Bond X is a premium bond making semiannual payments. The bond pays a 11 percent
ID: 2384424 • Letter: B
Question
Bond X is a premium bond making semiannual payments. The bond pays a 11 percent coupon, has a YTM of 9 percent, and has 11 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a 9 percent coupon, has a YTM of 11 percent, and also has 11 years to maturity.
What is the price of each bond today? (Round your answers to 2 decimal places. (e.g., 32.16))
If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In two years? In seven years? In 9 years? In 11 years? (Round your answers to 2 decimal places. (e.g., 32.16))
Bond X is a premium bond making semiannual payments. The bond pays a 11 percent coupon, has a YTM of 9 percent, and has 11 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a 9 percent coupon, has a YTM of 11 percent, and also has 11 years to maturity.
Explanation / Answer
Answer:Assume par value of bond=$1000
Calculation of the price of each bond today:
Bond X=$55*PVIFA(4.5%,22)+$1000PVIF(4.5%,22)
=$55(13.7844)+$1000*(0.3797)
=758.142+379.7
=$1137.842
Bond Y=$55*PVIFA(5.5%,22)+$1000PVIF(5.5%,22)
=$45(12.58316)+$1000*(0.3079)
=566.2422+307.926
=$874.1682
Answer:2 One year From now:
Bond X=$55*PVIFA(4.5%,20)+$1000PVIF(4.5%,20)
=$55(13.0079)+$1000*(0.415)
=715.4345+415
=$1130.4345
Bond Y=$55*PVIFA(5.5%,20)+$1000PVIF(5.5%,20)
=$45(11.950)+$1000*(0.343)
=537.7672+343
=$880.7672
Two years From Now:
Bond X=$55*PVIFA(4.5%,18)+$1000PVIF(4.5%,18)
=$55(12.1599)+$1000*(0.4528)
=668.80+452.80
=$1121.60
Bond Y=$55*PVIFA(5.5%,18)+$1000PVIF(5.5%,18)
=$45(11.246)+$1000*(0.38146)
=506.073+381.46
=$887.533
Seven years from now:
Bond X=$55*PVIFA(4.5%,8)+$1000PVIF(4.5%,8)
=$55(6.5958)+$1000*(0.703)
=362.77+703.18
=$1065.95
Bond Y=$55*PVIFA(5.5%,8)+$1000PVIF(5.5%,8)
=$45(6.33456)+$1000*(0.6516)
=285.055+651.6
=$936.655
9 years from now:
Bond X=$55*PVIFA(4.5%,4)+$1000PVIF(4.5%,4)
=$55(3.5875)+$1000*(0.83856)
=197.3139+838.56
=$1035.8739
Bond Y=$55*PVIFA(5.5%,4)+$1000PVIF(5.5%,4)
=$45(3.505)+$1000*(0.8072)
=157.73+807.2
=$964.946
11 years from now:
Bond X=$55*PVIFA(4.5%,0)+$1000PVIF(4.5%,0)
=$55(1)+$1000*(1)
=1055
Bond Y=$55*PVIFA(5.5%,0)+$1000PVIF(5.5%,0)
=$45(1)+$1000*(1)
=1045