Question

Bond J has a coupon of 7.6 percent. Bond K has a coupon of 11.6 percent. Both bonds have 12 years to maturity and have a YTM of 8.2 percent. a. If interest rates suddenly rise by 2.2 percent, what is the percentage price change of these bonds? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) b. If interest rates suddenly fall by 2.2 percent, what is the percentage price change of these bonds? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

Bond J has a coupon of 7.6%

Bond K has a coupon of 11.6%

12 years to maturity and YTM of 8.2%

first we must determine the current market price of both bonds using the yield to maturity formula:

YTM = {C + [(FV - PV) / n]} / [(FV + PV) / 2]

• YTM = 8.2%
• C = coupon payment = $76 and $116
• FV = face value or value at maturity = $1,000
• PV = present value or current market value = ???
• n = 12 years

current market value of Bond J:

0.082 = {76 + [(1,000 - PV) / 12]} / [(1,000 + PV) / 2]

[(1,000 + PV) / 2] x 0.082 = 76 + [(1,000 - PV) / 12]

41 + 0.041PV = 76 + 83.33 - 0.083PV

0.124PV = 118.33

PV = 118.33 / 0.124 = $954.27

current market value of Bond K:

41 + 0.041PV = 116 + 83.33 - 0.083PV

0.124PV = 158.33

PV = 158.33 / 0.124 = $1,276.85

a. If interest rates suddenly rise by 2.2 percent, what is the percentage price change of these bonds?

YTM = {C + [(FV - PV) / n]} / [(FV + PV) / 2]

• YTM = 8.2% + 2.2% = 10.4%
• C = coupon payment = $76 and $116
• FV = face value or value at maturity = $1,000
• PV = present value or current market value = ???
• n = 12 years

market value of Bond J:

0.102 = {76 + [(1,000 - PV) / 12]} / [(1,000 + PV) / 2]

[(1,000 + PV) / 2] x 0.102 = 76 + [(1,000 - PV) / 12]

102 + 0.051PV = 76 + 83.33 - 0.083PV

0.134PV = 157.33

PV = 57.33 / 0.134 = $427.84

market value of Bond K:

102 + 0.051PV = 116 + 83.33 - 0.083PV

0.134PV = 97.33

PV = 97.33 / 0.134 = $726.34

Bond J's market price will decrease by ($427.84 - $954.27) / $954.27 = -55.17%

Bond K's market price will decrease by ($726.34 - $1,276.85) / $1,276.85 = -43.11%

b. If interest rates suddenly fall by 2.2 percent, what is the percentage price change of these bonds?

YTM = {C + [(FV - PV) / n]} / [(FV + PV) / 2]

• YTM = 6%
• C = coupon payment = $76 and $116
• FV = face value or value at maturity = $1,000
• PV = present value or current market value = ???
• n = 12 years

current market value of Bond J:

0.06 = {76 + [(1,000 - PV) / 12]} / [(1,000 + PV) / 2]

[(1,000 + PV) / 2] x 0.06 = 76 + [(1,000 - PV) / 12]

30 + 0.030PV = 76 + 83.33 - 0.083PV

0.113PV = 129.33

PV = 129.33 / 0.113 = $1,144.51

current market value of Bond K:

30 + 0.030PV = 116 + 83.33 - 0.083PV

0.113PV = 169.33

PV = 169.33 / 0.113 = $1,498.50

Bond J's market price will increase by ($1,144.51 - $954.27) / $954.27 = 19.94%

Bond K's market price will increase by ($1,498.50 - $1,276.85) / $1,276.85 = 17.36%