1、Interest Rates and Bond ValuationChapter 6Summer 2008Summer 20081RoadmaplBond ValuationlTerminologylBasic valuationlRelationship Between The Bond Value&YTMlWhy the bond price changes?lInterest Risk&Default RisklBond Features and TypeslInflation,Nominal and Real RateslTerm Structure of Interest Rates
2、(Yield Curve)lDeterminates of bond yieldSummer 20082BondslA bond is a debt instrument requiring the issuer to repay to the investors the amount borrowed plus interest over a specified period of time.lInvolved Parties:lIssuers/Debtors/Borrowers:lThe parties(government or corporations)that borrow mone
3、y and issue debt securitieslInvestors/Creditors/Lenders/Bondholders:lThe parties(person,government or corporations that lend money to issuers.(they buy the debt securities).lOther parties:lUnderwriters:Investment banking firms that act as agents to distribute bonds to investors.They will charge a fe
4、e for the service.Summer 20083Bond Face valuelFace Value(Par Value)-FlThe total principal amount that will be repaid at the end of the loan.lIt is often different from market valuelBonds market value is the fair value a bond can be bought/sold in the market.lIn FINA 110,we assume bonds market value
5、is the same as its market price.Summer 20084Bond-CouponslStated annual interest payment make on a bond.lIt is determined upon issuance.Normally,it is expressed as a percentage of par value.lCoupon Payment=Coupon Rate(c)x Par Value.lCoupon rate is NOT the discount rate for discounting!Instead,it is o
6、nly the interest rate that issuer promises to pay periodically.lIf coupon rate is zero,bonds are called Zero-Coupon Bonds(Zeros)lCurrent Yield=the(annual)coupon/the market priceSummer 20085Bond-MaturitylThe number of years left until the face value is paid.lThe maturity date of a bond refers to the
7、date that the debt will cease to exist.lA calendar year can correspond to many compounding periods.Summer 20086IssuerFace ValueCoupon rateMaturity dateCouponFace value,coupon rate and maturity are stated in the bond and fixed.Market value(price),however,varies from time to timeSummer 20087ExamplelCo
8、mpany A has 8%coupon bonds on the market with 9 years left to maturity.The coupon is paid annually.Its par value is$1,000 and currently sells for$1,047.50.lFace value=lMarket value=lCoupon rate=lMaturity=lCompounding periods per year=$1,000$1,047.58%9 years1Summer 20088RoadmaplBond ValuationlTermino
9、logylBasic valuation An application of Discounted Cash Flow ValuationlRelationship Between The Bond Value&YTMlWhy the bond price changes?lInterest Risk&Default RisklBond Features and TypeslInflation,Nominal and Real RateslTerm Structure of Interest Rates(Yield Curve)lDeterminates of bond yieldSummer
10、 20089Bond ValuationlIf bond is correctly priced by the market,we should haveBond PricePV(Coupons)+PV(Face value)Summer 200810Bond Valuation(contd)lF:Face value Bond price:market valuelc:Coupon rate C:Coupon=c*FlT:Maturity r:YTM,or required discount rate21Bond Price.1(1)(1)(1)11*(1)*(1)(1)(1)(1)TTTt
11、TTTtCCCFrrrrCFCFrrrrr0T321 Time(years)$C$C$C$C$C+F.Summer 200811Bond-Yield to Maturity(YTM)lYTM tells you the annual return of the bondlWhat return(yield)we are receiving if we buy and hold this bond till maturitylExample:lCompany A has 8%coupon bonds on the market with 9 years left to maturity.The
12、coupon is paid annually.Its par value is$1,000 and currently sells for$1,047.50.What return are we receiving if we buy and hold these bonds till maturity?9911,000*8%1,0001,047.50(1)(1)ttrrr=7.26%Trial and errorYield to maturity of these bonds is 7.26%.(YTM fluctuates with bonds market price.)Summer
13、200812Bond-Yield to Maturity(YTM)lSince the bonds price is agreed by most investors in the market,YTM reflects the underlying fair level of required return in the market.lIt is also called“Market Interest Rate”lIt implies the current rate of interest or time value of money agreed in the market.lThis
14、 is the appropriate discount rate for the bond valuation.lThe yield is changing over time,which depends on the investors risk attitudes and investment opportunities.Summer 200813Example(YTM)lSuppose the par value(face value)of a bond is$1,000,which will mature in 2 years.It is sold at$1,035.67 and i
15、ts coupon rate is 10%,paid annually.What is YTM?lCoupon=par value*coupon rate =1,000*10%=$100Summer 200814Example(YTM)(contd)012yearMarket value:$1,035.67 Coupon=$100Coupon=$100,Par value=$1,000The bond has a yield to maturity of 8%.(or bonds yield is 8%)2$100$100$1,000$1,035.678%1(1)rrrSummer 20081
16、5Bond Valuation Example-PerpetuitylFace value=1000;Coupon rate=8%;Time to maturity=.Assume that investors require 10%yield to maturity on the bond,what would be the price of the bond?Bond Purchased$80$80$80t=1t=2t=3t=0What is the appropriate rate for bond valuation,10%or 8%?10%Since it is a perpetua
17、l bond,only coupon will be paid.Face value is just used to calculate annual coupon.Summer 200816Bond price at t=0 P=Recall price of perpetuity=C/rValuation of Perpetuity$80(1+0.1)+$80$80(1+0.1)2(1+0.1)3+=$800.1=$800What would be the price of the bond if YTM=8%?P=$80/8%=$1,000Summer 200817Answer to E
18、xamples(1 2)1.Zevon,Inc.,has 9%coupon bonds on the market that have 8 years left to maturity.The bonds make annual payments.If the YTM on these bonds is 7%,what is the current bond price?lAlways assume face value to be$1,000,unless stated otherwise.88881111,000*9%1,0001,000(17%)90*(17%)(17%)7%(17%)$
19、1,119.43ttPSummer 200818Answer to Examples(1 2),contd2.Merton Enterprises has bonds on the market making annual payments,with 16 years to maturity,and selling for$1,051.At this price,the bonds yield to maturity is 6.8%.What must the coupon rate be on Mertons bonds?(Coupon is paid annually.)161616161
20、111,000*1,0001,000(16.8%)$1,0511,000*(16.8%)(16.8%)6.8%(16.8%)7.333%ttcPccSummer 200819RoadmaplBond ValuationlTerminologylBasic valuationlRelationship Between The Bond Value&YTMlWhy the bond price changes?lInterest Risk&Default RisklBond Features and TypeslInflation,Nominal and Real RateslTerm Struc
21、ture of Interest Rates(Yield Curve)lDeterminates of bond yieldSummer 200820Relationship Between The Bond Value&YTMlFace value=1000;Coupon rate=8%,paid annually;Time to maturity=5 years.What would be the price of the bond iflYTM is 8%=coupon ratelYTM is 10%coupon ratelYTM is 6%Coupon RatePrice=C*1 1/
22、(1+r)T/r+F*1/(1+r)T=$80*1-1/1.15/0.1+$1,000/1.15=$303.26+$620.92=$924.18 (discounted by$75.82)Bond sells for less than its face value a Discount Bond If cr,Price=F*(c/r)*1 1/(1+r)T+F*1/(1+r)T F 1-1/(1+r)T+F*1/(1+r)T=FSummer 200824IntuitionlThe market interest rate is 10%,that is also the investors r
23、equired return on bond investment.lCoupon rate is 8%:the issuer only promises to pay 8%coupon per yearlWhats PV of the difference?l1000*(10%-8%)*1 1/(1+10%)5/10%=$78.82lHow to compensate investor?lInvestors pay$78.82 less at the beginningThis bond pays less than the going rate!Summer 200825If YTM=6%
24、r,Price=F*c*1 1/(1+r)T/r+F*1/(1+r)T F 1-1/(1+r)T+F*1/(1+r)T=FSummer 200826IntuitionlThe market interest rate is 6%,that is also the investors required return on bond investment.lCoupon rate is 8%:the issuer only promises to pay 8%coupon per yearlWhats PV of the difference?l1000*(6%-8%)*1 1/(1+6%)5/6
25、%=$-84.25lHow to compensate the issuer?lInvestors pay$84.25 more at the beginningThe coupon is 2%too high!Summer 200827Relationship Between Coupon and Yield SummarylIf YTM=coupon rate,then bond price=par valuelIf YTM coupon rate,then bond price par valuelSelling at a discount,called a discount bondl
26、If YTM par valuelSelling at a premium,called a premium bondSummer 200828ExamplelSuppose that a bond currently sells for$932.90.It pays an annual coupon of$70,and it matures in 10 years.It has a face value of$1,000.lWhat is its coupon rate?l7%lWhat is its current yield(A bonds annual coupon divided b
27、y its price)?l70/932.90=7.5%lWhat is the YTM,greater or less than coupon rate?l$932.90=70 x 1-1/(1+r)10/r+1,000/(1+r)10lTrial and Error-8%r=2.517%lR r+h r 5.9%-3.3%=2.6%Summer 200866Quick ChecklIf we require a 5%real return and we expect inflation to be 3%,what is the nominal rate?lR=(1+5%)(1+3%)1=8
28、.15%lApproximation:R=5%+3%=8%Summer 200867Inflation rate in HK(Monthly Inflation Rate)Source:http:/asianbondsonline.adb.org/asiabondindicators/Summer 200868OutlinelBond ValuationlTerminologylBasic valuationlRelationship Between The Bond Value&YTMlWhy the bond price changes?lInterest Risk&Default Ris
29、klBond Features and TypeslInflation,Nominal and Real RateslTerm Structure of Interest Rates(Yield Curve)lDeterminates of bond yieldSummer 200869Term Structure of Interest Rates(Yield Curve)lThe relationship between“pure”nominal interest rates and term to maturity.(YTM and t)lConditions:lFree of effe
30、ct of default risk,lYTM of single-payment bonds(pure discount loans)lPure time value of money for different length of timeMarket prices of US Treasure bonds(par=$1,000)Summer 200870Yield CurvelDifferent shapes of the term structure lUpward Sloping lLong-term rates Short term rateslDownward SlopinglL
31、ong-term rates Short and Long-term ratesl3 components underlying the term structure:lReal ratelInflation premiumlInterest rate risk premiumSummer 200871Upward-Sloping Yield Curve Fig.6.6 InterestrateTime tomaturityNominal Risk-free interestrateInterest raterisk premiumReal rateInflationpremiumpure t
32、ime value of money always flatTo compensate greater risk of loss resulting from changes in interest rate.Longer-term bond is riskier than shorter-term bonds always upward sloping.Summer 200872Downward-Sloping Yield Curve Fig 6.6InterestrateNominal Risk-free interestrateTime tomaturityReal rateInflat
33、ionpremiumInterest raterisk premiumSummer 200873Slope of the Yield Curve&Macroeconomic ConditionslHistorically,the slope of the yield curve has been a good leading indicator of economic activity.lA sharply upward sloping,or steep yield curve,has often preceded an economic upturn.lA flat yield curve
34、frequently signals an economic slowdown.lAn inverted yield curve can be a harbinger of recession.Source:PIMCOSummer 200874Benchmark Yield Curve-LCY BondsSource:http:/asianbondsonline.adb.org/asiabondindicators/benchmrk_yield_curve.php As of 29 May 2008Summer 200875OutlinelBond ValuationlTerminologyl
35、Basic valuationlRelationship Between The Bond Value&YTMlWhy the bond price changes?lInterest Risk&Default RisklBond Features and TypeslInflation,Nominal and Real RateslTerm Structure of Interest Rates(Yield Curve)lDeterminates of bond yieldSummer 200876Determinants of Bond YieldlFactors reflected in
36、 Yield CurvelReal ratelExpected InflationlInterest Rate Risk premiumlRisk not captured in Yield CurvelDefault RisklLiquidity Risk(Lack of Marketability)lTaxabilitySummer 200877Bond Characteristics and Required ReturnslThe required rate of a bond depends on its risk characteristicslMore risky =higher
37、 required returnl Safer =lower required return Which bonds will have the higher required rate,all else equal?l1-year Government Loan Vs.30-year Government Loanl30-year Government Loan(interest rate risk)l5-year bond with 8%coupon Vs.5-year bond with 12%couponl5-year bond with 8%coupon(interest rate
38、risk)lSecured bond Vs.unsecured bondlUnsecured bond(default risk)lSubordinated debt Vs.senior debtlSubordinated debt(default risk)l30-year Government bond Vs.30-year Corporate bondlCorporate bond(default risk)lAAA bond Vs.BBB bondlBBB bond(default risk)Summer 200878TakeawayslUnderstand bond values(p
39、rice)and why they fluctuatelAn application of Discounted Cash Flow ValuationlKnow the important bond features and bond typeslUnderstand the interest rate sensitivity of bondslUnderstand bond ratings and what they meanlUnderstand the impact of inflation on interest rateslUnderstand the term structure
40、 of interest rates and its determinantslUnderstand the determinants of bond yieldSummer 200879Individual HomeworklCritical Thinking and Concepts Reviewl6.1,6.6,6.15lQuestions and Problemsl1,7,9,15,17,32Summer 200880AppendixSummer 200881Essentials of Valuation in FinancelThe value of any financial as
41、set equals the present value of all of its future cash flowslHow to calculate present value of multiple CFs?(Ch.5)lBasic formula:lA period can be a month,a quarter,6 months,a year,etc.You need to match with the discount rate(r)of same time horizon,i.e.,monthly,quarterly,semiannually,or annual discou
42、nt rate.1221.1(1)(1)(1)TTtTttCFCFCFCFPVrrrrSummer 200882Present Value of Multiple CFs(Ch.5)l2 special cases of Multiple CFslAnnuities and PerpetuitiesCt=01234CCCCCCCCCCC.TT+1T+2.AnnuityPerpetuityCPV of perpetuityr()rrCrrrCTT)1(11111annuity of PVMostly used in bond valuationMostly used in stock valua
43、tionSummer 200883Apply for Handy Cash Personal Installment Loan to enjoy a monthly flat rate as low as 0.25%(Hang Seng Bank)lSuppose we borrow HK$10,000 now and plan to return in 24 months,what is the effective annual interest rate(EAR)Hang Seng Bank charging?Monthly installment24111501.5*1(1)(1)10,
44、0001.54%TCrrPVrrrSource:http:/ monthly rate.Need to find out annual rate.Effective annual rate=(1+r)12-1=20.11%Summer 200884Bond ValuationlF:Face value Bond price:market valuelc:Coupon rate C:Coupon=c*FlT:Maturity r:YTM,or required discount rate21Bond Price.1(1)(1)(1)11*(1)*(1)(1)(1)(1)TTTtTTTtCCCFrrrrCFCFrrrrr0T321 Time(years)$C$C$C$C$C+F.An application of PV of annuitySummer 200885
