Question

Miller Corporation has a premium bond making semiannual payments. The bond has a coupon rate of 10 percent, a YTM of 8 percent, and 14 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond has a coupon rate of 8 percent, a YTM of 10 percent, and also has 14 years to maturity. Both bonds have a par value of $1,000.

a. What is the price of each bond today?
b. If interest rates remain unchanged, what do you expect the prices of these bonds to be 1 year from now? In 4 years? In 9 years? In 13 years? In 14 years?

Price of bond Miller Corporation Bond Modigliani Company Bond
1 year $ _________ $ _________
4 years $ _________ $_________
9 years $ _________ $_________
13 years $ _________ $ _________
14 years $_________ $_________

Answer 1

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

Step-by-step 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