Answer:
a. What is the price of each bond today?
Miller Corporation bond = $1,179.71
Modigliani Company bond = $835.42
b. Miller Modigliani Company
Corporation Bond Bond
1 year $1,170.26 $841.89
4 years $1,142.86 $866.67
9 years $1,083.33 $920
13 years $1,019.23 $980.95
14 years $1,050 $1,040
Explanation:
YTM formula:
Miller Corporation
YTM = [coupon + (face value - market value)/n] / (face value + market value)/2
0.04 = [50 + (1,000 - x)/28] / (1,000 + x)/2
0.02(1,000 + x) = 85.71 - 0.0357x
20 + 0.02x = 85.71 - 0.0357x
0.0557x = 65.71
x = 65.71 / 0.0557 = $1,179.71
if we want to calculate the bond price in one year, we replace 28 by 26
0.04 = [50 + (1,000 - x)/26] / (1,000 + x)/2
0.02(1,000 + x) = 88.46 - 0.0385x
20 + 0.02x = 88.46 - 0.0385x
0.0585x = 68.46
x = 68.46 / 0.0585 = $1,170.26
if we want to calculate the bond price in 4 years, we replace 28 by 20
0.04 = [50 + (1,000 - x)/20] / (1,000 + x)/2
20 + 0.02x = 100 - 0.05x
0.07x = 80
x = 80 / 0.07 = $1,142.86
if we want to calculate the bond price in 9 years, we replace 28 by 10
0.04 = [50 + (1,000 - x)/10] / (1,000 + x)/2
20 + 0.02x = 150 - 0.1x
0.12x = 130
x = 130 / 0.12 = $1,083.33
if we want to calculate the bond price in 13 years, we replace 28 by 2
0.04 = [50 + (1,000 - x)/2] / (1,000 + x)/2
20 + 0.02x = 550 - 0.5x
0.52x = 530
x = 530 / 0.52 = $1,019.23
Modigliani Company
YTM = [coupon + (face value - market value)/n] / (face value + market value)/2
0.05 = [40 + (1,000 - x)/28] / (1,000 + x)/2
0.025(1,000 + x) = 75.71 - 0.0357x
25 + 0.025x = 75.71 - 0.0357x
0.0607x = 50.71
x = 50.71 / 0.0607 = $835.42
if we want to calculate the bond price in one year, we replace 28 by 26
0.05 = [40 + (1,000 - x)/26] / (1,000 + x)/2
0.025(1,000 + x) = 78.46 - 0.0385x
25 + 0.025x = 78.46 - 0.0385x
0.0635x = 53.46
x = 53.46 / 0.0635 = $841.89
if we want to calculate the bond price in 4 years, we replace 28 by 20
0.05 = [40 + (1,000 - x)/20] / (1,000 + x)/2
25 + 0.025x = 90 - 0.05x
0.075x = 65
x = 65 / 0.075 = $866.67
if we want to calculate the bond price in 9 years, we replace 28 by 10
0.05 = [40 + (1,000 - x)/10] / (1,000 + x)/2
25 + 0.025x = 140 - 0.1x
0.125x = 115
x = 115 / 0.125 = $920
if we want to calculate the bond price in 13 years, we replace 28 by 2
0.05 = [40 + (1,000 - x)/2] / (1,000 + x)/2
25 + 0.025x = 540 - 0.5x
0.525x = 515
x = 515 / 0.525 = $980.95
