Bonds and Their Valuation.ppt
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1、,CHAPTER 4Bonds and Their Valuation,Key features of bondsBond valuationMeasuring yieldAssessing risk,Key Features of a Bond,1.Par value: Face amount; paid at maturity. Assume $1,000.2.Coupon interest rate: Stated interest rate. Multiply by par value to get dollars of interest. Generally fixed.,(More
2、),3.Maturity: Years until bondmust be repaid. Declines.4.Issue date: Date when bondwas issued.5.Default risk: Risk that issuer will not make interest or principal payments.,How does adding a call provision affect a bond?,Issuer can refund if rates decline. That helps the issuer but hurts the investo
3、r.Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds.Most bonds have a deferred call and a declining call premium.,Whats a sinking fund?,Provision to pay off a loan over its life rather than all at maturity.Similar to amortization on a term loan.Reduces risk to
4、 investor, shortens average maturity.But not good for investors if rates decline after issuance.,1.Call x% at par per year for sinking fund purposes.2.Buy bonds on open market.Company would call if rd is below the coupon rate and bond sells at a premium. Use open market purchase if rd is above coupo
5、n rate and bond sells at a discount.,Sinking funds are generally handledin 2 ways,Financial Asset Valuation,PV,=,CF,1,+,r,.,.,.,+,CF,1,+,r,1,n,1,2,2,1,CF,r,n,.,r,.,+,+,+,The discount rate (ri) is the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal
6、 risk.,ri = r* + IP + LP + MRP + DRP,for debt securities.,Whats the value of a 10-year, 10% coupon bond if rd = 10%?,V,r,B,d,$100,$1,000,1,1,10,10,.,.,.,+,$100,1,+,r,d,100,100,10%,100 + 1,000,V = ?,.,= $90.91 + . . . + $38.55 + $385.54= $1,000.,+,+,+,1,r,+,d,10 10 100 1000NI/YR PV PMTFV -1,000,The b
7、ond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:,INPUTS,OUTPUT,10 13 100 1000NI/YR PV PMTFV -837.21,When kd rises, above the coupon rate, the bonds value falls below par, so it sells at a discount.,What would happen if expected inflation rose by 3%, causing r = 1
8、3%?,INPUTS,OUTPUT,What would happen if inflation fell, and rd declined to 7%?,10 7 100 1000NI/YR PV PMTFV -1,210.71,If coupon rate rd, price rises above par, and bond sells at a premium.,INPUTS,OUTPUT,Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its
9、 value over time if the required rate of return remained at 10%, or at 13%, or at 7%?,M,Bond Value ($),Years remaining to Maturity,1,372,1,211,1,000,837,775,3025 20 15 10 5 0,rd = 7%.,rd = 13%.,rd = 10%.,At maturity, the value of any bond must equal its par value.The value of a premium bond would de
10、crease to $1,000.The value of a discount bond would increase to $1,000.A par bond stays at $1,000 if rd remains constant.,Whats “yield to maturity”?,YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”,Whats the YTM on a 10-year, 9% annual coupon, $1,000 par val
11、ue bond that sells for $887?,90,90,90,0,1,9,10,rd=?,1,000,PV1 . . .PV10PVM,887,Find rd that “works”!,.,10 -887 90 1000NI/YR PV PMTFV10.91,V,INT,r,M,r,B,d,N,d,N,1,1,1,.,+,INT,1,+,r,d,887,90,1,1,000,1,1,10,10,r,r,d,d,+,90,1,+,r,d,Find rd,+,+,+,+,+,+,+,+,INPUTS,OUTPUT,.,If coupon rate rd, bond sells at
12、 a premium.If rd rises, price falls.Price = par at maturity.,Find YTM if price were $1,134.20.,10 -1134.2 90 1000NI/YR PV PMTFV7.08,Sells at a premium. Because coupon = 9% rd = 7.08%, bonds value par.,INPUTS,OUTPUT,Definitions,Current yield =Capital gains yield = = YTM = +,Annual coupon pmtCurrent p
13、rice,Change in priceBeginning price,Exp totalreturn,Exp Curr yld,Exp capgains yld,Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%.,Current yield= 0.1015 = 10.15%.,$90 $887,YTM= Current yield + Capital gains yield.Cap gains yield = YTM -
14、 Current yield = 10.91% - 10.15% = 0.76%.,Could also find values in Years 1 and 2,get difference, and divide by value inYear 1. Same answer.,Whats interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk?,rd,1-year,Change,10-year,Change,5%,$1,048,$1,386,10%,1,000,4.8%,1,000,38
15、.6%,15%,956,4.4%,749,25.1%,Interest rate risk: Rising rd causes bonds price to fall.,0,500,1,000,1,500,0%,5%,10%,15%,1-year,10-year,rd,Value,What is reinvestment rate risk?,The risk that CFs will have to be reinvested in the future at lower rates, reducing income.Illustration: Suppose you just won $
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