Bond J is a 4 percent coupon bond. Bond K is a 10 percent coupon bond. Both bond
ID: 2784136 • Letter: B
Question
Bond J is a 4 percent coupon bond. Bond K is a 10 percent coupon bond. Both bonds have 7 years to maturity, make semiannual payments, and have a YTM of 8 percent.
Requirement 1:
(a) If interest rates suddenly rise by 4 percent, what is the percentage price change of Bond J?
(b) If interest rates suddenly rise by 4 percent, what is the percentage price change of Bond K?
Requirement 2:
(a) If interest rates suddenly fall by 4 percent, what is the percentage price change of Bond J?
(b) If interest rates suddenly fall by 4 percent, what is the percentage price change of Bond K?
Explanation / Answer
Bond J Requirement 1 Requirement 2 Increase in interest by 4% Fall in interest by 4% 1/(1+.04)^n 1/(1+.06)^n 1/(1+.02)^n Semi Annual Int 0.0400 PV 0.06000 PV 0.02000 PV 1 20 0.9615 19.23077 0.94340 18.86792 0.98039 19.60784 2 20 0.9246 18.49112 0.89000 17.79993 0.96117 19.22338 3 20 0.8890 17.77993 0.83962 16.79239 0.94232 18.84645 4 20 0.8548 17.09608 0.79209 15.84187 0.92385 18.47691 5 20 0.8219 16.43854 0.74726 14.94516 0.90573 18.11462 6 20 0.7903 15.80629 0.70496 14.09921 0.88797 17.75943 7 20 0.7599 15.19836 0.66506 13.30114 0.87056 17.4112 8 20 0.7307 14.6138 0.62741 12.54825 0.85349 17.06981 9 20 0.7026 14.05173 0.59190 11.83797 0.83676 16.73511 10 20 0.6756 13.51128 0.55839 11.1679 0.82035 16.40697 11 20 0.6496 12.99162 0.52679 10.53575 0.80426 16.08526 12 20 0.6246 12.49194 0.49697 9.939387 0.78849 15.76986 13 20 0.6006 12.01148 0.46884 9.37678 0.77303 15.46065 14 1020 0.5775 589.0246 0.44230 451.147 0.75788 773.0325 788.7375 628.2006 1000 Increase/(Decrease) in price -160.537 211.2625 % Increase/( Decrease) in price -20.35% 26.78% Bond K Requirement 1 Requirement 2 Increase in interest by 4% Fall in interest by 4% 1/(1+.04)^n 1/(1+.06)^n 1/(1+.02)^n Semi Annual Int 0.0400 PV 0.06000 PV 0.02000 PV 1 50 0.9615 48.07692 0.94340 47.16981 0.98039 49.01961 2 50 0.9246 46.22781 0.89000 44.49982 0.96117 48.05844 3 50 0.8890 44.44982 0.83962 41.98096 0.94232 47.11612 4 50 0.8548 42.74021 0.79209 39.60468 0.92385 46.19227 5 50 0.8219 41.09636 0.74726 37.36291 0.90573 45.28654 6 50 0.7903 39.51573 0.70496 35.24803 0.88797 44.39857 7 50 0.7599 37.99589 0.66506 33.25286 0.87056 43.52801 8 50 0.7307 36.53451 0.62741 31.37062 0.85349 42.67452 9 50 0.7026 35.12934 0.59190 29.59492 0.83676 41.83776 10 50 0.6756 33.77821 0.55839 27.91974 0.82035 41.01741 11 50 0.6496 32.47905 0.52679 26.33938 0.80426 40.21315 12 50 0.6246 31.22985 0.49697 24.84847 0.78849 39.42466 13 50 0.6006 30.0287 0.46884 23.44195 0.77303 38.65163 14 1050 0.5775 606.3488 0.44230 464.416 0.75788 795.7688 1105.631 907.0502 1363.187 Increase/(Decrease) in price -198.581 257.5562 % Increase/( Decrease) in price -17.96% 23.29% Bond J Requirement 1 Requirement 2 Increase in interest by 4% Fall in interest by 4% 1/(1+.04)^n 1/(1+.06)^n 1/(1+.02)^n Semi Annual Int 0.0400 PV 0.06000 PV 0.02000 PV 1 20 0.9615 19.23077 0.94340 18.86792 0.98039 19.60784 2 20 0.9246 18.49112 0.89000 17.79993 0.96117 19.22338 3 20 0.8890 17.77993 0.83962 16.79239 0.94232 18.84645 4 20 0.8548 17.09608 0.79209 15.84187 0.92385 18.47691 5 20 0.8219 16.43854 0.74726 14.94516 0.90573 18.11462 6 20 0.7903 15.80629 0.70496 14.09921 0.88797 17.75943 7 20 0.7599 15.19836 0.66506 13.30114 0.87056 17.4112 8 20 0.7307 14.6138 0.62741 12.54825 0.85349 17.06981 9 20 0.7026 14.05173 0.59190 11.83797 0.83676 16.73511 10 20 0.6756 13.51128 0.55839 11.1679 0.82035 16.40697 11 20 0.6496 12.99162 0.52679 10.53575 0.80426 16.08526 12 20 0.6246 12.49194 0.49697 9.939387 0.78849 15.76986 13 20 0.6006 12.01148 0.46884 9.37678 0.77303 15.46065 14 1020 0.5775 589.0246 0.44230 451.147 0.75788 773.0325 788.7375 628.2006 1000 Increase/(Decrease) in price -160.537 211.2625 % Increase/( Decrease) in price -20.35% 26.78% Bond K Requirement 1 Requirement 2 Increase in interest by 4% Fall in interest by 4% 1/(1+.04)^n 1/(1+.06)^n 1/(1+.02)^n Semi Annual Int 0.0400 PV 0.06000 PV 0.02000 PV 1 50 0.9615 48.07692 0.94340 47.16981 0.98039 49.01961 2 50 0.9246 46.22781 0.89000 44.49982 0.96117 48.05844 3 50 0.8890 44.44982 0.83962 41.98096 0.94232 47.11612 4 50 0.8548 42.74021 0.79209 39.60468 0.92385 46.19227 5 50 0.8219 41.09636 0.74726 37.36291 0.90573 45.28654 6 50 0.7903 39.51573 0.70496 35.24803 0.88797 44.39857 7 50 0.7599 37.99589 0.66506 33.25286 0.87056 43.52801 8 50 0.7307 36.53451 0.62741 31.37062 0.85349 42.67452 9 50 0.7026 35.12934 0.59190 29.59492 0.83676 41.83776 10 50 0.6756 33.77821 0.55839 27.91974 0.82035 41.01741 11 50 0.6496 32.47905 0.52679 26.33938 0.80426 40.21315 12 50 0.6246 31.22985 0.49697 24.84847 0.78849 39.42466 13 50 0.6006 30.0287 0.46884 23.44195 0.77303 38.65163 14 1050 0.5775 606.3488 0.44230 464.416 0.75788 795.7688 1105.631 907.0502 1363.187 Increase/(Decrease) in price -198.581 257.5562 % Increase/( Decrease) in price -17.96% 23.29%