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1、Interest Rates and Bond ValuationChapter 5Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin5-1Know the important bond features and bond typesComprehend bond values and why they fluctuateCompute bond values and fluctuationsAppreciate bond ratings, their meaning,
2、and relationship to bond terms and valueUnderstand the impact of inflation on interest ratesGrasp the term structure of interest rates and the determinants of bond yieldsKey Concepts and SkillsKey Concepts and Skills5-25.1Bonds and Bond Valuation5.2More on Bond Features5.3Bond Ratings5.4Some Differe
3、nt Types of Bonds5.5Bond Markets5.6Inflation and Interest Rates5.7Determinants of Bond YieldsChapter OutlineChapter Outline5-3A bond is a legally binding agreement between a borrower and a lender that specifies the:Par (face) valueCoupon rateCoupon paymentMaturity DateThe yield to maturity is the re
4、quired market interest rate on the bond.Do not confuse the coupon rate with the required market interest rate5.1 Bonds and Bond Valuation5.1 Bonds and Bond Valuation5-4Primary Principle:Value of financial securities = PV of expected future cash flows Bond value is, therefore, determined by the prese
5、nt value of the coupon payments plus the present value of the par, or face, valueInterest rates are inversely related to present (i.e., bond) values.Bond Valuation Bond Valuation 5-5Xanth Co. has issued a 10 year bond with an 8% annual coupon. The cash flows from the bond would be paid as follows:Co
6、nceptual Cash Flow of a 10 Year BondConceptual Cash Flow of a 10 Year Bond5-65-6The Bond-Pricing EquationThe Bond-Pricing EquationNotice that:qThe first term is the present value of the coupon payments (an annuity); and,qThe second term is the present value of the bonds par value5-7Bond terms dictat
7、e the frequency of coupon paymentsThe coupon rate is expressed in annual termsIf the rate is expressed annually and the payments are more frequent, calculation of bond value requires:Dividing the annual coupon payment by the number of compounding periods per year to arrive at the value of each coupo
8、n payment (C);Dividing the annual required rate of return by the number of compounding periods per year to arrive at the desired periodic yield (r);Multiplying the remaining years of the bonds life by the number of compounding periods per year to arrive at the remaining number of coupon payments (T)
9、.Frequency of Coupon PaymentsFrequency of Coupon Payments5-8Consider a U.S. government bond with as 6 3/8% coupon that expires in December 2012.The Par Value of the bond is $1,000.Coupon payments are made semi-annually (June 30 and December 31 for this particular bond).Since the coupon rate is 6 3/8
10、%, the payment is $31.875.On January 1, 2008 the size and timing of cash flows are:Bond ExampleBond Example5-9On January 1, 2008, the required yield is 5%.The size and timing of the cash flows are:Bond ExampleBond Example5-10Bond Example: CalculatorBond Example: CalculatorPMTI/YFVPVNPV31.875 =2.51,0
11、00 1,060.17101,0000.063752Find the present value (as of January 1, 2008), of a 6 3/8% coupon bond with semi-annual payments, and a maturity date of December 2012 if the YTM is 5%.5-11Now assume that the required yield is 11%. How does this change the bonds price?Bond ExampleBond Example5-125-12YTM a
12、nd Bond ValueYTM and Bond Value800100011001200130000.010.020.030.040.050.060.070.080.090.1Discount RateBond Value6 3/8When the YTM coupon, the bond trades at a discount.5-13qBond prices and market interest rates move in opposite directions.qWhen coupon rate = YTM, price = par valueqWhen coupon rate
13、YTM, price par value (premium bond)qWhen coupon rate YTM, price par value (discount bond)Bond ConceptsBond Concepts5-14Price RiskChange in price due to changes in interest ratesLong-term bonds have more price risk than short-term bondsLow coupon rate bonds have more price risk than high coupon rate
14、bonds.Reinvestment Rate RiskUncertainty concerning rates at which cash flows can be reinvestedShort-term bonds have more reinvestment rate risk than long-term bonds.High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds.Interest Rate RiskInterest Rate Risk5-155-15Maturity
15、 and Bond Price Maturity and Bond Price VolatilityVolatilityCConsider two otherwise identical bonds.The long-maturity bond will have much more volatility with respect to changes in the discount rate.Discount RateBond ValueParShort Maturity BondLong Maturity Bond5-165-16Coupon Rates and Bond PricesCo
16、upon Rates and Bond PricesConsider two otherwise identical bonds.The low-coupon bond will have much more volatility with respect to changes in the discount rate.Discount RateBond ValueHigh Coupon BondLow Coupon BondParC5-17Yield to maturity is the rate implied by the current bond price.Finding the Y
17、TM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity.If 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).Computing Yiel
18、d to MaturityComputing Yield to Maturity5-18Consider a bond with a 10% annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09.Will the yield be more or less than 10%?N = 15; PV = -928.09; FV = 1,000; PMT = 100CPT I/Y = 11%YTM with Annual CouponsYTM with Ann
19、ual Coupons5-19Suppose a bond with a 10% coupon rate and semiannual coupons has a face value of $1,000, 20 years to maturity, and is selling for $1,197.93.Is the YTM more or less than 10%?What is the semi-annual coupon payment?How many periods are there?N = 40; PV = -1,197.93; PMT = 50; FV = 1,000;
20、CPT I/Y = 4% (Is this the YTM?)YTM = 4%*2 = 8%YTM with Semiannual CouponsYTM with Semiannual Coupons5-20Current Yield = annual coupon / priceYield to maturity = current yield + capital gains yieldExample: 10% coupon bond, with semi-annual coupons, face value of 1,000, 20 years to maturity, $1,197.93
21、 priceCurrent yield = 100 / 1197.93 = .0835 = 8.35%Price in one year, assuming no change in YTM = 1,193.68Capital gain yield = (1193.68 1197.93) / 1197.93 = -.0035 = -.35%YTM = 8.35 - .35 = 8%, which is the same YTM computed earlierCurrent Yield vs. Yield to Current Yield vs. Yield to MaturityMaturi
22、ty5-21Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate.If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond.This is a useful concept that can be transferred to valuing assets oth
23、er than bonds.Bond Pricing TheoremsBond Pricing Theorems5-22There are specific formulas for finding bond prices and yields on a spreadsheet.PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis)YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis)Settlement and maturity need to be
24、actual datesThe redemption and Pr need to given as % of par valueClick on the Excel icon for an example.Bond Pricing with a Bond Pricing with a SpreadsheetSpreadsheet5-23There are two kinds of securities issued by corporations:Equity Ownership InterestDebt Short or Long Term BorrowingBonds are class
25、ified as Debt5.2 More on Bond Features5.2 More on Bond Features5-245-24DebtNot an ownership interestCreditors do not have voting rightsInterest is considered a cost of doing business and is tax deductibleCreditors have legal recourse if interest or principal payments are missedExcess debt can lead t
26、o financial distress and bankruptcyEquityOwnership interestCommon stockholders vote for the board of directors and other issuesDividends are not considered a cost of doing business and are not tax deductibleDividends are not a liability of the firm, and stockholders have no legal recourse if dividen
27、ds are not paidAn all-equity firm cannot go bankruptDebt versus EquityDebt versus Equity5-25Contract between the company and the bondholders that includes:The basic terms of the bondsThe total amount of bonds issuedA description of property used as security, if applicableSinking fund provisionsCall
28、provisionsDetails of protective covenantsThe Bond IndentureThe Bond Indenture5-26Features of a recent Pepsico bond issue demonstrate the range of topics covered in the bond indenture:Sample Bond FeaturesSample Bond Features5-27Registered vs. Bearer FormsSecurityCollateral secured by financial securi
29、tiesMortgage secured by real property, normally land or buildingsDebentures unsecuredNotes unsecured debt with original maturity less than 10 yearsSeniorityBond ClassificationsBond Classifications5-28Sinking FundsCall Provisions:Deferred CallCall PremiumProtective CovenantsBond Classifications (Cont
30、.)Bond Classifications (Cont.)5-29The coupon rate depends on the risk characteristics of the bond when issued.Which bonds will have the higher coupon, all else equal?Secured debt versus a debentureSubordinated debenture versus senior debtA bond with a sinking fund versus one withoutA callable bond v
31、ersus a non-callable bondRequired YieldsRequired Yields5-30High GradeMoodys Aaa and S&P AAA capacity to pay is extremely strongMoodys Aa and S&P AA capacity to pay is very strongMedium GradeMoodys A and S&P A capacity to pay is strong, but more susceptible to changes in circumstancesMoodys Baa and S
32、&P BBB capacity to pay is adequate, adverse conditions will have more impact on the firms ability to pay5.3 Bond Ratings Investment 5.3 Bond Ratings Investment QualityQuality5-31Low GradeMoodys Ba and BS&P BB and BConsidered speculative with respect to capacity to pay. Very Low GradeMoodys C S&P C &
33、 DHighly uncertain repayment and, in many cases, already in default, with principal and interest in arrears.Bond Ratings - SpeculativeBond Ratings - Speculative5-32There are many different types of bondsSome common bonds include:Government BondsFederalState and MunicipalZero Coupon Bonds (AKA Pure D
34、iscount Bonds)Floating Rate BondsEach are discussed below5.4 Some Different Types of 5.4 Some Different Types of BondsBonds5-33Treasury SecuritiesFederal government debtT-bills pure discount bonds with original maturity less than one year T-notes coupon debt with original maturity between one and te
35、n yearsT-bonds coupon debt with original maturity greater than ten yearsMunicipal SecuritiesDebt of state and local governmentsVarying degrees of default risk, rated similar to corporate debtInterest received is tax-exempt at the federal levelGovernment BondsGovernment Bonds5-34A taxable bond has a
36、yield of 8%, and a municipal bond has a yield of 6%.If you are in a 40% tax bracket, which bond do you prefer?8%(1 - .4) = 4.8%The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipalAt what tax rate would you be indifferent between the two bonds?8%(1 T) = 6%T = 2
37、5%After-tax YieldsAfter-tax Yields5-35Make no periodic interest payments (coupon rate = 0%)The entire yield to maturity comes from the difference between the purchase price and the par valueCannot sell for more than par valueSometimes called zeroes, deep discount bonds, or original issue discount bo
38、nds (OIDs)Treasury Bills and principal-only Treasury strips are good examples of zeroesZero Coupon BondsZero Coupon Bonds5-36Information needed for valuing pure discount bonds:Time to maturity (T) = Maturity date - todays dateFace value (F)Discount rate (r)Pure Discount BondsPure Discount BondsPrese
39、nt value of a pure discount bond at time 0:5-37Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.Pure Discount Bonds: ExamplePure Discount Bonds: Example5-38Coupon rate floats depending on some index valueExamples adjustable rate mortgages and inflation-linked Trea
40、suriesThere is less price risk with floating rate bonds.The coupon floats, so it is less likely to differ substantially from the yield to maturity.Coupons may have a “collar” the rate cannot go above a specified “ceiling” or below a specified “floor.”Floating Rate BondsFloating Rate Bonds5-39Income
41、bondsConvertible bondsPut bondsThere are many other types of provisions that can be added to a bond, and many bonds have several provisions it is important to recognize how these provisions affect required returns.Other Bond TypesOther Bond Types5-40Primarily over-the-counter transactions with deale
42、rs connected electronicallyExtremely large number of bond issues, but generally low daily volume in single issuesMakes getting up-to-date prices difficult, particularly on a small company or municipal issuesTreasury securities are an exception5.5 Bond Markets5.5 Bond Markets5-418 Nov 21 140:00140:05
43、+65.14What is the coupon rate on the bond?When does the bond mature?What is the bid price? What does this mean?What is the ask price? What does this mean?How much did the price change from the previous day?What is the yield based on the ask price?Treasury QuotationsTreasury Quotations5-42Clean price
44、: quoted priceDirty price: price actually paid = quoted price plus accrued interestExample: Consider T-bond in previous slide, assume today is July 15, 2008Number of days since last coupon = 61Number of days in the coupon period = 184Accrued interest = (61/184)(.04*1,000) = 13.26Prices (based on ask
45、):Clean price = 1,404.17Dirty price = 1,404.17 + 13.26 = 1,417.43So, you would actually pay $1,417.43 for the bond.Clean versus Dirty PricesClean versus Dirty Prices5-43Real rate of interest change in purchasing powerNominal rate of interest quoted rate of interest, change in purchasing power and in
46、flationThe ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation.Fisher notes that investors realize inflation reduces purchasing power and insist on high returns during inflationary times:“A rise in the rate of inflation causes the nomin
47、al rate to rise just enough so that the real rate of interest is unaffected.”5.6 Inflation and Interest Rates5.6 Inflation and Interest Rates5-44The Fisher Effect defines the relationship between real rates, nominal rates, and inflation.(1 + R) = (1 + r)(1 + h), whereR = nominal rater = real rateh =
48、 expected inflation rateApproximationR = r + hThe Fisher EffectThe Fisher Effect5-45If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?R = (1.1)(1.08) 1 = .188 = 18.8%Approximation: R = 10% + 8% = 18%Because the real return and expected inflation are relativel
49、y high, there is a significant difference between the actual Fisher Effect and the approximation.The Fisher Effect: ExampleThe Fisher Effect: Example5-46Term structure is the relationship between time to maturity and yields, all else equal.It is important to recognize that we pull out the effect of
50、default risk, different coupons, etc.Yield curve graphical representation of the term structureNormal upward-sloping, long-term yields are higher than short-term yieldsInverted downward-sloping, long-term yields are lower than short-term yields5.7 Determinants of Bond 5.7 Determinants of Bond Yields
51、Yields5-47Sample Treasury Yield CurveSample Treasury Yield Curve5-48Default risk premium remember bond ratingsTaxability premium remember municipal versus taxableLiquidity premium bonds that have more frequent trading will generally have lower required returns (remember bid-ask spreads)Anything else
52、 that affects the risk of the cash flows to the bondholders will affect the required returns.Factors Affecting Required Factors Affecting Required ReturnReturn5-49How do you find the value of a bond, and why do bond prices change?What is a bond indenture, and what are some of the important features?What are bond ratings, and why are they important?How does inflation affect interest rates?What is the term structure of interest rates?What factors determine the required return on bonds? Quick QuizQuick Quiz
