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FIN222 Week 10_T CH13:RQ 3, P6,7,10,12,15,21 (7 Questions)RQ 3 Why is the coupon rate of existing debt irrelevant for finding the cost of debt capital? The coupon rate sets the level of coupon payments (Remember, CPN!) over the life of the bond.  This rate is locked in when the bond is issued; thu...

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FIN222Week10_TCH13:RQ3,P6,7,10,12,15,21(7Questions) RQ3Whyisthecouponrateofexistingdebtirrelevantforfindingthecostofdebtcapital?  Thecouponratesetsthelevelofcouponpayments(Remember,CPN!)overthelifeofthebond.  Thisrateislockedinwhenthebondisissued;thus,thisisahistoricalrateofreturn.  Marketconditionschangecausingthefluctuationofbondprices.  Forthecostofdebtthefirmshouldusetherateofreturnthatbondinvestorscurrentlydemandon thedebt.Thisistheyieldtomaturity. P13.6LaurelLimitedhasdebtoutstandingwithacouponrateof6%andayieldtomaturityof7%. Itstaxrateis30%.WhatisLaurel’seffective(after‐tax)costofdebt? Assumingannualcouponpayments,  Thepre‐taxcostofdebtistheyieldtomaturityontheexistingdebt,7%.Wedonotneedtoconvert thistoEARasEAR=7%.  Theafter‐taxcostofdebtis 7%  1  30%  4.9%  Assumingsemi‐annualcouponpayments,  Thepre‐taxcostofdebt=EAR= (1 

0.07 2 )  1  0.071225  2

 Theafter‐taxcostofdebtis0.071225*(1‐0.3)=0.0499or4.99% Note:Fortherestoftutorialquestions,assumeannualcouponpayments.  P7Dewycohaspreferencesharestradingat$50each.Thenextpreferencedividendof$4isduein oneyear.WhatisDewyco’scostofcapitalforpreferenceshares?  Pp=$50,Divp=$4 Pp 

Div p rP

 rP 

Div p Pp

 Dewyco’scostofpreferencesharesis8%.        Page1of4 



4  8%  50

P10   

HighGrowthCompanyhasasharepriceof$20.PE=$20 Thefirmwillpayadividendnextyearof$1andDiv1=$1 Itsdividendisexpectedtogrowatarateof4%peryearthereafter. g=0.04 WhatisyourestimateofHighGrowth’scostofequitycapital?



o Constantdividendgrowthmodelshouldcometoyourmind. From PE 

rE 

Div1 Div1 ,weknow rE   g rE  g PE

1  0.04  0.09or9%  20

 o HighGrowth’scostofequityis9%. P12 

MackenzieCompanyhasasharepriceof$36andwillissueadividendof$2nextyear. PE=$36,Div1=$2  Ithasabetaof1.2,therisk‐freerateis5.5%anditestimatesthemarketriskpremiumto be5%.  a. EstimatetheequitycostofcapitalforMackenzie.  o Tocalculatecostofequity,theCAPMshouldbechosenovertheconstantdividendgrowth modelasthegrowthrateisunknown.  o E[Ri]=rf+beta(E[Rmkt]‐rf)=0.055+1.2(0.05)=0.115or11.5% b.UndertheCDGM,atwhatratedoyouneedtoexpectMackenzie’sdividendstogrowtogetthe sameequitycostofcapitalasinpart(a)?   PE 



Div1 P =$36,Div1=$2,g=? rE  g E 36 

2 2  g  0.115   5.94%  0.115  g 36

     Page2of4 

P15   Growth Company’s current share price is $20 and it is expected to pay a $1 dividend per sharenextyear.PE=$20,Div1=$1  Afterthat,thefirm’sdividendsareexpectedtogrowatarateof4%peryear.g=0.04 a. WhatisanestimateofGrowthCompany’scostofequity? From PE 

20 

Div1 Div 1 ,weknowrE  g rE  g PE 1 1  rE   0.04  9%  r E  0.04 20

b. GrowthCompanyalsohaspreferencesharesoutstandingthatpaya$2fixeddividend.If thisshareiscurrentlypricedat$28,whatisGrowthCompany’scostofpreferenceshares? Pp 

Div p rP

 rP 

Div p Pp



2  0.0714or7.14%  28

c. GrowthCompanyhasexistingdebt issuedthreeyearsagowithacouponrateof6%. The firmjustissuednew debt at parwithacouponrate of6.5%. What isGrowthCompany’s pre‐taxcostofdebt? o Thepre‐taxcostofdebtisthefirm’sYTMoncurrentdebtwhencouponsarepaidannually. o Since the firm recently issued debt at par, then the YTM of that debt must be equal to the couponrateofthedebt.Thus,thepre‐taxcostofdebtis6.5%. d.   Growth Company has five million ordinary shares outstanding and one million preferencesharesoutstanding,  anditsequityhasatotalbookvalueof$50million(irrelevant!).  Itsliabilitieshaveamarketvalueof$20million.  IfGrowthCompany’sordinaryandpreferencesharesarepriced asinparts(a)and(b), whatisthemarketvalueofGrowthCompany’sassets? o o o o

Marketvalueofdebt=$20million Marketvalueofpreferenceshares=$281millionshares=$28million Marketvalueofequity=$205millionshares=$100million Marketvalueofassets=$20mil+$28mil+$100mil=$148million

e. Growth Company faces a 30% tax rate. Given the information in Problems (a)–(d), and youranswerstothoseproblems,whatisGrowthCompany’sWACC?

rWACC  rE E%  rP P%  rD (1 TC )D%   100   28   20    0.0714    0.065  1  0.3  rwacc   0.09      8.05%   148   148   148  o ThecalculationleadstoaWACCof8.05%.  Page3of4 

P21  

Yourcompanyhastwodivisions: onedivisionsellssoftwareandtheotherdivisionsellscomputersthroughadirectsales channel,primarilytakingordersovertheInternet.  YouhavedecidedthatDellComputerisverysimilartoyourcomputerdivision,intermsof bothriskandfinancing.Yougoonlineandfindthefollowinginformation: o Dell’sbetais1.21,therisk‐freerateis4.5%,itsmarketvalueofequityis$67billion andithas$700millionworthofdebtwithayieldtomaturityof6%.  Yourtaxrateis30%andyouuseamarketriskpremiumof5%inyourWACCestimates. a. WhatisanestimateoftheWACCforyourcomputersalesdivision?  o TofindtheWACCofthecomputersalesdivision,wewillcalculatetheWACCofDellComputers.

o CostofEquity(rE)forDellis4.5%+1.21×5%=10.55%. o Thepre‐taxreturnondebt(rD)forDellis6%. o Dellhasamarketvalueofequityof$67billionandamarketvalueofdebtof$0.7billion. o Dell’sWACCis

rWACC  rEE%  rPP%  rD (1  TC )D%   67   0.7   0.06  1  0.3   rWACC  0.1055      0.1048 or10.48%   67.7   67.7 

b.IfyouroverallcompanyWACCis12%andthecomputersalesdivisionrepresents40%ofthe valueofyourfirm,whatisanestimateoftheWACCforyoursoftwaredivision? o Thefirm’sWACCshouldbetheweightedaverageofthedivisionalWACCs.

0.12  0.4 0.1048   0.6   WACCsoftware   WACCsoftware  0.1301or 13.01%   

Page4of4 



FIN222Week10WorkshopSolution  FIN222Ltdhasdecidedtousetheweighted averagecostofcapital (WACC) to discount the free cash flows associated with project evaluation.Youhavebeengiventhetaskofdeterminingtheafter‐tax WACC of the firm. You are informed that FIN 222 Ltd uses the followingsecuritiestofunditsoperations:  7,000 individual bonds with a face value of $1000 that will mature in 10 years’ time offer a coupon that is paid half‐ yearly.Thecouponrateforthesebondsis8%perannum. The currentmarketinterestrateforthesebondsis9%perannum. Hint:Fromthisinformation,  How would you compute the after‐tax cost of debt when coupons are paid semi‐ annually?EARformulashouldcometoyourmind!  rDisthebefore‐taxreturnsowhatdoyouhavetodointheend?  Howwouldyoucomputethemarketvalueofbonds?PB*numberofsecurities.

  ThebetaofFIN222Ltdis1.2,therisk‐freerateiscurrently4% per annum, and the market risk premium is 6%. Currently 800,000 ordinary shares are outstanding and each share is tradingatamarketpriceof$5. Hint:Fromthisinformation,  How would you compute the cost of ordinary shares? Use CAPM or Constant dividendgrowthmodel?Choose!  Howwouldyoucomputethemarketvalueofshares?PE*numberofsecurities.

  400,000 preference shares, which pay an annual dividend of 1%onastatedvalueof$100.Eachpreferenceshareistrading atamarketpriceof$10. Hint:Fromthisinformation,  Howwouldyoucomputethecostofpreferenceshares?Thedividendisfixed!  Howwouldyoucomputethemarketvalueofshares?Pp*numberofsecurities.

  Thecompanytaxrateis30percent.  ComputetheWACCbasedontheaboveinformation.

 DEBT   Costofdebt(rD) o Thecurrentmarketinterestrate=annualYTM=9%perannum o Therefore 9%/2 =4.5% indicates the semi‐annual YTM.  We need to convert this to effectiveannualrate(EAR)whichrepresentspre‐taxrD o rD= (1  0.045)  1  0.09203 (Pre‐tax) MVofdebt  n=10x2=20  CPN=1,000*(0.08/2)=$40  y=9%/2=4.5%=0.045 2



   40  1 1000    $934.96 PB 120  0.045  (1+ 0.045)  (1+ 0.045)20  MVofdebt=7,000x$934.96=$6,544,720  ORDINARYSHARES   Costofordinaryshares(rE)=rf+beta(E(RMkt)‐rf)=0.04+1.2*0.06=0.112or11.2%(after‐ tax)  MVofordinaryshares=800,000*$5=$4,000,000  PREFERENCESHARES   Costofpreferenceshares(rp) o Dividendamount=0.01*100=$1

Pp 

Div p rp

1 10  ,rp  0.10 rp



o Therefore,rp=0.10or10%(after‐tax) 

 MVofpreferenceshares=400,000*$10=$4,000,000  COMPUTATIONOFWACC

rWACC  rEE%  rPP%  rD (1 TC )D%   Totalmarketvalueofthesecurities=$6,544,720+4,000,000+4,000,000=$14,544,720  WACC=($6,544,720/$14,544,720)*0.09203(1‐0.3) +($4,000,000/$14,544,720)*0.112 +($4,000,000/$14,544,720)*0.10 =0.02899+0.0308+0.0275=0.08729or8.729 ThereforetheWACCforFIN222=8.729...