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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Fall 2003,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Fall 2003,*,Bond Valuation and Term Structure of Interest Rates,Fall 2003,1,Definition and Features of Bonds,A bond is an IOU.,A bond represents a,loan,made by investors to the,issuer.,The issuer promises to:,Make,coupon payments,until maturity,Pay the,face value,at maturity,Coupon rate,Current yield,Fall 2003,2,Definition and Features of Bonds,Bond issuers,Federal government,Private Corporations,Government agencies(in the US),Municipal governments,Default,Fall 2003,3,Valuing a Bond:An Example,If a bond has five years to maturity,an$80 annual coupon,and a$1000 face value,its cash flows would look like this:,Time012345,Coupons$80$80$80$80$80,Face Value$1000,Market Price today=?,How much is this bond worth?,Coupon rate?,Current yield?,Fall 2003,4,Valuing a Bond:An Example(Contd),If the going rate on bonds like this one is 10%,then this bond has a market value of,$924.18,.,Alternatively,Fall 2003,5,Valuing a Bond:Another Example,Assume you have the following information.,Seagrams bonds have a$1000 face value.,The promised annual coupon is$100.,The bonds mature in 20 years.,What is the bonds value if the markets required return on similar bonds is 10%?What are the coupon rate and current yield?,What if the rate of return is 8%?,What if the rate of return is 12%?,Fall 2003,6,Bond Valuation:A Summary,Bond Value=Present Value of the Coupons,+Present Value of the Face Value,If the interest rate is constant,Bond Value=,C,1-1/(1+,r,),t,/,r,+,F,1/(1+,r,),t,where:,C,=Coupon paid each period,r,=Rate per period,t,=Number of periods,F,=Bonds face value,Fall 2003,7,Bond Valuation:A Summary(Contd),Some terminology,P,0,(C)F,sell at a premium.,Inverse relation between bond prices and interest rates,Results for constant interest rates,If C/F r,then,P,0,(C)F.,If C/F=r,then,P,0,(C)=F.,If C/F r,then,P,0,(C),zero yield curve.,Fall 2003,15,Term Structure of Interest Rates,A zero yield curve is a graphical representation of the term structure of interest rates,Each point on the zero yield curve corresponds to a spot rate which is the appropriate discount rate only for cash flows occurred at that point of time.,At any time,there is only one zero yield curve.All points on a zero yield curve are with respect to periods starting from the same time.,Fall 2003,16,Bond Valuation with Non-Flat Term Structures:An Example,Suppose you are given the following term structure of interest rates,What are the prices of 1-,2-,and 3-year pure discount bonds with$100 principal?,Suppose that there is a 3-year 6%annual coupon bond with face value of$1000.What is the bond price?,Fall 2003,17,Bond Valuation with Non-Flat Term Structures:An Example(Contd),Pure discount bond prices:,1-year bond price=$100/(1.04)=$96.15,2-year bond price=$100/(1.05),2,=$90.70,3-year bond price=$100/(1.055),3,=$85.16,3-year 6%annual coupon bond,Or more directly,Q.,If,in the example,pure-discount bond prices are given,can you calculate the spot rates?,Fall 2003,18,Yield to Maturity(YTM),the rate of return that makes the market price of the bond equal to the present value of its future cash flows,i.e.,the number y that solves,YTM used as discount rate,YTM is different from spot rates,When is YTM=r?,Fall 2003,19,Yield to Maturity(YTM):An Example,Q.,A two-year 10%annual coupon bond with face value of$1000.r,1,=8%,r,2,=10%.What is the YTM of the bond?,A.,First,solve for the bond price,Second,solve for the YTM,y,Fall 2003,20,Finding Yield to Maturity,In general,YTM can be found only by trial and error,An example:,A 5-year annual bond is selling for$924.18.The coupon rate is 8%and the face value is$1000.What is the YTM of the bond?,Try 8%,P=1000,Try 9%:P=$961.10,Try 10%:P=,$924.18,Fall 2003,21,Properties of Yield to Maturity,If the term structure of interest rates is flat(constant),then YTM=r.In general,YTM is a complicated average of interest rates.,Spot rates are market-wide.,YTM is bond specific:yields on bonds with different coupons cannot be compared.,Eg.Consider a 2-year 2%coupon bond under the same term structure as in Slide 20.,YTM=9.98%,Fall 2003,22,Properties of Yield to Maturity,YTM does not guarantee realized rate of return.,Sell bond before maturity=subject to interest rate risk,Reinvestment of coupon=unknown rate of retun,Yield to maturity does not provide reliable estimates of the time value of money.,Fall 2003,23,Bond Price Sensitivity to YTM,4%,6%,8%,10%,12%,14%,16%,$1,800,$1,600,$1,400,$1,200,$1,000,$800,$600,Bond price,Yield to maturity,YTM,Coupon=$10020 years to maturity$1,000 face value,Key Insight:Bond prices and YTMs are,inversely,related.,copyright,2002 McGraw-Hill Ryerson,Ltd,Fall 2003,24,Interest Rate Risk and Time to Maturity(Figure 7.2),copyright,2002 McGraw-Hill Ryerson,Ltd,Fall 2003,25,A Couple of Facts,Given two b
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