he coec poceue is: 1. ompue he fims unlevee cos of capial wih he fims ol numbes % % 10.67% 2. ompue he new WA WA WA 10.67% % 40% 9.34% Assume hough, ha wih he incease in eb (if you incease he eb-o-value aio you eihe incease eb o euce equiy, you have a highe eb cos of capial of 7.34%. hen he WA becomes: WA 10.67% % 40% 9.2% Impoan conceps o emembe fo a pojecs incemenal financing: ash is negaive eb. ash can be use o pay off eb immeiaely. You shoul use Ne eb in you calculaions Fo a fim ha is hoaing cash o highly leveage, he WA is he opimal leveage epens on he fim an he pojec afe cash flows can be 100% eb finance, if 100% finance he appopiae iscoun ae o use is 1 which is jus he nomal WA fomula wih /+ = ( 18.6 AP wih Ohe eveage Policies onsan Inees oveage Raio: If a fim inceases is eb level as income ises o shiel is income fom axes, i is naual o specify he fim s inees paymens as a age facion of he pojec s fee cash flows. e k epesen his. Inees Pai in Yea = k FF XP Acuaial Founaions of opoae Finance an RM xam 11

12 Memoizaion: efiniion opoae Finance - hape 18: apial Bugeing an aluaion wih eveage onsan Inees oveage Raio: when a fim s inees paymens on is eb ae a consan pecenage of is fee cash flow. We can hen eemine he value of he pojec/fim using he AP meho. By having a onsan Inees oveage Raio i simplifies he calculaion fo he P(Inees ax hiel. P(Inees ax hiel = P( k FF k P( FF k hen he levee value is: k ( 1 k xample: A fim s pojec will conibue $3.8M in Fee ash Flow he fis yea gowing by 3% each yea heeafe. he fim has an unlevee cos of capial of 8% an a ax ae of 40%. he acquisiion cos is $80M an will be finance by $50M in new eb a 6%. ompue he value of he pojec using he AP meho. he fim will mainain a consan inees coveage aio. oluion: 3.8 $ 76M 8% 3% Wih 50M in new eb an a 6% inees ae he fis yea inees expense is 50 x 6% = $3M. ince he fim mainains a consan inees coveage aio, k 3.0/ % fo all yeas. ( 1 k ( % 76 $100M Peeemine eb evels: A fim may choose o se is eb levels o a pe-eemine amoun. Memoizaion: oncep When eb levels ae se accoing o a fixe scheule, we can iscoun he peeemine inees ax shiels using he eb cos of capial. A paicula simple example is if a fim has pemanen fixe eb, mainaining he same level of eb foeve. he P(Inees ax hiels becomes: P( In. ax. hiel an heefoe, XP Acuaial Founaions of opoae Finance an RM xam 12

13 18.7 Ohe ffecs of Financing opoae Finance - hape 18: apial Bugeing an aluaion wih eveage Issuance oss: Banks ha offe eb financing fo companies chage fees o accommoae his. hese fees mus be subace fom he. ecuiy Mispicing: quiy may be issue in he public makes a a pice ha is highe han he ue value o lowe han he ue value. his iffeence mus be incopoae ino he levee value calculaion. Banks coul also give he company an inees ae ha oes no epesen he ue isk of he company. his iffeence nees o be inclue in he levee value calculaion. Financial isess an Agency oss: One consequence of eb financing is he possibiliy of financial isess an agency coss. As eb inceases, hese poenial coss incease. his is bes moelle using opion echniques Avance opics In apial Bugeing Peioically Ajuse eb: A special case is when he eb is ajuse annually. he expece inees expense fo ime is known in avance a ime -1. heefoe, since we know he nex inees paymen we can iscoun a an hen iscoun i fom ae -1 o 0 a. P ( In 1 (1 In In (1 (1 1 1 imilaly, he Pojec Base WA fo annually ajuse eb is: Pojec WA 1 1 imilaly, he levee value of a fim wih a consan inees coveage is: 1 1 k 1 XP Acuaial Founaions of opoae Finance an RM xam 13

14 eveage an he os of apial: opoae Finance - hape 18: apial Bugeing an aluaion wih eveage When eb is se o a peeemine level fo some ime, he inees ax shiels fo he eb ae elaively safe. he value of hese safe ax shiels shoul be euce fom he eb he fim has. We label he amoun of peeemine ax shiels ha will be euce fom eb as. eb Ne of Peeemine ax hiels: he unlevee cos of capial an equiy cos of capial heefoe become: ( Pojec WA wih a Fixe eb cheule becomes: WA ( hee cases commonly use in pacice: Whee,, 1. oninuously Ajuse eb: 0,, an 0 2. Annually Ajuse eb:, 1, 1 1 an 1 3. Pemanen eb: (1, an 1, he WA o F Meho wih hanging eveage: When a fim oes no keep a consan eb-equiy aio, he AP Meho is usually he bes alenaive. Howeve, he WA an F meho can sill be use afe some aiional calculaions. he equiy cos of capial an WA mus be compue fo each ime peio. o calculae he levee value of he pojec/fim, you woul hen iscoun he FF using a iffeen WA fo each yea. Pesonal axes: eveage has ax consequences fo boh invesos an copoaions. Pesonal axes ale he equaions fo AP. Fo he WA meho, equiy an eb aleay faco in he cos of inveso (pesonal axes. he WA meho oes no change in he pesence of pesonal axes. he AP meho oes howeve change. XP Acuaial Founaions of opoae Finance an RM xam 14

15 opoae Finance - hape 18: apial Bugeing an aluaion wih eveage e e be he ax invesos pay on iviens/equiy income an le i be he ax invesos pay on inees income. efine as: 1 i 1 e nlevee os of apial wih Pesonal axes is: Nex, we mus compue he inees ax shiel using he effecive ax avanage of eb, (1 c (1 e 1 (1 i We hen calculae he pesen value of he inees ax shiels using an. We woul iscoun he inees ax shiels using if he fim mainains a age leveage aio o a if he eb is se accoing o a peeemine scheule. XP Acuaial Founaions of opoae Finance an RM xam 15