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1、Chapter 7Chapter 7Interest Rates and Interest Rates and Bond ValuationBond Valuation2024/7/22Chapter OutlineBonds and Bond ValuationBond FeaturesBond RatingsSome Different Types of BondsBond MarketsInflation and Interest RatesDeterminants of Bond Yields7-22024/7/22Market Values ($ Trillion)Value of
2、outstanding issues2024/7/22Bonds and Bond ValuationA 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 required market interest rate on the bond.Do not confuse the coupon rate with
3、 the required market interest rateBond DefinitionsBondPar value (face value)Coupon rateCoupon paymentMaturity dateYield or Yield to maturity (required return, market rate)7-52024/7/22 The Bond-Pricing EquationNotice that:qThe first term is the present value of the coupon payments (an annuity); and,q
4、The second term is the present value of the bonds par valueBond = Present Value of Cash FlowsBond Value = PV of coupons + PV of parBond Value = PV of annuity + PV of lump sumAs interest rates increase, present values decreaseSo, as interest rates increase, bond prices decrease and vice versa7-72024/
5、7/22Valuing a Discount Bond with Annual CouponsConsider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000, and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond?Using the formula:B = PV of annuity + PV of lump sumB = 1001 1/(1.11
6、)5 / .11 + 1,000 / (1.11)5Using the calculator:N = 5; I/Y = 11; PMT = 100; FV = 1,0007-82024/7/22Valuing a Premium Bond with Annual CouponsSuppose you are reviewing a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity, and the yield to maturity is 8%. What is
7、 the price of this bond?Using the formula:B = PV of annuity + PV of lump sumB = 1001 1/(1.08)20 / .08 + 1000 / (1.08)20Using the calculator:N = 20; I/Y = 8; PMT = 100; FV = 10007-92024/7/22Graphical Relationship Between Price and Yield-to-maturity (YTM)Bond PriceYield-to-maturity (YTM)7-102024/7/22B
8、ond Prices: Relationship Between Coupon and YieldIf YTM = coupon rate, then par value = bond priceIf YTM coupon rate, then par value bond priceWhy? The discount provides yield above coupon ratePrice below par value, called a discount bondIf YTM coupon rate, then par value bond priceWhy? Higher coupo
9、n rate causes value above parPrice above par value, called a premium bond7-112024/7/22The Bond Pricing Equation7-122024/7/22Coupon rate = 14%, semiannual couponsYTM = 16%; Maturity = 7 yearsPar value = $1,000Find present values based on the payment periodHow many coupon payments are there?What is th
10、e semiannual coupon payment?What is the semiannual yield?B = 701 1/(1.08)14 / .08 + 1,000 / (1.08)147-132024/7/22Interest Rate RiskPrice 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
11、coupon rate bondsReinvestment Rate RiskUncertainty concerning rates at which cash flows can be reinvestedShort-term bonds have more reinvestment rate risk than long-term bondsHigh coupon rate bonds have more reinvestment rate risk than low coupon rate bonds7-142024/7/227-152024/7/22Computing Yield t
12、o MaturityYield to Maturity (YTM) is the rate implied by the current bond priceIt is not the coupon rate!Finding the YTM requires trial and error if you do not have a financial calculator If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need t
13、o have the same sign, PV the opposite sign)7-162024/7/22YTM with Annual CouponsConsider 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 = 11%7-1
14、72024/7/22YTM with Semiannual CouponsSuppose 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 semiannual coupon payment?How many periods are there?N = 40; PV = -1,197.93; P
15、MT = 50; FV = 1,000; CPT i = 4% (Is this the YTM?)YTM = 4%*2 = 8%7-182024/7/22Current Yield vs. Yield to MaturityCurrent Yield = annual coupon / priceYield to maturity = current yield + capital gains yieldExample: 10% coupon bond, with semiannual coupons, face value of 1,000, 20 years to maturity, $
16、1,197.93 priceCurrent yield = 100 / 1,197.93 = .0835 = 8.35%Capital gain yield = (1,193.68 1,197.93) / 1,197.93 = -.0035 = -.35%YTM = 8.35 - .35 = 8%, which is the same YTM computed earlier7-202024/7/22Bond Pricing TheoremsBonds of similar risk (and maturity) will be priced to yield about the same r
17、eturn, regardless of the coupon rateIf you know the price of one bond, you can estimate its YTM and use that to find the price of the second bondThis is a useful concept that can be transferred to valuing assets other than bonds7-212024/7/22Bond Prices with a SpreadsheetThere is a specific formula f
18、or finding bond prices on a spreadsheetPRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis)YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis)Settlement and maturity need to be actual datesThe redemption and Pr need to be input as % of par valueClick on the Excel icon for an ex
19、ample7-222024/7/22Differences - Debt and EquityDebtNot 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 to financial distress and
20、 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 dividends are not paid7-232024/
21、7/22The Bond IndentureContract between the company and the bondholders that includesThe basic terms of the bondsThe total amount of bonds issuedA description of property used as security, if applicableSinking fund provisionsCall provisionsDetails of protective covenants7-242024/7/225-25Sample Bond F
22、eaturesFeatures of a recent Pepsico bond issue indenture:Bond ClassificationsRegistered vs. Bearer FormsSecurityCollateral secured by financial securitiesMortgage secured by real property, normally land or buildingsDebentures unsecuredNotes unsecured debt with original maturity less than 10 yearsSen
23、iority7-262024/7/22Bond Characteristics and Required ReturnsThe coupon rate depends on the risk characteristics of the bond when issuedWhich 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
24、 withoutA callable bond versus a non-callable bond7-272024/7/22Bond Ratings Investment QualityHigh 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 chang
25、es in circumstancesMoodys Baa and S&P BBB capacity to pay is adequate, adverse conditions will have more impact on the firms ability to pay7-282024/7/22Bond Ratings - SpeculativeLow GradeMoodys Ba and BS&P BB and BConsidered possible that the capacity to pay will degenerate. Very Low GradeMoodys C (
26、and below) and S&P C (and below) income bonds with no interest being paid, or in default with principal and interest in arrears7-292024/7/22Default Rates vs. Rating2024/7/22Government BondsTreasury Securities = Federal government debtT-bills pure discount bonds with original maturity of one year or
27、lessT-notes coupon debt with original maturity between one and ten 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 feder
28、al level7-312024/7/22A taxable bond has a 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 indifferen
29、t between the two bonds?8%(1 T) = 6%T = 25%7-322024/7/22Zero Coupon BondsMake 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 b
30、onds, or original issue discount bonds (OIDs)Treasury Bills and principal-only Treasury strips are good examples of zeroes7-332024/7/22Floating-Rate BondsCoupon rate floats depending on some index valueExamples adjustable rate mortgages and inflation-linked TreasuriesThere is less price risk with fl
31、oating rate bondsThe coupon floats, so it is less likely to differ substantially from the yield-to-maturityCoupons may have a “collar” the rate cannot go above a specified “ceiling” or below a specified “floor”7-342024/7/22Other Bond TypesDisaster bondsIncome bondsConvertible bondsPut bondsThere are
32、 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 returns7-352024/7/22Bond MarketsPrimarily over-the-counter transactions with dealers connected electronicallyExtremely large number of
33、bond issues, but generally low daily volume in single issuesMakes getting up-to-date prices difficult, particularly on small company or municipal issuesTreasury securities are an exception7-362024/7/22Treasury QuotationsWhat is the coupon rate on the bond?When does the bond mature?What is the bid pr
34、ice? 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 (ytm) based on the ask price?7-372024/7/22Clean vs. Dirty PricesClean price: quoted priceDirty price: price actually paid = quoted price plus accrued interestExam
35、ple: Consider a T-bond with a 4% semiannual yield and a clean price of $1,282.50:Number of days since last coupon = 61Number of days in the coupon period = 184So, you would actually pay $ 1,295.76 for the bond7-382024/7/22Inflation and Interest RatesReal rate of interest change in purchasing powerNo
36、minal rate of interest quoted rate of interest, change in actual number of dollarsThe forecast nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation7-392024/7/22The Fisher EffectThe Fisher Effect defines the relationship between real rates, nomin
37、al rates, and inflation(1 + R) = (1 + r)(1 + h), whereR = nominal rater = real rateh = expected inflation rateApproximationR = r + h7-402024/7/22If 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
38、%Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.7-412024/7/22Term Structure of Interest RatesTerm structure is the relationship between time to maturity and yields, all else equalIt is importa
39、nt to recognize that we pull out the effect of 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 yields7-422024/
40、7/227-43Figure 7.6 Downward-Sloping Yield Curve7-44Factors Affecting Bond YieldsDefault risk premium remember bond ratingsTaxability premium remember municipal versus taxableLiquidity premium bonds that have more frequent trading will generally have lower required returnsAnything else that affects t
41、he risk of the cash flows to the bondholders will affect the required returns7-462024/7/22Comprehensive ProblemWhat is the price of a $1,000 par value bond with a 6% coupon rate paid semiannually, if the bond is priced to yield 5% and it has 9 years to maturity?What would be the price of the bond if
42、 the yield rose to 7%.What is the current yield on the bond if the YTM is 7%?7-482024/7/22Key Concepts and SkillsKnow the important bond features and bond typesUnderstand 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 yields7-492024/7/22Homework Ch. 7Review self-test problems p. 227Homework assignment 10, 11, 20, 29, 30, 322024/7/22
