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Q16) Bond X is a premium bond making annual payments. The bond pays a 8% coupon, has a Y TM of 6%, and has 13 years to maturity. Bond Y is a discount bond making annual payments. This bond pays a 6% coupon, has a YTM of 8%, and also has 13 years to maturity. If interest rates remain unchanged, what do you expect the peice of these bonds to bo one year from now? In three years? In eight years? In 12 years? In 13 years? What's going on here? lilustrate your answers by graphing bond prices versus time to maturity. Answer: Price of any bond (P)=PV of the interest payment + PV of the par value PVAnminy=C[r1(1+r)1]BondValue=C[r1(1+r)r1]+(1+r)tFPVIFR1=1/(1+r);PVIFAARt=({1[1/(1+r)])/r) PVIFA = Present value interest factor of an annuaty, PVIF = Present value interest factor, PV= Present value, r= intorest rate (discount fate), t= Time penod (e. g, number of years), C = Cash flow Bond price (P)= C(PVIFA.N. )+$1,000(PVIFros) Coupon payment = Pariface value ($1,000) Coupon rate =100008=$80 X:P0=$80(PVAAis,11)+$1,000PPVAXa)P1=500(PVIFA(w+12)+$1,000(PVIF=12)=P3=580(PV/Aex10)+$1,000(PVIF=10) P8=$80(PVIFA6s)+$1,000(PVIF6ss)=P12=$80(PVIFA01)+$1,000(PV/F,1)=P13=Y:P0=$60(PVIFA=x,13)+$1,000(P1F0:13)=P1=$60(PVIFAss,12)+$1,000(PVIFw,12)=P3=$60(PVIFAss,10)+$1,000(PVIFsw,10)=P8=$60(PVIFAss.5)+$1,000(PVIFows)=P12=$60(PVIFA0,1)+$1,000(PVIF,w1)=P13= All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the ciscount from par value for a discount bond declines as maturity approaches. This is called "pull to par - In both cases, the tarpust percentage price changes occur at the shortest maturity lengths. Also, notice that the price of each bond wen no time is left to maturity is the par value, even though the purchaser would recewe the par vabuo plus ltie coupon payment immediately. This is because we calculate the ciean paice of the bond