Answer:
a. What are the prices of these bonds today?
price of bond X:
0.03 = {37.5 + [(1,000 - MV)/26]} / [(1,000 + MV)/2]
0.03 x [(1,000 + MV)/2] = 37.5 + [(1,000 - MV)/26]
0.03 x (500 + 0.5MV) = 37.5 + 38.46 - 0.03846MV
15 + 0.015MV = 75.96 - 0.03846MV
0.05346MV = 60.96
MV = 60.96 / 0.05346 = $1,140.29
price of bond Y:
0.0375 = {30 + [(1,000 - MV)/26]} / [(1,000 + MV)/2]
0.0375 x [(1,000 + MV)/2] = 30 + [(1,000 - MV)/26]
0.0375 x (500 + 0.5MV) = 30 + 38.46 - 0.03846MV
18.75 + 0.01875MV = 68.46 - 0.03846MV
0.05721MV = 49.71
MV = 49.71 / 0.05721 = $868.90
b. What do you expect the prices of these bonds to be in one year?
price of bond X:
0.03 = {37.5 + [(1,000 - MV)/24]} / [(1,000 + MV)/2]
0.03 x [(1,000 + MV)/2] = 37.5 + [(1,000 - MV)/24]
0.03 x (500 + 0.5MV) = 37.5 + 41.67 - 0.04167MV
15 + 0.015MV = 79.17 - 0.04167MV
0.05667MV = 64.17/0.05667 = $1,132.29
price of bond Y:
0.0375 = {30 + [(1,000 - MV)/24]} / [(1,000 + MV)/2]
0.0375 x [(1,000 + MV)/2] = 30 + [(1,000 - MV)/24]
0.0375 x (500 + 0.5MV) = 30 + 41.67 - 0.04167MV
18.75 + 0.01875MV = 71.67 - 0.04167MV
0.06042MV = 52.92
MV = 52.92 / 0.06042 = $875.87
c. What do you expect the prices of these bonds to be in three years?
price of bond X:
0.03 = {37.5 + [(1,000 - MV)/20]} / [(1,000 + MV)/2]
0.03 x [(1,000 + MV)/2] = 37.5 + [(1,000 - MV)/20]
0.03 x (500 + 0.5MV) = 37.5 + 50 - 0.05MV
15 + 0.015MV = 87.5 - 0.05MV
0.065MV = 72.5
MV = 72.5 / 0.065 = $1,115.38
price of bond Y:
0.0375 = {30 + [(1,000 - MV)/20]} / [(1,000 + MV)/2]
0.0375 x [(1,000 + MV)/2] = 30 + [(1,000 - MV)/20]
0.0375 x (500 + 0.5MV) = 30 + 50 - 0.05MV
18.75 + 0.01875MV = 80 - 0.05MV
0.06875MV = 61.25
MV = 61.251 / 0.06875 = $890.91
d. What do you expect the prices of these bonds to be in eight years?
price of bond X:
0.03 = {37.5 + [(1,000 - MV)/10]} / [(1,000 + MV)/2]
0.03 x [(1,000 + MV)/2] = 37.5 + [(1,000 - MV)/10]
0.03 x (500 + 0.5MV) = 37.5 + 100 - 0.1MV
15 + 0.015MV = 137.5 - 0.1MV
0.115MV = 122.5
MV = 122.5 / 0.115 = $1,065.22
price of bond Y:
0.0375 = {30 + [(1,000 - MV)/10]} / [(1,000 + MV)/2]
0.0375 x [(1,000 + MV)/2] = 30 + [(1,000 - MV)/10]
0.0375 x (500 + 0.5MV) = 30 + 100 - 0.1MV
18.75 + 0.01875MV = 130 - 0.1MV
0.11875V = 111.25
MV = 111.25 / 0.11875 = $936.84
