Fundamentals-of-Corporate-Finance-3rd-ed-Jonathan-

©2015PearsonEducationLimitedChapter13TheCostofCapitalNote:AllproblemsinthischapterareavailableinMyFinanceLab.Anasterisk(*)indicatesproblemswithahigherlevelofdifficulty.1.Plan:ComputetheweightsfortheWACC.Execute:Valueofdebt:$100millionValueofpreferredstock:$20millionMarketvalueofcommonequity:$50pershare6millionshares$300millionTotalmarketvalueoffirm:$10020300$420millionWeightsforWACCcalculation:100Debt23.81%42020PreferredStock4.76%420300CommonEquity71.43%420Evaluate:Thetotalmarketvalueofthefirmis$420million.Debtis23.81%ofthetotalvalue,preferredstockis4.76%,andcommonequityis71.43%.2.Plan:ComputethemarketvalueweightstocomputetheWACC.Execute:Bookvalueofequity$600Marketvalueofequity$6001.5$900Bookvalueofdebt$400Totalmarketvalueoffirm$1300WeightsforWACCcalculation:400Debt30.77%1300900CommonEquity69.23%1300Evaluate:Debtis30.77%ofthecapitalstructureandequityis69.23%.Chapter13TheCostofCapital177©2015PearsonEducationLimited3.Plan:ThebookvalueofitsequityanddebtarenotrelevantforcomputingtheweightsforitsWACC.Thoseweightsshouldbebasedonmarketvalues.Weneedtocalculatethemarketvalueofitsdebtandofitsequity.TheMVofitsequityequalsthenumberofsharesoutstandingtimesitscurrentpricepershare.TheMVofitsdebtcanbecalculatedbymultiplyingitspricerelativetoparbytheparvalue.Execute:a.MVequity:2millionshares$25pershare=$50millionb.MVdebt:105%ofpar$40millionpar=$42millionc.Equityweight:$50million/($50million+$42million)=54.35%Debtweight:$42million/($50million+$42million)=45.65%Evaluate:Thebookvalueswouldgiveyouthewrongweights.TheWACCshouldbebasedontherelativemarketvaluesofthecompany’scapitalsources,notthehistoricalbookvalues.4.Plan:Computethefirm’spretaxWACCandthevalueofaportfoliocontaining40%ofthefirm’sdebtand60%ofthefirm’sequity.Showthattheexpectedreturnsareidentical.Execute:Ifthefirm’sassetsaretobewortheither$1,200or$960inoneyear(withequalprobability),whatdoesthismeanforthevalueofthedebtandequityofthefirm?Ata5%interestrate,thedebtwillbeworth$420inoneyear.Becausethedebthasseniorityoverequityonitsclaimofthefirm’sassets,theassetswillbelargeenoughinoneyeartofulfillthedebtobligations,sothedebtwillbeworth$420ineithercase.Thus,theequitywillbewortheither$780or$540inoneyear.Expectedreturnonassets:50%chanceof$1,200inoneyear:1,2001,000Return1,00020%50%chanceof$960inoneyear:9601,000Return1,0004%Expectedreturnonassets(50%)(20%)(50%)(4%)8%.Portfolioof40%debtand60%equity:Expectedreturnondebt:4204005%400178Berk/DeMarzo/Harford•FundamentalsofCorporateFinance,ThirdEdition,GlobalEdition©2015PearsonEducationLimitedExpectedreturnonequity:50%chanceof$780inoneyear:780600Return60030%50%chanceof$540inoneyear:540600Return60010%Expectedreturnonequity(50%)(30%)(50%)(10%)10%.Expectedreturnonportfolioof40%debtand60%equity(40%)(5%)(60%)(10%)8%.Evaluate:Theexpectedreturnontheportfolioof40%debtand60%equityisidenticaltotheexpectedreturnontheassetsofthefirm.5.Plan:ComputeAvocorp’spretaxcostofdebtanditsafter-taxcostofdebt.Execute:Thepre-taxcostofdebtistheYTMontheoutstandingdebtissue.Wesolveforthesix-monthYTMonthebond,andthencomputetheEAR.2166month6month6month6month444$98(1YTM)1YTM1YTMYTM?.175%EAR=(1+4.175%)2–1=8.5243%Thepre-taxcostofdebtis4.175%every6months,or8.5243%peryear.After-taxcostofdebt8.5243×(1–35%)=5.54%Evaluate:Avocorp’sbefore-taxcostofdebtis8.5243%peryear,whileitafter-taxcostofdebt(reflectingthetaxdeductibilityofinterest)is5.54%.6.Plan:ComputeLaurel’safter-taxcostofdebt.Execute:Thepre-taxcostofdebtistheyieldtomaturityontheexistingdebt,or8%.Thus,theeffectiveafter-taxcostofdebtisafter-taxcostofdebt8×(1–40%)=4.8%Evaluate:Laurel’sbefore-taxcostofdebtis8%;itsafter-taxcostofdebtis4.8%.Chapter13TheCostofCapital179©2015PearsonEducationLimited7.Plan:ComputethecostofpreferredstockforDewyco.Execute:Thepriceofthepreferredstockis$80,andthispriceshouldbethepresentvalueoftheperpetuityofpreferredstockdividends.Therefore,thecostofcapitalforpreferredstockis:$80=$5/rpsrps=$5/$80=6.25%Evaluate:Dewyco’scostofpreferredstockis6.25%.8.Plan:ComputeSteadyCompany’scostofequity.Execute:UsingtheCapitalAssetPricingModel,Steady’scostofequitycapitalis:5%1.89%21.2%.Evaluate:SteadyCompany’scostofequityis21.2%.9.Plan:ComputeWildSwing’scostofequity.Execute:UsingtheCapitalAssetPricingModel,WildSwing’scostofequitycapitalis:5%3.29%33.8%.Evaluate:WildSwing’scostofequityis33.8%.10.Plan:ComputeHighGrowth’scostofequitycapital.Execute:Thepriceofthestockis$50,andthispriceshouldbethepresentvalueofthegrowingperpetuityofstockdividends.Therefore,thecostofequitycapitalforHighGrowthCompanyis:$50=$2.5/(re–0.03)re=8%Evaluate:HighGrowth’scostofequitycapitalis8%.11.Plan:ComputeSlow’nSteady’scostofequitycapital.Execute:Thepriceofthestockis$80,andthispriceshouldbethepresentvalueofthegrowingperpetuityofstockdividends.Therefore,thecostofequitycapitalforSlow’nSteadyis:$80=$5/(re–0.04)re=10.25%Evaluate:Slow’nandSteady’scostofequitycapitalis10.25%.12.Plan:ComputethecostofequitycapitalforMackenzieandthedividendgrowthratethatwouldyieldthesamecostofequit