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1、Interest Rates and Bond ValuationChapter 5Key Concepts and SkillsUnderstand bond values and why they fluctuateUnderstand bond ratings and what they meanUnderstand the impact of inflation on interest ratesUnderstand the term structure of interest rates and the determinants of bond yieldsChapter Outli
2、ne5.1Bonds and Bond Valuation5.2More on Bond Features5.3Inflation and Interest Rates5.4Determinants of Bond Yields5.1 Bonds and Bond ValuationA bond is a legally binding agreement between a borrower and a lender that specifies the:Par(face)value(面值面值)Coupon rate(票面利率票面利率)Coupon payment(票面利息票面利息)Matu
3、rity Date(到期日到期日)The yield to maturity(到期收益率到期收益率)is the required market interest rate on the bond.Bond ValuationBond Valuation Primary Principle:Value of financial securities=PV of expected future cash flows Bond value is,therefore,determined by the present value of the coupon payments and par valu
4、e.Interest rates are inversely related to present(i.e.,bond)values.The Bond Pricing EquationSuppose a corporate issued a 5-year bond with 8%coupon on January 1 of 2013.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 th
5、e coupon rate is 8%,the payment is$40.On January 1 of 2013 the size and timing of cash flows will be:Bond ExampleBond ExampleOn January 1,2013,the required yield is 6%.How can we calculate the bond value?Now assume that the required yield is 12%.What is the bonds value now?Now assume that the requir
6、ed yield is also 8%.What is the bonds value now?Bond ConceptsqBond prices and market interest rates move in opposite directions.qWhen coupon rate=YTM,price=par value (par bond)qWhen coupon rate YTM,price par value(premium bond)qWhen coupon rate YTM,price par value(discount bond)Suppose a firm were t
7、o issue a bond with 10 years to maturity.The face value of the bond is$1,000 and the annual coupon is$100.What is the value of the bond if the required market interest rate is 8%/10%/12%?When the required market interest rate is 8%When the required market interest rate is 10%When the required market
8、 interest rate is 12%What is the value of the bond 2 years after issuing?When the required market interest rate is 8%When the required market interest rate is 10%When the required market interest rate is 12%qWhen the required market interest rate is constant:qThe value of par bond will maintain unch
9、anged.qThe value of premium bond will gradually decrease with the coming of maturity date.It=par value at maturity date.qThe value of discount bond will gradually increase with the coming of maturity date.It=par value at maturity date.Interest Rate RiskInterest Rate RiskqChange in price due to chang
10、es in interest rates:qAll other things being equal,the longer the time to maturity,the greater the interest rate risk.qAll other things being equal,the lower the coupon rate,the greater the interest rate risk.Have a try!Suppose a firm has a bond with 20 years to maturity.The face value of the bond i
11、s$20,000.The bond makes no payments for the first six years,then pays$800 every six months over the subsequent eight years,and finally pays$1,000 every six months over the last 6 years.If the required return on the bond is 8%compounded semiannually,What is the current price of the bond?Computing Yie
12、ld to MaturityYield to maturity is the rate implied by the current bond price.Finding the YTM requires trial and error and is similar to the process for finding R with an annuity.Suppose we are interested in a 6-year,8%coupon bond.The face value of the bond is$1000 and the price of the bond is$1115.
13、What is the YTM of this bond?Current Yield vs.Yield to MaturityCurrent Yield vs.Yield to MaturityCurrent Yield=annual coupon/priceYield to maturity=Current yield+Capital gains yieldExample:10%coupon bond,with annual coupons,face value of 1,000,20 years to maturity,$1,196.31 priceCurrent yield=100/11
14、96.31=8.36%Price in one year(assuming no change in YTM)=1,192.06Capital gains yield=(1192.06 1196.31)/1196.31=-.36%YTM=8.36-.36=8%Pure Discount Bonds(纯贴现债券纯贴现债券)Make no periodic interest payments(coupon rate=0%)The entire yield to maturity comes from the difference between the purchase price and the
15、 par value.Cannot sell for more than par valueSometimes called zeroes,deep discount bonds,or original issue discount bonds(OIDs)Information needed for valuing pure discount bonds:Time to maturity(T)Face value(F)Discount rate(r)Present value of a pure discount bond at time 0:Pure Discount Bonds:Examp
16、leFind the value of a 30-year zero-coupon bond with a$1,000 par value and a YTM of 6%.Consols(金边债券金边债券金边债券金边债券)Not all bonds have a final maturity.British consols pay a set amount(i.e.,coupon)every period forever.These are examples of a perpetuity.DebtNot an ownership interestCreditors do not have v
17、oting 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 to financial distress and bankruptcyEquityOwnership interestCommon stockholders vote for the board of directors and other is
18、suesDividends 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 dividends are not paidAn all equity firm can not go bankruptDebt versus Equity5.2 More on Bond FeaturesBond Ratings:Investment Qual
19、ityHigh GradeMoodys Aaa and S&P AAA capacity to pay interest and principal 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 the adverse effects of changes in circumstances and economic conditionsMoo
20、dys Baa and S&P BBB capacity to pay is adequate,adverse conditions will have more impact on the firms ability to payBond Ratings:SpeculativeLow GradeMoodys Ba and BS&P BB and BConsidered speculative with respect to capacity to payVery Low GradeMoodys C and S&P C income bonds with no interest being p
21、aidS&P D in default with principal and interest in arrearsGovernment BondsGovernment BondsTreasury Securities国库券国库券Federal government debtT-bills pure discount bonds with original maturity less than one yearT-notes coupon debt with original maturity between one and ten yearsT-bonds coupon debt with
22、original maturity greater than ten yearsMunicipal Securities市政证券市政证券Debt of state and local governmentsVarying degrees of default risk,rated similar to corporate debtInterest received is tax-exempt at the federal levelAfter-tax YieldsA taxable bond has a yield of 8%,and a municipal bond has a yield
23、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=25%5.3 Inflation and Interest RatesSuppose the one-year int
24、erest rate is 15.5%.Imagine a pizza costs$5 today.Assume the inflation rate is 5%.If you have$100 today,how many pizzas can you buy today?If you deposit$100 in a bank,how many pizzas can you buy next year?Real rate of interest change in purchasing powerNominal rate of interest quoted rate of interes
25、t,change in purchasing power and inflationThe ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation.The Fisher EffectThe Fisher Effect defines the relationship between real rates,nominal rates,and inflation.1+R=(1+r)(1+h),whereR=nominal r
26、ater=real rateh=expected inflation rateApproximationR=r+hThe Fisher Effect:ExampleIf 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 relatively high,there is a
27、significant difference between the actual Fisher Effect and the approximation.5.4 Determinants of Bond YieldsTerm structure of interest rates is the relationship between time to maturity and yields,all else equal.It is important to recognize that we pull out the effect of default risk,different coup
28、ons,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 yieldsFactors Affecting Required ReturnFactors Affecting Required ReturnDefault risk premium
29、remember bond ratingsTaxability premium remember municipal versus taxableLiquidity premium bonds that have more frequent trading will generally have lower required returnsAnything else that affects the risk of the cash flows to the bondholders will affect the required returns.Quick QuizHow do you fi
30、nd the value of a bond,and why do bond prices change?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?ConclusionThe bond yields represent the combined effect of n
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