Copyright2009PearsonAddison-Wesley.Allrightsreserved.Chapter 4InterestRateMeasurementandBehaviorLearning ObjectivesDescribepresentvalueandthemechanicsofcalculatinginterestratesComprehendthedifferenttypesofbondsandloansandhowtheirstructureinfluencestheirpresentvalueUnderstandinterestratedeterminationandthesupplyanddemandcausesofinterestratefluctuations2IntroductionINTEREST RATES SERVE AS A YARDSTICK FOR COMPARING DIFFERENT TYPES OF SECURITIES AND MATURITIESCannot compare amount of total earning between different securitiesMust consider the amount of funds in the initial investment to compute the rate of return (interest) on the different securities3Calculating Interest RatesSimple InterestInterestearnedontheprincipleinoneyearstime.Time is worth moneyAdollartodayisworthmorethanadollarinthefutureAdollardueinthefutureisworthlessthanadollartodayInterest earned=principalratetime(inyears)4Calculating Interest Rates (Cont.)Compound InterestInterest that accumulates during a year is added to the principal at years end, thereby earning more interest in the following yearBanks automatically add interest earned to the principle at specified time intervalsFuture Value FVamount todays principle will be worth in “n years after adding compounded interest of rate “r.FV = principle(PV) (1 + r)n5Calculating Interest Rates (Cont.)Compound Interest (Cont.)Present Value PVamount a future sum of money in “n years will be worth today after discounting back to the present at rate “r Future value/(1 + r)n = present value 6Calculating Interest Rates (Cont.)Coupon Rate on BondsAmountprintedonthefaceofthebondAnnual(semiannual)interestpayment(coupon payment)Returnbasedonface value of the bond,notamountpaidforthebondCurrent YieldYieldonannualinterestreceivedbasedonpurchase price of bondIgnorescapital gaindifferencebetweenpurchasepriceandamountwhenredeemedatmaturity(facevalue)7Calculating Interest Rates (Cont.)Yield to MaturityMostaccurateandwidelyusedmeasureofinterestratesAssumethebondisheldtomaturityIncludescapitalgainsbetweenpurchaseandsalespricesofthebondInterestrate(rate of discount)whichmakessumofpresentvaluesofallexpectedfuturepayments(annualinterestplusfacevalue)equaltopurchaseprice8Calculating Interest Rates (Cont.)Yield to Maturity (Cont.)Where:P = Purchase price of bondC = Annual coupon paymentFn = Face value at maturityr = rate of discount 9Calculating Interest Rates (Cont.)Zero-Coupon BondsBondholderreceivednocouponinterestpayments,only the face value of the bond when it maturesRateofdiscount(returnonthebond)equatesdiscountedfacevalue(nnumberofyearstomaturity)withpurchaseprice10Calculating Interest Rates (Cont.)Inverse Relationship Between Yields and Bond PricesHigherinterestratesmeanlowerbondpricesandviceversaIfeithertheinterestrateorpriceisknown,theothercanbecomputedIfeithertherateofinterestorpurchasepricechanges,theotherwillautomaticallychangeintheoppositedirection11Calculating Interest Rates (Cont.)Why Long-Term Bonds are Riskier than Short-TermForlong-termsecurities,asmallchangeininterestratesinvolvesalargechangeinpriceForshort-termsecurities,evenabigchangeinyieldinvolvesonlyasmallchangeinpriceLongerabondsmaturity,themoreitspricewillbeaffectedbyachangeinthegenerallevelofinterestrates12Calculating Interest Rates (Cont.)Why Long-Term Bonds are Riskier than Short-Term (Cont.)Long-termbondsareriskierbecausethreatofpotentiallossisgreaterprovidedthebondsmustbesoldpriortomaturityGreaterlikelihoodwithlong-termbondsofneedingtosellbeforematurityOwnerswhocanholdbondsuntilmaturitywillhavetemporary paper lossesbuteventuallyreceivefacevalueuponredemptionatmaturity13Real interest rate = Nominal rate Inflation rateCalculating Interest Rates (Cont.)Nominal Versus Real Interest RatesNominal Interest RatesMoneyamountofinterestreceivedReal Interest RatesPurchasing powerofinterestreceivedRealinterestrateisthenominalinterestadjustedforinflationWhere:“ex-anti is based on the expected rate of inflation“ex-post is based on the actual or realized rate of inflation14Calculating Interest Rates (Cont.)Return Versus Yield to MaturityRate of returnmeasuresthecashflowsreceivedduringaperiodrelativetotheamountinvestedatthebeginningForabondheldforoneyear,thereturniscomputedasfollows:15What Determines the Level of Interest Rates Supply/Demand Determine Interest Rate (Figure 4.1)InterestrateispriceofcreditorborrowingmoneyMarketforCreditorLoanable Funds(Interestratevs.Quantityoffunds)Supply of FundsUpward sloping,lendersarewillingtoextendmore creditathigherinterestratesDemand for FundsDownward sloping,borrowersarewillingtoborrow lessathigherinterestratesEquilibriumIntersectionofsupplyanddemand,notendencytochangeFinancial MarketsCompetitivesosupplyanddemandpressureswillresultininterestratechanges16FIGURE 4.1 Supply and demand determine the interest rate.17What Determines the Level of Interest Rates (Cont.)Why Does the Interest Rate FluctuateU.S.Treasurybondyieldschangedaytoday(Figure 4.2)Movement along a single curveChangesintheinterestrateresultsinamovementalongasingledemandorsupplycurve(Figure 4.3)Shifts of a CurveChangeindeterminantsofsupplyordemand(otherthaninterestrate)causestherespectivecurvetoshift(Figure 4.4)Changes in EquilibriumShiftofeitherthesupplyordemandcurvewillreflectachangeintheequilibriuminterestrate18FIGURE 4.2 U.S. Treasury bond yields fluctuate from day to day (2007).19FIGURE 4.3 Movement along a demand curve versus a shift in demand.20FIGURE 4.4 Shifts in demand (1) or supply (2) curves can change the equilibrium interest rate.21What Determines the Level of Interest Rates (Cont.)Behind Supply and DemandBorrowing (demand)BusinessfirmsfinanceinventoryorbuycapitalequipmentHouseholdsbuycars,consumergoods,orhomesStateandlocalgovernmentprovideinfrastructureorpublicservicesFederalgovernmentfinanceFederalBudgetDeficitINCREASES IN BORROWINGSHIFT DEMAND TO RIGHT AND RAISE INTEREST22What Determines the Level of Interest Rates (Cont.)Behind Supply and Demand (Cont.)Lending or Credit (supply)FinancialinstitutionsorindividualslendtomarketGovernmentauthoritiesmayrestrictlendingbybanksAbilityofindividualstolenddependsontheirsavingslesssavingsresultsinloweramountoflendingDECREASES IN LENDINGSHIFT SUPPLY TO LEFT AND RAISE INTEREST23What Determines the Level of Interest Rates (Cont.)The Importance of Inflationary ExpectationsEffectofachangeinexpectations of increasing inflationDemandBorrowersincreasedemandsincetheywillberepayingindepreciateddollarsanddesiretopurchasebeforethepricesincreaseSupplyLendersdecreasesupplysincetheywillberepaidwithmoneyofdiminishedpurchasingpowerSHIFTS OF THE DEMAND AND SUPPLY CURVE WILL CAUSE THE INTEREST RATE TO INCREASE24What Determines the Level of Interest Rates (Cont.)The Importance of Inflationary Expectations (Cont.)Self-fulfilling ProphesiesIfindividualsandinstitutionsexpectinflationandinterestratestoincrease,theywillalterbehaviorthatcausesthehigherratesthatwereanticipated25What Determines the Level of Interest Rates (Cont.)Cyclical and Long-term Trends in Interest Rates (Figure 4.5)Levelofinterestratestendstoriseduringcyclicalexpansionandfallduringrecessions.Duringeconomicexpansion:FirmsandhouseholdsincreaseborrowingdemandcurverightFEDusuallytightenscreditduringexpansionsupplycurveleft26What Determines the Level of Interest Rates (Cont.)Cyclical and Long-term Trends in Interest Rates (Figure 4.5) (Cont.)Levelofinterestratesonupwardlong-termtrendbetween1950and1981LargefederalbudgetdeficitforcedUSTreasurytoincreaseborrowingpushingupinterestratesExpectationsofincreasinginflationSinceearly1980srateshavetrendeddownwardFederaldeficitscontinuedtoincreasein1980sExpectationsoflowerinflationhasbeenmajorreasonforfallofinterestrates.27FIGURE 4.5 Trends in interest and inflation rates since 1960.28