CORPORATEFINANCE
REVIEWFORTHIRDQUIZ
AswathDamodaran
BasicSkillsNeeded
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Whatisthetradeoffinvolvedinthecapitalstructure
choice?
Canyouestimatetheoptimaldebtratioforafirmusing
thecostofcapitalapproach,andcanyouestimatethe
effectonfirmvalueofmovingtotheoptimal?
Basedonthefirm’sfinancialfundamentals,canyou
determinehowtheyshouldmovetotheiroptimal?
Canyouusethemacroeconomicregressiontoevaluate
whatkindoffinancingyoushouldbeusingasafirm?
2
Debt:TheTradeOff
Advantages of Borrowing
Disadvantages of Borrowing
1. Tax Benefit:
1. Bankruptcy Cost:
Higher tax rates --> Higher tax benefit
Higher business risk --> Higher Cost
2. Added Discipline:
2. Agency Cost:
Greater the separation between managers
Greater the separation between stock-
and stockholders --> Greater the benefit
holders & lenders --> Higher Cost
3. Loss of Future Financing Flexibility:
Greater the uncertainty about future
financing needs --> Higher Cost
3
QualitativeAnalysis:Asimpleexample
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Assumethatlegislatorsareconsideringataxreform
planthatwillallowcompaniestodeductdividends
fortaxpurposes?Whateffectwillthishaveon
optimaldebtratios?Why?
Alternatively,assumethatlegislatorsaretalking
aboutputtingacapontheinterestexpensetax
deduction(i.e.,itcannotexceed50%ofoperating
income).Whateffectwillthishaveontheoptimal
debtratio?Why?
4
TheCostofCapital:Definition
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Market Value
Weight of Debt
CostofCapital=ke(E/(D+E))+After-taxkd
(D/(D+E))
Weighted average
of costs of
financing
Riskfree
Rate + Beta
(Risk
Premium)
Beta: is the
levered beta
based on D/E
ratio
Market Value Weight of Equity
Today’s long term
Borrowing rate (1-tax
rate)
Borrowing rate = Riskfree
rate + Default spread
Default spread: based on
rating (actual or
synethetic)
5
ComputingMarketValues
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Themarketvalueofequityisusuallyfairlysimpleto
compute,atleastforapubliclytradedfirm.
Themarketvalueofdebtcanusuallybecomputed
bytakingthepresentvalueoftheexpected
paymentsonthedebtanddiscountingbacktothe
presentatthecurrentborrowingrate.
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ComputingCostofCapital:Example
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Youhavebeen asked toassessthecostofcapitalandreturnon
capitalforCVXCorporation. Thefollowing information isprovided
toyou:
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Thefirmhas15millionsharesoutstanding,tradingat$10pershare.The
bookvalueofequityis$50million.
Thefirmhas$50millionbondofferingoutstanding,withacouponrateof
7%,tradingatpar.Inaddition,thefirmhasanoldbankloanonitsbooks,
with5yearslefttomaturity,an8%statedinterestrate,andafacevalueof
$50million.
Thefirmalsohadoperatingleaseexpensesof$10millionforthecurrent
year,andhascommitmentstomakethesesameleasepaymentsforthe
next7years.
Thefirm’scurrentbetais1.20,thetreasurybondrateis6%andthe
marketriskpremiumis5.5%
Thefirmalsoreportedearningsbeforeinterestandtaxesof$40million
(afteroperatingleaseexpenses),andhasamarginaltaxrateof40%.
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EstimatingMarketValueofDebt
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Step1:Getacurrentlongtermborrowingrate.Therearetwo
ratesprovidedintheproblem– thecouponrateonthebond
(7%)andtheinterestrateonthebankloan(8%).Theyare
bothhistoricalratesandcannotbeusedgenerallyascostsof
debt.However,thebondtradesatpar,indicatingthatthe
couponrateonthebond=currentmarketinterestrateon
thebond=currentcostofdebt
Step2:Computemarketvalueofdebt
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5-yearbankloan;Face value=$50million;Interest expense =$4
million(8%)
ValueofBankLoan=4(PVA,7%,5) +50/(1.07)5 =
$52.05
ValueofBondsOutstanding (tradingatpar) =
$50.00
PVofOperatingLeases =10(PVA,7%,7) =
$53.89
Market ValueofOutstanding Debt=
$155.94
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EstimatingCostofCapital
¨
Step1:Getthemarketvalueweights
MarketValueofEquity=15*10=
¤ DebtRatio=155.94/(150+155.94)=
¤
¨
$150.00
50.97%
Step2:Computethecostofcapital
CostofEquity=6%+1.2(5.5%)=
12.60%
¤ CostofCapital=12.60%(.49)+7%(1-.4)(.51)=8.32%
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EstimatingReturnonCapital
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UnadjustedReturnoncapital=40(1-.4)/(50+50+50)=16%
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AdjustedEBIT=40+53.89*.07=
$43.77
AdjustedBVofCapital=50+(50+50+53.89)= 203.89
AdjustedReturnonCapital=43.77(1-.4)/203.89 =12.88%
TheLongWay
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BVofdebt=100(Bankloan+Bond)
Sinceoperating leases aredebt,youhavetoadjusttheoperating
income toreflectimputed interestexpenses onthelease debt.
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BVofequity=50
AdjustedEBIT=EBIT+OperatingLeaseExp - DepreciationonLeasedAsset
=40+10- 53.89/7=$42.30
TheShortCut
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AdjustedEBIT=EBIT+ImputedInterestexpenseonLeaseDebt=40+
53.89*.07=$43.77
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OptimalFinancingMixandCostofCapital
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Thevalueofafirmisthepresentvalueofthe
expectedcashflowstothefirmdiscountedbackat
thecostofcapital.
Whentheoperatingincomeisunaffectedby
changesindefaultrisk(ratings),thevalueofthefirm
willbemaximizedwherecostofcapitalisminimized.
Thisistheoptimaldebtratio.
Inthemoregeneralcase,wherebothcashflowsand
thecostofcapitalchangeasthefinancingmix
changes,theoptimaldebtratioiswherethefirm
valueismaximized.
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ComputingCostofCapitalasDebtRatios
Change
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CostofEquity
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Estimate theunlevered betaforthefirm
Estimate thebetaateach debtratio.Asdebtratioschange, thedebt to
equityratiowillalsochange,leadingtoahigherbeta.
D/E=DebtRatio/(1 - DebtRatio)
Use thelevered betatoestimate thecostofequityateachdebtratio.
CostofDebt
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Estimate thetotalvalueofthefirm(Value ofEquity+ValueofDebt)
Estimate thedollardebtateachdebtratio
Estimate theinterest expenses ateach debtratio:Debt*Interest rate
Estimate theinterest coverage ratio
Estimate theratingandinterest rate
Checktomakesurethatyouhaveconsistency.Ifnot,loopback.
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EstimatingCostofCapital;Example
DebtRatio
10%
$Debt
$1,500
EBIT
$1,000
InterestExpenses
$120
InterestCoverageRatio8.33
BondRating
AA
InterestRate
8.00%
After-taxCostofDebt 4.80%
Beta
1.06
CostofEquity
12.83%
CostofCapital
12.03%
20% ExtraColumn
$3,000
$1,000
$240
$270
4.17
3.70
BBB
BBB
9.00%
9.00%
5.40%
1.14
13.29%
11.71%
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CoverageRatiosandSpreads
CoverageRatio
>10
7-10
5- 7
3- 5
2- 3
1.25- 2
0.75- 1.25
0.50- 0.75
0.25- 0.50
<0.25
Rating SpreadoverTreasury
AAA 0.30%
AA
1.00%
A
1.50%
BBB 2.00%
BB
2.50%
B
3.00%
CCC 5.00%
CC
6.50%
C
8.00%
D
10.00%
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ThePayoffinTermsofFirmValue
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When thecostofcapitalchanges,thevalueofthefirmwillalso
change.Thesimplest waytocompute thechangeistodothe
following:
1.Estimatetheannualchangeinfinancingcostsfrommoving from
onecostofcapitaltoanother.
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ChangeinFinancingCost=(WACCb - WACCa)Current FirmValue
Firmvalue=Marketvalueofequity+MarketvalueofDebt
2.Estimatethepresentvalueofthesavingsinfinancing costs,by
a.assuming aperpetuity withnogrowth
ChangeinFirmValue=AnnualChange/WACCa
b.assumingagrowingperpetuity
ChangeinFirmValue=AnnualChange/(WACCa - g)
[gcanbeestimatedfromcurrentmarketvaluebutshouldbe<growthratein
economy]
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ComputingPerShareValues&MaximumOffer
prices
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Ifweassume rationality, where allinvestorsincludingthose whosellback
theirshares tothefirmgetanequalshare ofthevalueincrease:
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Ifweassume thatwecanbuybackstockatthecurrent price,thevalue
increase totheremaining stockholders willbeevengreater:
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ValueIncreaseperShare=TotalIncrease/(Number ofShares- Sharesbought back)
Sharesbought back=NewDebttakenon/Currentstockprice
Inthemostgeneralcase, where theshares areboughtbackat$Px,the
divisionwillbeasfollows($Pistheoriginalprice):
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ValueIncreaseperShare=TotalIncrease/Numberof Shares
BuybackPrice=CurrentPrice+ValueIncrease
Selling Shareholders =(PX-P)*Number ofsharesbought back
Holding Shareholders =ValueIncrease- (Px-P) *Number ofsharesbought back
Ifwecanlockincurrent debtatexistingrates, whilemovingtohigher
leverage andgreater defaultrisk,theincrease invalue willbeeven
greater.
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ComputingChangeinFirmValue:Example
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CSLCorporationisamid-sizedtransportationfirm
with10millionsharesoutstanding,tradingat$25
pershareanddebtoutstandingof$50million.
Itisestimatedthatthecostofcapital,whichiscurrently
11%,willdropto10%,ifthefirmborrows$100million
andbuysbackstock.
¤ Estimatetheexpectedchangeinthestockpriceifthe
expectedgrowthrateinoperatingearningsovertimeis
5%.
¤
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Ifinvestorsarerational:ComputingChangein
FirmValueandshareprice
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Hereisthefirstwaytodothis
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Savingseachyear=(250+50)(.11- .10)=3
ChangeinFirmValue=3/(.10-.05) =60
Changeinstockprice=60/10=$6.00
Newstockprice=25+6.00=31.00
Hereisanotherwayofshowingwhathappens:
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Valueoffirmbefore changeincapitalstructure =250+50=
Valueoffirmafter changeincapitalstructure =300+60=
Debtoutstanding afterrecapitalization =50+100=
Valueofequityafter recapitalization =
Numberofshares after recap=10– 100/31.00=
Valuepershare = 210/6.774=
300
360
150
210
6.774
$31.00
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Buybackatthecurrentprice?
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Whatwouldthechangeinstockpricebe,ifyouwereableto
buybackstockatthecurrentprice?
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Numberofshares boughtback=$100mil/$25=4millionshares
Changeinstockprice=60/(10- 4)=$10
Newstockprice=$25+$10=35.00
Hereisanotherwayofshowingwhathappens:
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Valueoffirmbefore changeincapitalstructure =250+50=
300
Valueoffirmafter changeincapitalstructure =300+60=
360
Debtoutstanding afterrecapitalization =50+100=
150
Valueofequityafter recapitalization =
210
Numberofshares after recap=
10– 100/25=
6
Valuepershare = 210/6=
$35.00
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Buybackattoohighaprice…
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Whatiftheyhadpaid$33.33pershare?
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Numberofsharesboughtback=$100/$33.33=3millionshares
Sellingshareholdersgain=3millionshares*(33.33-25) =$25million
Changeinstockprice=(60- 25)/7=35/7=$5.00
Newstockprice=$25+$5=$30.00
Hereisanother wayofshowing whathappens:
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Valueoffirmbeforechangeincapitalstructure=250+50=
300
Valueoffirmafterchangeincapitalstructure=300+60=
360
Debtoutstandingafterrecapitalization=50+100=
150
Valueofequityafterrecapitalization=
210
Numberofsharesafterrecap=10– 100/33.33=
7million
Valuepershare=
210/7
$30.00
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Lookingatthepremium
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Premiumpaidtobuybackstockholders=Numberof
sharesboughtback*(Priceonbuyback– Priceprior
torecap)=3*(33.33– 25)=$25million
Premiumleftfornon-tenderingstockholders=
Remainingshares*(Priceafterrecap– Pricepriorto
recap)=7*(30-25)=$35million
Totalvalueaddedbyrecap=$25million+$35
million=$60million
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GettingtotheOptimal
Conditionofthefirm
Actiontotake
Underlevered,Targetoftakeover
Borrowmoney,buybackstocknow
Underlevered,Nottargetofatakeover,
Goodprojects
Borrowmoney,Takeprojects(nowand
overtime)
Underlevered,Nottargetofatakeover,
Badprojects
Borrowmoney,Buybackstock&pay
dividends overtime
Overlevered,threatofbankruptcyhigh
Issueequitytoretiredebtorequityfor
debtswap,Restructure debt
Overlevered,nonear-term threatof
bankruptcy,Goodprojects
Useretainedearnings(equity)totake
projectsovertime
Overlevered,nonear-term threatof
bankruptcy,Badprojects
Useretainedearnings(equity)toretire
debtovertime
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TheRightFinancingType
MacroRegression
ImplicationsforDebtDesign
Δ V=a+b(Δ Interestrate)
Ifbisnegative:Measures asset duration
Ifbis0orpositive: Suggestsshort
duration
(Setdebt duration=asset duration)
Δ V=a+b(Δ GDP)
Ifbispositive,firm iscyclical
Ifbiszero,firmisnon-cyclical
Ifbisnegative,firmiscountercyclical
(Becautious inmovingtooptimal)
Δ OI=a+b(Δ Inflationrate)
Δ V=a+b(Δ Inflationrate)
Ifbispositive,firm haspricingpower
Ifbiszero,firmhasnopricingpower
Ifbisnegative,firmhasnopricingpower
&hascoststhatarepronetoinflation
(Ifpricingpower,usefloatingratedebt)
Δ OI=a+b(Δ Weighted Dollar)
Δ V=a+b(Δ Weighted Dollar)
Ifbispositive,firm gainsfromstronger$
Ifbisnegative,firmlosesfromstronger$
(Witheither, youneedforeigncurrency
debt)
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Abalancesheetviewofduration…
Objective: Duration of the debt = Duration of the assets
Assets
Business/ Asset 1
Business/ Asset 2
Business/ Asset 3
V 1 D1
V 2 D2
V 3 D3
Duration of the firm = Weighted average
of the durations of the individual
businesses or assets (Weights are
value weights)
[V1D1+ V2D2 + V3D3]/(V1+ V2+ V3)
Liabilities
Debt 1 B1 D1
Debt 2 B2 D2
Equity
Duration of the debt is the
weighted average of the durations
of the individual debt issues
(weights are based on amount)
[B1D1+ B 2D2] /(B1+ B 2)
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ExampleofDurationUsage
Youhaverunaregression ofchangesinfirmvalueagainstchanges inlong
termbondratesandarrived atthefollowingregression:
ChangeinFirmValue=0.16- 5.00ChangeinLongTermBondRate
¨ Thefirmhas$100millioninzero-coupon two-year notesoutstanding,
andplanstoborrowanother $150millionusingzero-coupon securities. If
yourobjective istomatchthedurationofthefinancingtothose ofthe
assets, whatshouldthematurityofthese zero-coupon notesbe?
Step1:Estimate theduration ofyourassets
Regression coefficient =Duration=5years
Step2:Settheduration ofyourdebtequal tothedurationofyourassets
¨
(100/250) (2)+(150/250) (X)=5
Solvefor X,
X=7years
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Bottom-upDuration:Amorecomplicated
example
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Youhaverunaregressionoffirmvaluechangesagainst
interestratechangesforSteelProductsInc,anoffice
suppliesmanufacturer.
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ChangeinFirmValue=0.06– 7.5(Change inInterestRates)
Thefirmhastwotypesofdebtoutstanding– aone-year
$200millionbondissue(withadurationof1year),and
afive-year$100millionbankloan(withadurationof4
years),and70millionsharesoutstandingat$10per
share.Itisplanninga$250millionbondissuetofinance
expansionintotheinternetretailingbusiness.Ifthe
durationofassetsoffirmsinthissectorisonly1year,
whatshouldthedurationofthebondissuebe?
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TheSolution
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Step1:Computethedurationofthefirmafterexpansion
Valueoffirmbeforeexpansion =300+70*10=1000
¤ Durationofassetsafterexpansion
=7.5(1000/1250)+1(250/1250)=6.2
¤ Weighted DurationofAssetshastobeequal to6.2years
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Step2:Solveforthedurationofyournewdebt
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(200/550)(1)+(100/550)(4)+(250/550)(X)=6.2
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SolveforX
X=11.24years
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