商业财务学英文版课后答案：CHAPTER 12

CHAPTER14B-PAGE342CHAPTER12CAPITALSTRUCTURE:BASICCONCEPTSAnswerstoConceptQuestions1. AssumptionsoftheModigliani-Millertheoryinaworldwithouttaxes:1)Individualscanborrowatthesameinterestrateatwhichthefirmborrows.Sinceinvestorscanpurchasesecuritiesonmargin,anindividual’seffectiveinterestrateisprobablynohigherthanthatforafirm.Therefore,thisassumptionisreasonablewhenapplyingMM’stheorytotherealworld.Ifafirmwereabletoborrowataratelowerthanindividuals,thefirm’svaluewouldincreasethroughcorporateleverage.AsMMPropositionIstates,thisisnotthecaseinaworldwithnotaxes.2)Therearenotaxes.Intherealworld,firmsdopaytaxes.Inthepresenceofcorporatetaxes,thevalueofafirmispositivelyrelatedtoitsdebtlevel.Sinceinterestpaymentsaredeductible,increasingdebtreducestaxesandraisesthevalueofthefirm.3)Therearenocostsoffinancialdistress.Intherealworld,costsoffinancialdistresscanbesubstantial.Sincestockholderseventuallybearthesecosts,thereareincentivesforafirmtolowertheamountofdebtinitscapitalstructure.Thistopicwillbediscussedinmoredetailinlaterchapters.2. False.Areductioninleveragewilldecreaseboththeriskofthestockanditsexpectedreturn.ModiglianiandMillerstatethat,intheabsenceoftaxes,thesetwoeffectsexactlycanceleachotheroutandleavethepriceofthestockandtheoverallvalueofthefirmunchanged.3. False.Modigliani-MillerPropositionII(NoTaxes)statesthattherequiredreturnonafirm’sequityispositivelyrelatedtothefirm’sdebt-equityratio[RS=R0+(B/S)(R0–RB)].Therefore,anyincreaseintheamountofdebtinafirm’scapitalstructurewillincreasetherequiredreturnonthefirm’sequity.4. Interestpaymentsaretaxdeductible,wherepaymentstoshareholders(dividends)arenottaxdeductible.5. Businessriskistheequityriskarisingfromthenatureofthefirm’soperatingactivity,andisdirectlyrelatedtothesystematicriskofthefirm’sassets.Financialriskistheequityriskthatisdueentirelytothefirm’schosencapitalstructure.Asfinancialleverage,ortheuseofdebtfinancing,increases,sodoesfinancialriskand,hence,theoverallriskoftheequity.Thus,FirmBcouldhaveahighercostofequityifitusesgreaterleverage.6. No,itdoesn’tfollow.Whileitistruethattheequityanddebtcostsarerising,thekeythingtorememberisthatthecostofdebtisstilllessthanthecostofequity.Sinceweareusingmoreandmoredebt,theWACCdoesnotnecessarilyrise,sothevalueofthefirmdoesnotnecessarilyfall.7. Becausemanyrelevantfactorssuchasbankruptcycosts,taxasymmetries,andagencycostscannoteasilybeidentifiedorquantified,it’spracticallyimpossibletodeterminetheprecisedebt/equityratiothatmaximizesthevalueofthefirm.However,ifthefirm’scostofnewdebtsuddenlybecomesmuchmoreexpensive,it’sprobablytruethatthefirmistoohighlyleveraged.

8. It’scalledleverage(or“gearing”intheUK)becauseitmagnifiesgainsorlosses.9. Homemadeleveragereferstotheuseofborrowingonthepersonallevelasopposedtothecorporatelevel.10. Thebasicgoalistominimizethevalueofnon-marketedclaims,whichwillmaximizeshareholderwealth.

SolutionstoQuestionsandProblemsNOTE:Allend-of-chapterproblemsweresolvedusingaspreadsheet.Manyproblemsrequiremultiplesteps.Duetospaceandreadabilityconstraints,whentheseintermediatestepsareincludedinthissolutionsmanual,roundingmayappeartohaveoccurred.However,thefinalanswerforeachproblemisfoundwithoutroundingduringanystepintheproblem. Basic1. a. Atableoutliningtheincomestatementforthethreepossiblestatesoftheeconomyisshownbelow.TheEPSisthenetincomedividedbythe2,500sharesoutstanding.ThelastrowshowsthepercentagechangeinEPSthecompanywillexperienceinarecessionoranexpansioneconomy. RecessionNormalExpansionEBIT$7,800$13,000$17,550Interest000NI$7,800$13,000$17,550EPS$1.95$3.25$4.39%EPS–40–+35 b. Ifthecompanyundergoestheproposedrecapitalization,itwillrepurchase: Shareprice=Equity/Sharesoutstanding Shareprice=$250,000/4,000 Shareprice=$62.50 Sharesrepurchased=Debtissued/Shareprice Sharesrepurchased=$80,000/$62.50 Sharesrepurchased=1,280 Theinterestpaymenteachyearunderallthreescenarioswillbe: Interestpayment=$80,000(.06)=$4,800

ThelastrowshowsthepercentagechangeinEPSthecompanywillexperienceinarecessionoranexpansioneconomyundertheproposedrecapitalization. RecessionNormalExpansionEBIT$7,800$13,000$17,550Interest4,8004,8004,800NI$3,000$8,200$12,750EPS$1.10$3.01$4.69%EPS–63.41––+55.492. a. Atableoutliningtheincomestatementwithtaxesforthethreepossiblestatesoftheeconomyisshownbelow.Thesharepriceisstill$62.50,andtherearestill4,000sharesoutstanding.ThelastrowshowsthepercentagechangeinEPSthecompanywillexperienceinarecessionoranexpansioneconomy.RecessionNormalExpansionEBIT$7,800$13,000$17,550Interest000Taxes2,7304,5506,143NI$5,070$8,450$11,408EPS$1.27$2.11$2.85%EPS–40––+35 b. Atableoutliningtheincomestatementwithtaxesforthethreepossiblestatesoftheeconomyandassumingthecompanyundertakestheproposedcapitalizationisshownbelow.TheinterestpaymentandsharesrepurchasedarethesameasinpartbofProblem1.RecessionNormalExpansionEBIT$7,800$13,000$17,550Interest4,8004,8004,800Taxes1,0502,8704,463NI$1,950$5,330$8,288EPS$0.72$1.96$3.05%EPS–63.41––+55.49 NoticethatthepercentagechangeinEPSisthesamebothwithandwithouttaxes.3. a. Sincethecompanyhasamarket-to-bookratioof1.0,thetotalequityofthefirmisequaltothemarketvalueofequity.UsingtheequationforROE: ROE=NI/$250,000

TheROEforeachstateoftheeconomyunderthecurrentcapitalstructureandnotaxesis: RecessionNormalExpansionROE.0312.0520.0702%ROE–40–––+35 ThesecondrowshowsthepercentagechangeinROEfromthenormaleconomy. b. Ifthecompanyundertakestheproposedrecapitalization,thenewequityvaluewillbe: Equity=$250,000–80,000 Equity=$170,000 So,theROEforeachstateoftheeconomyis: ROE=NI/$170,000RecessionNormalExpansionROE.0176.0482.0750%ROE–63.41––+55.49 c. Iftherearecorporatetaxesandthecompanymaintainsitscurrentcapitalstructure,theROEis:ROE.0203.0338.0456%ROE–40–––+35 Ifthecompanyundertakestheproposedrecapitalization,andtherearecorporatetaxes,theROEforeachstateoftheeconomyis:ROE.0115.0314.0488%ROE–63.41––+55.49 NoticethatthepercentagechangeinROEisthesameasthepercentagechangeinEPS.ThepercentagechangeinROEisalsothesamewithorwithouttaxes.4. a. UnderPlanI,theunleveredcompany,netincomeisthesameasEBITwithnocorporatetax.TheEPSunderthiscapitalizationwillbe: EPS=$300,000/170,000shares EPS=$1.76 UnderPlanII,theleveredcompany,EBITwillbereducedbytheinterestpayment.Theinterestpaymentistheamountofdebttimestheinterestrate,so: NI=$300,000–.08($1,675,000) NI=$166,000

AndtheEPSwillbe: EPS=$166,000/120,000shares EPS=$1.38 PlanIhasthehigherEPSwhenEBITis$300,000. b. UnderPlanI,thenetincomeis$600,000andtheEPSis: EPS=$600,000/170,000shares EPS=$3.53 UnderPlanII,thenetincomeis: NI=$600,000–.08($1,675,000) NI=$466,000 AndtheEPSis: EPS=$466,000/120,000shares EPS=$3.88 PlanIIhasthehigherEPSwhenEBITis$600,000. c. TofindthebreakevenEBITfortwodifferentcapitalstructures,wesimplysettheequationsforEPSequaltoeachotherandsolveforEBIT.ThebreakevenEBITis: EBIT/170,000=[EBIT–.08($1,675,000)]/120,000 EBIT=$455,6005. Wecanfindthepricepersharebydividingtheamountofdebtusedtorepurchasesharesbythenumberofsharesrepurchased.Doingso,wefindthesharepriceis: Shareprice=$1,675,000/(170,000–120,000) Shareprice=$33.50pershare Thevalueofthecompanyundertheall-equityplanis: V=$33.50(170,000shares)=$5,695,000 Andthevalueofthecompanyundertheleveredplanis: V=$33.50(120,000shares)+$1,675,000debt=$5,695,000

6. a. Theincomestatementforeachcapitalizationplanis:IIIAll-equityEBIT$7,000$7,000$7,000Interest2,2564,7940NI$4,744$2,206$7,000EPS$2.06$1.58$2.26 Theall-equityplanhasthehighestEPS;PlanIIhasthelowestEPS. b. ThebreakevenlevelofEBIToccurswhenthecapitalizationplansresultinthesameEPS.TheEPSiscalculatedas: EPS=(EBIT–RDD)/Sharesoutstanding Thisequationcalculatestheinterestpayment(RDD)andsubtractsitfromtheEBIT,whichresultsinthenetincome.DividingbythesharesoutstandinggivesustheEPS.Fortheall-equitycapitalstructure,theinteresttermiszero.TofindthebreakevenEBITfortwodifferentcapitalstructures,wesimplysettheequationsequaltoeachotherandsolveforEBIT.ThebreakevenEBITbetweentheall-equitycapitalstructureandPlanIis: EBIT/3,100=[EBIT–.10($22,560)]/2,300 EBIT=$8,742 AndthebreakevenEBITbetweentheall-equitycapitalstructureandPlanIIis: EBIT/3,100=[EBIT–.10($47,940)]/1,400 EBIT=$8,742 Thebreak-evenlevelsofEBITarethesamebecauseofM&MPropositionI. c. SettingtheequationsforEPSfromPlanIandPlanIIequaltoeachotherandsolvingforEBIT,weget: [EBIT–.10($22,560)]/2,300=[EBIT–.10($47,940)]/1,400 EBIT=$8,742 Thisbreak-evenlevelofEBITisthesameasinpartbagainbecauseofM&MPropositionI.

d. Theincomestatementforeachcapitalizationplanwithcorporateincometaxesis:IIIAll-equityEBIT$7,000$7,000$7,000Interest2,2564,7940Taxes1,8988822,800NI$2,846$1,324$4,200EPS$1.24$0.95$1.35 Theall-equityplanstillhasthehighestEPS;PlanIIstillhasthelowestEPS. WecancalculatetheEPSas: EPS=[(EBIT–RDD)(1–tC)]/Sharesoutstanding Thisissimilartotheequationweusedbefore,exceptthatnowweneedtoaccountfortaxes.Again,theinterestexpensetermiszerointheall-equitycapitalstructure.So,thebreakevenEBITbetweentheall-equityplanandPlanIis: EBIT(1–.40)/3,100=[EBIT–.10($22,560)](1–.40)/2,300 EBIT=$8,742 ThebreakevenEBITbetweentheall-equityplanandPlanIIis: EBIT(1–.40)/3,100=[EBIT–.10($47,940)](1–.40)/1,400 EBIT=$8,742 AndthebreakevenbetweenPlanIandPlanIIis: [EBIT–.10($22,560)](1–.40)/2,300=[EBIT–.10($47,940)](1–.40)/1,400 EBIT=$8,742 Thebreak-evenlevelsofEBITdonotchangebecausetheadditionoftaxesreducestheincomeofallthreeplansbythesamepercentage;therefore,theydonotchangerelativetooneanother.7. Tofindthevaluepershareofthestockundereachcapitalizationplan,wecancalculatethepriceasthevalueofsharesrepurchaseddividedbythenumberofsharesrepurchased.Thedollarvalueofthesharesrepurchasedistheincreaseinthevalueofthedebtusedtorepurchaseshares,or: Sharesrepurchased=3,100–2,300=800 So,underPlanI,thevaluepershareis: P=$22,560/800shares P=$28.20pershare AndunderPlanII,thenumberofsharesrepurchasedare: Sharesrepurchased=3,100–1,400=1,700 So,thevaluepershareis: P=$47,940/1,700shares P=$28.20pershare Thisshowsthatwhentherearenocorporatetaxes,thestockholderdoesnotcareaboutthecapitalstructuredecisionofthefirm.ThisisM&MPropositionIwithouttaxes.8. a. Theearningspershareare: EPS=$30,000/8,000shares EPS=$3.75 So,thecashflowfortheshareholderis: Cashflow=$3.75(100shares) Cashflow=$375 b. Todeterminethecashflowtotheshareholder,weneedtodeterminetheEPSofthefirmundertheproposedcapitalstructure.Themarketvalueofthefirmis: V=$70(8,000) V=$560,000 Undertheproposedcapitalstructure,thefirmwillraisenewdebtintheamountof: D=0.35($560,000) D=$196,000 Thismeansthenumberofsharesrepurchasedwillbe: Sharesrepurchased=$196,000/$70 Sharesrepurchased=2,800 Underthenewcapitalstructure,thecompanywillhavetomakeaninterestpaymentonthenewdebt.Thenetincomewiththeinterestpaymentwillbe: NI=$30,000–.08($196,000) NI=$14,320

ThismeanstheEPSunderthenewcapitalstructurewillbe: EPS=$14,320/(8,000–2,800shares) EPS=$2.75 Sinceallearningsarepaidasdividends,theshareholderwillreceive: Shareholdercashflow=$2.75(100shares) Shareholdercashflow=$275.38 c. Toreplicatetheproposedcapitalstructure,theshareholdershouldsell35percentoftheirshares,or35shares,andlendtheproceedsat8percent.Theshareholderwillhaveaninterestcashflowof: Interestcashflow=35($70)(.08) Interestcashflow=$196 Theshareholderwillreceivedividendpaymentsontheremaining65shares,sothedividendsreceivedwillbe: Dividendsreceived=$2.75(65shares) Dividendsreceived=$179 Thetotalcashflowfortheshareholderundertheseassumptionswillbe: Totalcashflow=$196+179 Totalcashflow=$375 Thisisthesamecashflowwecalculatedinparta. d. Thecapitalstructureisirrelevantbecauseshareholderscancreatetheirownleverageorunleverthestocktocreatethepayofftheydesire,regardlessofthecapitalstructurethefirmactuallychooses.9. a. Therateofreturnearnedwillbethedividendyield.Thecompanyhasdebt,soitmustmakeaninterestpayment.Thenetincomeforthecompanyis: NI=$53,000–.07($250,000) NI=$35,500 Theinvestorwillreceivedividendsinproportiontothepercentageofthecompany’ssharetheyown.Thetotaldividendsreceivedbytheshareholderwillbe: Dividendsreceived=$35,500($20,000/$250,000) Dividendsreceived=$2,840

Sothereturntheshareholderexpectsis: R=$2,840/$20,000 R=.1420or14.20% b. Togenerateexactlythesamecashflowsintheothercompany,theshareholderneedstomatchthecapitalstructureofABC.TheshareholdershouldsellallsharesinXYZ.Thiswillnet$20,000.Theshareholdershouldthenborrow$20,000.Thiswillcreateaninterestcashflowof: Interestcashflow=.07($20,000) Interestcashflow=–$1,400 TheinvestorshouldthenusetheproceedsofthestocksaleandtheloantobuysharesinABC.Theinvestorwillreceivedividendsinproportiontothepercentageofthecompany’ssharetheyown.Thetotaldividendsreceivedbytheshareholderwillbe: Dividendsreceived=$53,000($40,000/$500,000) Dividendsreceived=$4,240 Thetotalcashflowfortheshareholderwillbe: Totalcashflow=$4,240–1,400 Totalcashflow=$2,840 Theshareholdersreturninthiscasewillbe: R=$2,840/$20,000 R=.1420or14.20% c. ABCisanallequitycompany,so: RE=RA=$53,000/$500,000 RE=.1060or10.60% TofindthecostofequityforXYZ,weneedtouseM&MPropositionII,so: RE=RA+(RA–

RD)(D/E)(1–tC) RE=.1060+(.1060–.07)(1)(1) RE=.1420or14.20%

d. TofindtheWACCforeachcompany,weneedtousetheWACCequation: WACC=(E/V)RE+(D/V)RD(1–tC) So,forABC,theWACCis: WACC=(1)(.1060)+(0)(.10) WACC=.1060or10.60% AndforXYZ,theWACCis: WACC=(1/2)(.1420)+(1/2)(.07) WACC=.1060or10.60% Whentherearenocorporatetaxes,thecostofcapitalforthefirmisunaffectedbythecapitalstructure;thisisM&MPropositionIIwithouttaxes.10. Withnotaxes,thevalueofanunleveredfirmistheinterestratedividedbytheunleveredcostofequity,so: V=EBIT/WACC $38,750,000=EBIT/.105 EBIT=.105($38,750,000) EBIT=$4,068,75011. Iftherearecorporatetaxes,thevalueofanunleveredfirmis: VU=EBIT(1–tC)/RU Usingthisrelationship,wecanfindEBITas: $38,750,000=EBIT(1–.35)/.105 EBIT=$6,259,615.38 TheWACCremainsat10.5percent.Duetotaxes,EBITforanall-equityfirmwouldhavetobehigherforthefirmtostillbeworth$38.75million.12. a. Withtheinformationprovided,wecanusetheequationforcalculatingWACCtofindthecostofequity.TheequationforWACCis: WACC=(E/V)RE+(D/V)RD(1–tC) Thecompanyhasadebt-equityratioof1.3,whichimpliestheweightofdebtis1.3/2.3,andtheweightofequityis1/2.3,so WACC=.11=(1/2.3)RE+(1.3/2.3)(.08)(1–.35) RE=.1854or18.54%

b. TofindtheunleveredcostofequityweneedtouseM&MPropositionIIwithtaxes,so: RE=RU+(RU–RD)(D/E)(1–tC) .1854=RU+(RU–.08)(1.3)(1–.35) RU=.1371or13.71% c. Tofindthecostofequityunderdifferentcapitalstructures,wecanagainuseM&MPropositionIIwithtaxes.Withadebt-equityratioof2,thecostofequityis: RE=RU+(RU–RD)(D/E)(1–tC) RE=.1371+(.1371–.08)(2)(1–.35) RE=.2114or21.14% Withadebt-equityratioof1.0,thecostofequityis: RE=.1371+(.1371–.08)(1)(1–.35) RE=.1743or17.43% Andwithadebt-equityratioof0,thecostofequityis: RE=.1371+(.1371–.08)(0)(1–.35) RE=RU=.1371or13.71%13. a. Foranall-equityfinancedcompany: WACC=R0=RE=.1150or11.50% b. Tofindthecostofequityforthecompanywithleverage,weneedtouseM&MPropositionIIwithtaxes,so: RE=R0+(R0–RD)(D/E)(1–tC) RE=.115+(.115–.0625)(.25/.75)(1–.35) RE=.1264or12.64% c. UsingM&MPropositionIIwithtaxesagain,weget: RE=R0+(R0–RD)(D/E)(1–tC) RE=.115+(.115–.0625)(.50/.50)(1–.35) RE=.1491or14.91% d. TheWACCwith25percentdebtis: WACC=(E/V)RE+(D/V)RD(1–tC) WACC=.75(.1264)+.25(.0625)(1–.35) WACC=.1049or10.49% AndtheWACCwith50percentdebtis: WACC=(E/V)RE+(D/V)RD(1–tC) WACC=.50(.1491)+.50(.0625)(1–.35) WACC=.0949or9.49%

14. a. Thevalueoftheunleveredfirmis: V=EBIT(1–tC)/R0 V=$57,500(1–.35)/.15 V=$249,166.67 b. Thevalueoftheleveredfirmis: V=VU+tCD V=$249,166.67+.35($120,000) V=$291,166.6715. WecanfindthecostofequityusingM&MPropositionIIwithtaxes.Doingso,wefind: RE=R0+(R0–RD)(D/E)(1–tC) RE=.15+(.15–.08)[$120,000/($291,166.67–120,000)](1–.35) RE=.1819or18.19% Usingthiscostofequity,theWACCforthefirmafterrecapitalizationis: WACC=(E/V)RE+(D/V)RD(1–tC) WACC=.1819[($291,166.67–120,000)/$291,166.67]+.08(1–.35)($120,000/$291,166.67) WACC=.1284or12.84% Whentherearecorporatetaxes,theoverallcostofcapitalforthefirmdeclinesthemorehighlyleveragedisthefirm’scapitalstructure.ThisisM&MPropositionIwithtaxes.16. SinceUnleveredisanall-equityfirm,itsvalueisequaltothemarketvalueofitsoutstandingshares.Unleveredhas24,000sharesofcommonstockoutstanding,worth$62pershare.Therefore,thevalueofUnlevered: VU=24,000($62)=$1,488,000 Modigliani-MillerPropositionIstatesthat,intheabsenceoftaxes,thevalueofaleveredfirmequalsthevalueofanotherwiseidenticalunleveredfirm.SinceLeveredisidenticaltoUnleveredineverywayexceptitscapitalstructureandneitherfirmpaystaxes,thevalueofthetwofirmsshouldbeequal.Therefore,themarketvalueofLevered,Inc.,shouldbe$1,488,000also.SinceLeveredhas18,000outstandingshares,worth$60pershare,themarketvalueofLevered’sequityis: EL=18,000($60)=$1,080,000 ThemarketvalueofLevered’sdebtis$230,000.Thevalueofaleveredfirmequalsthemarketvalueofitsdebtplusthemarketvalueofitsequity.Therefore,thecurrentmarketvalueofLevered,Inc.is: VL=B+S VL=$1,080,000+230,000 VL=$1,310,000

ThemarketvalueofLevered’sequityneedstobe$1,488,000,$178,000higherthanitscurrentmarketvalueof$1,310,000,forMMPropositionItohold.SinceLevered’smarketvalueislessthanUnlevered’smarketvalue,Leveredisrelativelyunderpricedandaninvestorshouldbuysharesofthefirm’sstock. Intermediate17. Tofindthevalueoftheleveredfirm,wefirstneedtofindthevalueofanunleveredfirm.So,thevalueoftheunleveredfirmis: VU=EBIT(1–tC)/R0 VU=($24,000)(1–.35)/.13 VU=$120,000 Nowwecanfindthevalueoftheleveredfirmas: VL=VU+tCD VL=$120,000+.35($65,000) VL=$142,750 ApplyingM&MPropositionIwithtaxes,thefirmhasincreaseditsvaluebyissuingdebt.AslongasM&MPropositionIholds,thatis,therearenobankruptcycostsandsoforth,thenthecompanyshouldcontinuetoincreaseitsdebt/equityratiotomaximizethevalueofthefirm.18. a. Withnodebt,wearefindingthevalueofanunleveredfirm,so: V=EBIT(1–tC)/R0 V=$19,500(1–.35)/.15 V=$85,583.33 b. Thegeneralexpressionforthevalueofaleveragedfirmis:

VL=VU

+tCD Ifdebtis50percentofVU,thenD=(.50)VU,andwehave:

VL=VU

+tC[(.50)VU]

VL=$85,583.33+.35(.50)($85,583.33)

VL=$100,560.42 Andifdebtis50percentofVU,thenD=(1.0)VU,andwehave:

VL=VU

+tC[(1.0)VU] VL=$85,583.33+.35(1.0)($85,583.33) VL=$115,537.50

c. AccordingtoM&MPropositionIwithtaxes: VL=VU+tCD Withdebtbeing50percentofthevalueoftheleveredfirm,VUmustequaltC(.50)D,so: $85,583.33=.35(.50)D D=$489,047.62 Thismeansthevalueoftheleveredfirmis: VL=$85,583.33+.35($489,047.62) VL=$256,750.00 Ifthedebtis100percentoftheleveredvalue,VUmustequaltC(1)VU,so: $85,583.33=.35D D=$244,523.81 Thismeansthevalueoftheleveredfirmis: VL=$85,583.33+.35($244,523.81) VL=$171,166.6719. AccordingtoM&MPropositionIwithtaxes,theincreaseinthevalueofthecompanywillbethepresentvalueoftheinteresttaxshield.Sincetheloanwillberepaidinequalinstallments,weneedtofindtheloaninterestandtheinteresttaxshieldeachyear.Theloanschedulewillbe:YearLoanBalanceInterestTaxShield0$640,0001320,000$51,200.35($51,200)=$17,9202025,600.35($25,600)=$8,960 So,theincreaseinthevalueofthecompanyis: Valueincrease=$17,920/1.08+$8,960/(1.08)2 Valueincrease=$24,274.3520. a. SinceAlphaCorporationisanall-equityfirm,itsvalueisequaltothemarketvalueofitsoutstandingshares.Alphahas7,000sharesofcommonstockoutstanding,worth$20pershare,sothevalueofAlphaCorporationis: VAlpha=7,000($23)=$161,000 b. Modigliani-MillerPropositionIstatesthatintheabsenceoftaxes,thevalueofaleveredfirmequalsthevalueofanotherwiseidenticalunleveredfirm.SinceBetaCorporationisidenticaltoAlphaCorporationineverywayexceptitscapitalstructureandneitherfirmpaystaxes,thevalueofthetwofirmsshouldbeequal.So,thevalueofBetaCorporationis$161,000aswell.

c. Thevalueofaleveredfirmequalsthemarketvalueofitsdebtplusthemarketvalueofitsequity.So,thevalueofBeta’sequityis: VL=B+S $161,000=$38,000+S S=$123,000 d. Theinvestorwouldneedtoinvest20percentofthetotalmarketvalueofAlpha’sequity,whichis: AmounttoinvestinAlpha=.20($161,000)=$32,200 Betahaslessequityoutstanding,sotopurchase20percentofBeta’sequity,theinvestorwouldneed: AmounttoinvestinBeta=.20($123,000)=$24,600 e. Alphahasnointerestpayments,sothedollarreturntoaninvestorwhoowns20percentofthecompany’sequitywouldbe: DollarreturnonAlphainvestment=.20($32,000)=$6,400 BetaCorporationhasaninterestpaymentdueonitsdebtintheamountof: InterestonBeta’sdebt=.09($38,000)=$3,420 So,theinvestorwhoowns20percentofthecompanywouldreceive20percentofEBITminustheinterestexpense,or: DollarreturnonBetainvestment=.20($32,000–3,420)=$5,716 f. Frompartd,weknowtheinitialcostofpurchasing20percentofAlphaCorporation’sequityis$32,200,butthecosttoaninvestorofpurchasing20percentofBetaCorporation’sequityisonly$24,600.Inordertopurchase$32,200worthofAlpha’sequityusingonly$24,600ofhisownmoney,theinvestormustborrow$7,600tocoverthedifference.TheinvestorwillreceivethesamedollarreturnfromtheAlphainvestment,butwillpayinterestontheamountborrowed,sothenetdollarreturntotheinvestmentis: Netdollarreturn=$6,400–.09($7,600)=$5,716 Noticethatthisamountexactlymatchesthedollarreturntoaninvestorwhopurchases20percentofBeta’sequity. g. TheequityofBetaCorporationisriskier.Betamustpayoffitsdebtholdersbeforeitsequityholdersreceiveanyofthefirm’searnings.Ifthefirmdoesnotdoparticularlywell,allofthefirm’searningsmaybeneededtorepayitsdebtholders,andequityholderswillreceivenothing.

21. a. Afirm’sdebt-equityratioisthemarketvalueofthefirm’sdebtdividedbythemarketvalueofafirm’sequity.So,thedebt-equityratioofthecompanyis: Debt-equityratio=MVofdebt/MVofequity Debt-equityratio=$4,200,000/$9,000,000 Debt-equityratio=.4667 b. Wefirstneedtocalculatethecostofequity.Todothis,wecanusetheCAPM,whichgivesus: RS=RF+[E(RM)–RF] RS=.05+1.15(.12–.05) RS=.1305or13.05% Intheabsenceoftaxes,afirm’sweightedaveragecostofcapitalisequalto: RWACC=[B/(B+S)]RB+[S/(B+S)]RS RWACC=($4,200,000/$13,200,000)(.09)+($9,000,000/$13,200,000)(.1305) RWACC=.1176or11.76% c. AccordingtoModigliani-MillerPropositionIIwithnotaxes: RS=R0+(B/S)(R0–RB) .1305=R0+(.4667)(R0–.09) R0=.1176or11.76% ThisisconsistentwithModigliani-Miller’spropositionthat,intheabsenceoftaxes,thecostofcapitalforanall-equityfirmisequaltotheweightedaveragecostofcapitalofanotherwiseidenticalleveredfirm.22. a. Topurchase5percentofKnight’sequity,theinvestorwouldneed: Knightinvestment=.05($1,350,000)=$67,500 Andtopurchase5percentofVeblenwithoutborrowingwouldrequire: Vebleninvestment=.05($2,200,000)=$110,000 Inordertocomparedollarreturns,theinitialnetcostofbothpositionsshouldbethesame.Therefore,theinvestorwillneedtoborrowthedifferencebetweenthetwoamounts,or: Amounttoborrow=$110,000–67,500=$42,500 Aninvestorwhoowns5percentofKnight’sequitywillbeentitledto5percentofthefirm’searningsavailabletocommonstockholdersattheendofeachyear.WhileKnight’sexpectedoperatingincomeis$280,000,itmustpay$78,000todebtholdersbeforedistribu