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1、Interest Rates and Bond ValuationChapter 8Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin8-1Key Concepts and SkillsoKnow the important bond features and bond typesoUnderstand bond values and why they fluctuateoUnderstand bond ratings and what they meanoUnderst
2、and the impact of inflation on interest ratesoUnderstand the term structure of interest rates and the determinants of bond yields8-2Chapter Outline8.1Bonds and Bond Valuation8.2Government and Corporate Bonds8.3Bond Markets8.4Inflation and Interest Rates8.5Determinants of Bond Yields8-38.1 Bonds and
3、Bond ValuationoA bond is a legally binding agreement between a borrower and a lender that specifies the:nPar (face) valuenCoupon ratenCoupon paymentnMaturity DateoThe yield to maturity is the required market interest rate on the bond.8-4Bond Valuation oPrimary Principle:nValue of financial securitie
4、s = PV of expected future cash flows oBond value is, therefore, determined by the present value of the coupon payments and par value.oInterest rates are inversely related to present (i.e., bond) values.8-5The Bond-Pricing EquationTTr)(1Frr)(11-1C Value Bond8-6Bond ExampleoConsider a U.S. government
5、bond with as 6 3/8% coupon that expires in December 2013.nThe Par Value of the bond is $1,000.nCoupon payments are made semiannually (June 30 and December 31 for this particular bond).nSince the coupon rate is 6 3/8%, the payment is $31.875.nOn January 1, 2009 the size and timing of cash flows are:0
6、9/1/1875.31$09/30/6875.31$09/31/12875.31$13/30/6875.031, 1$13/31/128-7Bond ExampleoOn January 1, 2009, the required yield is 5%.oThe current value is:17.060, 1$)025. 1 (000, 1$)025. 1 (11205.875.31$1010PV8-8Bond Example: CalculatorPMTI/YFVPVNPV31.875 =2.51,000 1,060.17101,0000.063752Find the present
7、 value (as of January 1, 2009), of a 6 3/8% coupon bond with semi-annual payments, and a maturity date of December 2013 if the YTM is 5%.8-9Bond ExampleoNow assume that the required yield is 11%. oHow does this change the bonds price?69.825$)055. 1 (000, 1$)055. 1 (11211.875.31$1010PV8-10YTM and Bon
8、d Value800100011001200130000.010.020.030.040.050.060.070.080.090.1Discount RateBond Value6 3/8When the YTM coupon, the bond trades at a discount.8-11Bond ConceptsqBond prices and market interest rates move in opposite directions.qWhen coupon rate = YTM, price = par valueqWhen coupon rate YTM, price
9、par value (premium bond)qWhen coupon rate YTM, price par value (discount bond)8-12Interest Rate RiskoPrice RisknChange in price due to changes in interest ratesnLong-term bonds have more price risk than short-term bondsnLow coupon rate bonds have more price risk than high coupon rate bonds.oReinvest
10、ment Rate RisknUncertainty concerning rates at which cash flows can be reinvestednShort-term bonds have more reinvestment rate risk than long-term bonds.nHigh coupon rate bonds have more reinvestment rate risk than low coupon rate bonds.8-13Maturity and Bond Price VolatilityCConsider two otherwise i
11、dentical bonds.The long-maturity bond will have much more volatility with respect to changes in the discount rate.Discount RateBond ValueParShort Maturity BondLong Maturity Bond8-14Coupon Rates and Bond PricesConsider two otherwise identical bonds.The low-coupon bond will have much more volatility w
12、ith respect to changes in the discount rate.Discount RateBond ValueHigh Coupon BondLow Coupon BondParC8-15Computing Yield to MaturityoYield to maturity is the rate implied by the current bond price.oFinding the YTM requires trial and error if you do not have a financial calculator and is similar to
13、the process for finding r with an annuity.oIf you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign).8-16YTM with Annual CouponsoConsider a bond with a 10% annual coupon rate, 15 years to maturity, and
14、a par value of $1,000. The current price is $928.09.nWill the yield be more or less than 10%?nN = 15; PV = -928.09; FV = 1,000; PMT = 100nCPT I/Y = 11%8-17YTM with Semiannual CouponsoSuppose a bond with a 10% coupon rate and semiannual coupons has a face value of $1,000, 20 years to maturity, and is
15、 selling for $1,197.93.nIs the YTM more or less than 10%?nWhat is the semi-annual coupon payment?nHow many periods are there?nN = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4% (Is this the YTM?)nYTM = 4%*2 = 8%8-18Current Yield vs. Yield to MaturityoCurrent Yield = annual coupon / priceoYie
16、ld to maturity = current yield + capital gains yieldoExample: 10% coupon bond, with semi-annual coupons, face value of 1,000, 20 years to maturity, $1,197.93 pricenCurrent yield = 100 / 1197.93 = .0835 = 8.35%nPrice in one year, assuming no change in YTM = 1,193.68nCapital gain yield = (1193.68 1197
17、.93) / 1197.93 = -.0035 = -.35%nYTM = 8.35 - .35 = 8%, which is the same YTM computed earlier8-19Bond Pricing TheoremsoBonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate.oIf you know the price of one bond, you can estimate its YTM and us
18、e that to find the price of the second bond.oThis is a useful concept that can be transferred to valuing assets other than bonds.8-20Zero Coupon BondsoMake no periodic interest payments (coupon rate = 0%)oThe entire yield to maturity comes from the difference between the purchase price and the par v
19、alueoCannot sell for more than par valueoSometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs)oTreasury Bills and principal-only Treasury strips are good examples of zeroes8-21Pure Discount BondsInformation needed for valuing pure discount bonds:nTime to maturity (T)
20、= Maturity date - todays datenFace value (F)nDiscount rate (r)TrFPV)1 ( Present value of a pure discount bond at time 0:00$10$20$1TF$T8-22Pure Discount Bonds: ExampleFind the value of a 15-year zero-coupon bond with a $1,000 par value and a YTM of 12%.11.174$)06. 1 (000, 1$)1 (30TrFPV00$10$20$29000,
21、 1$308-23Bond Pricing with a SpreadsheetoThere are specific formulas for finding bond prices and yields on a spreadsheet.nPRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis)nYIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis)nSettlement and maturity need to be actual datesnThe
22、 redemption and Pr need to given as % of par valueoClick on the Excel icon for an example.8-248.2 Government and Corporate BondsoTreasury SecuritiesnFederal government debtnT-bills pure discount bonds with original maturity less than one year nT-notes coupon debt with original maturity between one a
23、nd ten yearsnT-bonds coupon debt with original maturity greater than ten yearsoMunicipal SecuritiesnDebt of state and local governmentsnVarying degrees of default risk, rated similar to corporate debtnInterest received is tax-exempt at the federal level8-25After-tax YieldsoA taxable bond has a yield
24、 of 8%, and a municipal bond has a yield of 6%.nIf you are in a 40% tax bracket, which bond do you prefer?o8%(1 - .4) = 4.8%oThe after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipalnAt what tax rate would you be indifferent between the two bonds?o8%(1 T) = 6%oT =
25、25%8-26Corporate BondsoGreater default risk relative to government bondsoThe promised yield (YTM) may be higher than the expected return due to this added default risk8-27Bond Ratings Investment QualityoHigh GradenMoodys Aaa and S&P AAA capacity to pay is extremely strongnMoodys Aa and S&P AA capaci
26、ty to pay is very strongoMedium GradenMoodys A and S&P A capacity to pay is strong, but more susceptible to changes in circumstancesnMoodys Baa and S&P BBB capacity to pay is adequate, adverse conditions will have more impact on the firms ability to pay8-28Bond Ratings - SpeculativeoLow GradenMoodys
27、 Ba and BnS&P BB and BnConsidered speculative with respect to capacity to pay. oVery Low GradenMoodys C nS&P C & DnHighly uncertain repayment and, in many cases, already in default, with principal and interest in arrears.8-298.3 Bond MarketsoPrimarily over-the-counter transactions with dealers conne
28、cted electronicallyoExtremely large number of bond issues, but generally low daily volume in single issuesoMakes getting up-to-date prices difficult, particularly on a small company or municipal issuesoTreasury securities are an exception8-30Treasury Quotations8 Nov 25 132:23132:24-125.14oWhat is th
29、e coupon rate on the bond?oWhen does the bond mature?oWhat is the bid price? What does this mean?oWhat is the ask price? What does this mean?oHow much did the price change from the previous day?oWhat is the yield based on the ask price?8-31Clean versus Dirty PricesoClean price: quoted priceoDirty pr
30、ice: price actually paid = quoted price plus accrued interestoExample: Consider T-bond in previous slide, assume today is July 15, 2009nNumber of days since last coupon = 61nNumber of days in the coupon period = 184nAccrued interest = (61/184)(.04*1,000) = 13.26oPrices (based on ask):nClean price =
31、1,327.50nDirty price = 1,327.50 + 13.26 = 1,340.76oSo, you would actually pay $1,340.76 for the bond.8-328.4 Inflation and Interest RatesoReal rate of interest change in purchasing poweroNominal rate of interest quoted rate of interest, change in purchasing power and inflationoThe ex ante nominal ra
32、te of interest includes our desired real rate of return plus an adjustment for expected inflation.8-33Real versus Nominal Rateso(1 + R) = (1 + r)(1 + h), wherenR = nominal ratenr = real ratenh = expected inflation rateoApproximationnR = r + h8-34Inflation-Linked BondsoMost government bonds face infl
33、ation riskoTIPS (Treasury Inflation-Protected Securities), however, eliminate this risk by providing promised payments specified in real, rather than nominal, terms8-35The Fisher Effect: ExampleoIf we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?oR = (1.1)(1.0
34、8) 1 = .188 = 18.8%oApproximation: R = 10% + 8% = 18%oBecause the real return and expected inflation are relatively high, there is a significant difference between the actual Fisher Effect and the approximation.8-368.5 Determinants of Bond YieldsoTerm structure is the relationship between time to ma
35、turity and yields, all else equal.oIt is important to recognize that we pull out the effect of default risk, different coupons, etc.oYield curve graphical representation of the term structurenNormal upward-sloping, long-term yields are higher than short-term yieldsnInverted downward-sloping, long-te
36、rm yields are lower than short-term yields8-37Factors Affecting Required ReturnoDefault risk premium remember bond ratingsoTaxability premium remember municipal versus taxableoLiquidity premium bonds that have more frequent trading will generally have lower required returns (remember bid-ask spreads
37、)oAnything else that affects the risk of the cash flows to the bondholders will affect the required returns.8-38Quick QuizoHow do you find the value of a bond, and why do bond prices change?oWhat are bond ratings, and why are they important?oHow does inflation affect interest rates?oWhat is the term structure of interest rates?oWhat factors determine the required return on bonds?