1、4-1CHAPTER 4Bonds and Their ValuationnKey features of bondsnBond valuationnMeasuring yieldnAssessing risk4-2Key Features of a Bond1.Par value:Face amount;paid at maturity.Assume$1,000.2.Coupon interest rate:Stated interest rate.Multiply by par value to get dollars of interest.Generally fixed.(More)4
2、-33.Maturity:Years until bondmust be repaid.Declines.4.Issue date:Date when bondwas issued.5.Default risk:Risk that issuer will not make interest or principal payments.4-4How does adding a call provision affect a bond?nIssuer can refund if rates decline.That helps the issuer but hurts the investor.n
3、Therefore,borrowers are willing to pay more,and lenders require more,on callable bonds.nMost bonds have a deferred call and a declining call premium.4-5Whats a sinking fund?nProvision to pay off a loan over its life rather than all at maturity.nSimilar to amortization on a term loan.nReduces risk to
4、 investor,shortens average maturity.nBut not good for investors if rates decline after issuance.4-61.Call x%at par per year for sinking fund purposes.2.Buy bonds on open market.Company would call if rd is below the coupon rate and bond sells at a premium.Use open market purchase if rd is above coupo
5、n rate and bond sells at a discount.Sinking funds are generally handledin 2 ways4-7Financial Asset ValuationPV=CF1+r.+CF1+r1n1221CFrn.012nrCF1CFnCF2Value.+4-8nThe discount rate(ri)is the opportunity cost of capital,i.e.,the rate that could be earned on alternative investments of equal risk.ri =r*+IP
6、+LP+MRP+DRPfor debt securities.4-9Whats the value of a 10-year,10%coupon bond if rd=10%?VrBd$100$1,000111010.+$1001+rd1001000121010%100+1,000V=?.=$90.91+.+$38.55 +$385.54=$1,000.+1r+d4-1010 10 100 1000NI/YR PV PMTFV-1,000The bond consists of a 10-year,10%annuity of$100/year plus a$1,000 lump sum at
7、t=10:$614.46 385.54$1,000.00PV annuity PV maturity value Value of bond =INPUTSOUTPUT4-1110 13 100 1000NI/YR PV PMTFV -837.21When kd rises,above the coupon rate,the bonds value falls below par,so it sells at a discount.What would happen if expected inflation rose by 3%,causing r=13%?INPUTSOUTPUT4-12W
8、hat would happen if inflation fell,and rd declined to 7%?10 7 100 1000NI/YR PV PMTFV -1,210.71If coupon rate rd,price rises above par,and bond sells at a premium.INPUTSOUTPUT4-13Suppose the bond was issued 20 years ago and now has 10 years to maturity.What would happen to its value over time if the
9、required rate of return remained at 10%,or at 13%,or at 7%?4-14MBond Value($)Years remaining to Maturity1,3721,2111,0008377753025 20 15 10 5 0rd=7%.rd=13%.rd=10%.4-15nAt maturity,the value of any bond must equal its par value.nThe value of a premium bond would decrease to$1,000.nThe value of a disco
10、unt bond would increase to$1,000.nA par bond stays at$1,000 if rd remains constant.4-16Whats“yield to maturity”?nYTM is the rate of return earned on a bond held to maturity.Also called“promised yield.”4-17Whats the YTM on a 10-year,9%annual coupon,$1,000 par value bond that sells for$887?9090 900191
11、0rd=?1,000PV1 .PV10PVM887Find rd that“works”!.4-1810 -887 90 1000NI/YR PV PMTFV10.91 VINTrMrBdNdN 111.+INT1+rd 8879011000111010 rrdd+901+rd,Find rd+INPUTSOUTPUT.4-19n If coupon rate rd,bond sells at a premium.n If rd rises,price falls.n Price=par at maturity.4-20Find YTM if price were$1,134.20.10 -1
12、134.2 90 1000NI/YR PV PMTFV7.08Sells at a premium.Because coupon=9%rd=7.08%,bonds value par.INPUTSOUTPUT4-21DefinitionsCurrent yield=Capital gains yield=YTM =+Annual coupon pmtCurrent priceChange in priceBeginning priceExp totalreturnExp Curr yldExp capgains yld4-22Find current yield and capital gai
13、ns yield for a 9%,10-year bond when the bond sells for$887 and YTM=10.91%.Current yield=0.1015=10.15%.$90$8874-23YTM=Current yield+Capital gains yield.Cap gains yield=YTM-Current yield =10.91%-10.15%=0.76%.Could also find values in Years 1 and 2,get difference,and divide by value inYear 1.Same answe
14、r.4-24Whats interest rate(or price)risk?Does a 1-year or 10-year 10%bond have more risk?rd1-yearChange 10-year Change5%$1,048$1,38610%1,0004.8%1,00038.6%15%9564.4%74925.1%Interest rate risk:Rising rd causes bonds price to fall.4-2505001,0001,5000%5%10%15%1-year10-yearrdValue4-26What is reinvestment
15、rate risk?The risk that CFs will have to be reinvested in the future at lower rates,reducing income.Illustration:Suppose you just won$500,000 playing the lottery.Youll invest the money and live off the interest.You buy a 1-year bond with a YTM of 10%.4-27Year 1 income=$50,000.At year-end get back$50
16、0,000 to reinvest.If rates fall to 3%,income will drop from$50,000 to$15,000.Had you bought 30-year bonds,income would have remained constant.4-28nLong-term bonds:High interest rate risk,low reinvestment rate risk.nShort-term bonds:Low interest rate risk,high reinvestment rate risk.nNothing is riskl
17、ess!4-29True or False:“All 10-year bonds have the same price and reinvestment rate risk.”False!Low coupon bonds have lessreinvestment rate risk but more price risk than high coupon bonds.4-30Semiannual Bonds1.Multiply years by 2 to get periods=2n.2.Divide nominal rate by 2 to get periodic rate=rd/2.
18、3.Divide annual INT by 2 to get PMT=INT/2.2nrd/2 OK INT/2OK NI/YR PV PMTFVINPUTSOUTPUT4-31 2(10)13/2 100/220 6.5 50 1000NI/YR PV PMTFV -834.72Find the value of 10-year,10%coupon,semiannual bond if rd=13%.INPUTSOUTPUT4-32Spreadsheet Functions for Bond ValuationnSee Ch 04 Mini Case.xls for details.lPR
19、ICElYIELD4-33You could buy,for$1,000,either a 10%,10-year,annual payment bond or an equally risky 10%,10-year semiannual bond.Which would you prefer?The semiannual bonds EFF%is:10.25%10%EFF%on annual bond,so buy semiannual bond.EFFimNomm%.1110 102110 25%2.4-34If$1,000 is the proper price for the sem
20、iannual bond,what is the proper price for the annual payment bond?nSemiannual bond has rNom=10%,with EFF%=10.25%.Should earn same EFF%on annual payment bond,so:INPUTSOUTPUT 10 10.25 100 1000 N I/YRPV PMT FV -984.804-35nAt a price of$984.80,the annual and semiannual bonds would be in equilibrium,beca
21、use investors would earn EFF%=10.25%on either bond.4-36A 10-year,10%semiannual coupon,$1,000 par value bond is selling for$1,135.90 with an 8%yield to maturity.It can be called after 5 years at$1,050.Whats the bonds nominal yield tocall(YTC)?10 -1135.9 50 1050 N I/YR PV PMT FV 3.765 x 2=7.53%INPUTSO
22、UTPUT4-37rNom=7.53%is the rate brokers would quote.Could also calculate EFF%to call:EFF%=(1.03765)2-1=7.672%.This rate could be compared to monthly mortgages,and so on.4-38If you bought bonds,would you be more likely to earn YTM or YTC?nCoupon rate=10%vs.YTC=rd=7.53%.Could raise money by selling new
23、 bonds which pay 7.53%.nCould thus replace bonds which pay$100/year with bonds that pay only$75.30/year.nInvestors should expect a call,hence YTC=7.5%,not YTM=8%.4-39nIn general,if a bond sells at a premium,then(1)coupon rd,so(2)a call is likely.nSo,expect to earn:lYTC on premium bonds.lYTM on par&d
24、iscount bonds.4-40nDisney recently issued 100-year bonds with a YTM of 7.5%-this represents the promised return.The expected return was less than 7.5%when the bonds were issued.nIf issuer defaults,investors receive less than the promised return.Therefore,the expected return on corporate and municipa
25、l bonds is less than the promised return.4-41Bond Ratings Provide One Measureof Default RiskInvestment GradeJunk BondsMoodysAaaAaABaaBaBCaaCS&PAAAAAABBBBBBCCCD4-42What factors affect default risk and bond ratings?nFinancial performancelDebt ratiolCoverage ratios,such as interest coverage ratio or EB
26、ITDA coverage ratiolCurrent ratios(More)4-43nProvisions in the bond contractlSecured versus unsecured debtlSenior versus subordinated debtlGuarantee provisionslSinking fund provisionslDebt maturity(More)4-44nOther factorslEarnings stabilitylRegulatory environmentlPotential product liabilitylAccounti
27、ng policies4-45Top Ten Largest U.S.Corporate Bond Financings,as of July 1999IssuerFord Motor Co.AT&TRJR HoldingsWorldComSprintDateJuly 1999Mar 1999May 1989Aug 1998Nov 1998 Amount$8.6 billion$8.0 billion$6.1 billion$6.1 billion$5.0 billion4-46BankruptcynTwo main chapters of Federal Bankruptcy Act:lCh
28、apter 11,ReorganizationlChapter 7,LiquidationnTypically,company wants Chapter 11,creditors may prefer Chapter 7.4-47nIf company cant meet its obligations,it files under Chapter 11.That stops creditors from foreclosing,taking assets,and shutting down the business.nCompany has 120 days to file a reorg
29、anization plan.lCourt appoints a“trustee”to supervise reorganization.lManagement usually stays in control.4-48n Company must demonstrate in its reorganization plan that it is“worth more alive than dead.”Otherwise,judge will order liquidation under Chapter 7.4-49nIf the company is liquidated,heres th
30、e payment priority:1.Secured creditors from sales of secured assets.2.Trustees costs3.Wages,subject to limits4.Taxes5.Unfunded pension liabilities6.Unsecured creditors7.Preferred stock8.Common stock4-50nIn a liquidation,unsecured creditors generally get zero.This makes them more willing to participate in reorganization even though their claims are greatly scaled back.nVarious groups of creditors vote on the reorganization plan.If both the majority of the creditors and the judge approve,company“emerges”from bankruptcy with lower debts,reduced interest charges,and a chance for success.
