Answer:
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%
