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4 October, 22:23

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.)

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  1. 4 October, 22:48
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    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%
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