Bond J has a coupon rate of 5 percent and Bond K has a coupon rate of 11 percent
ID: 2749267 • Letter: B
Question
Bond J has a coupon rate of 5 percent and Bond K has a coupon rate of 11 percent. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 8 percent.
If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
What if rates suddenly fall by 2 percent instead? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Bond J has a coupon rate of 5 percent and Bond K has a coupon rate of 11 percent. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 8 percent.
Explanation / Answer
Bond J Bond K Coupon rate 5% Coupon rate 11% Discount rate =YTM 8% Discount rate =YTM 8% Face Value 1,000 Face Value 1,000 Period Cash Flow Dsicount Factor @4% PV of cash flows PV*Period Period Cash Flow Dsicount Factor @4% PV of cash flows PV*Period 1 25 0.962 24.04 24.04 1 55 0.962 52.88 52.88 2 25 0.925 23.11 46.23 2 55 0.925 50.85 101.70 3 25 0.889 22.22 66.67 3 55 0.889 48.89 146.68 4 25 0.855 21.37 85.48 4 55 0.855 47.01 188.06 5 25 0.822 20.55 102.74 5 55 0.822 45.21 226.03 6 25 0.790 19.76 118.55 6 55 0.790 43.47 260.80 7 25 0.760 19.00 132.99 7 55 0.760 41.80 292.57 8 25 0.731 18.27 146.14 8 55 0.731 40.19 321.50 9 25 0.703 17.56 158.08 9 55 0.703 38.64 347.78 10 25 0.676 16.89 168.89 10 55 0.676 37.16 371.56 11 25 0.650 16.24 178.63 11 55 0.650 35.73 393.00 12 25 0.625 15.61 187.38 12 55 0.625 34.35 412.23 13 25 0.601 15.01 195.19 13 55 0.601 33.03 429.41 14 25 0.577 14.44 202.12 14 55 0.577 31.76 444.66 15 25 0.555 13.88 208.22 15 55 0.555 30.54 458.09 16 25 0.534 13.35 213.56 16 55 0.534 29.36 469.84 17 25 0.513 12.83 218.18 17 55 0.513 28.24 480.00 18 25 0.494 12.34 222.13 18 55 0.494 27.15 488.69 19 25 0.475 11.87 225.46 19 55 0.475 26.11 496.00 20 25 0.456 11.41 228.19 20 55 0.456 25.10 502.03 21 25 0.439 10.97 230.39 21 55 0.439 24.14 506.85 22 25 0.422 10.55 232.08 22 55 0.422 23.21 510.57 23 25 0.406 10.14 233.29 23 55 0.406 22.31 513.24 24 25 0.390 9.75 234.07 24 55 0.390 21.46 514.96 25 25 0.375 9.38 234.45 25 55 0.375 20.63 515.79 26 25 0.361 9.02 234.45 26 55 0.361 19.84 515.79 27 25 0.347 8.67 234.10 27 55 0.347 19.07 515.02 28 25 0.333 8.34 233.43 28 55 0.333 18.34 513.56 29 25 0.321 8.02 232.47 29 55 0.321 17.64 511.44 30 25 0.308 7.71 231.24 30 55 0.308 16.96 508.73 31 25 0.296 7.41 229.76 31 55 0.296 16.31 505.46 32 25 0.285 7.13 228.05 32 55 0.285 15.68 501.70 33 25 0.274 6.85 226.13 33 55 0.274 15.08 497.48 34 25 0.264 6.59 224.02 34 55 0.264 14.50 492.84 35 25 0.253 6.34 221.74 35 55 0.253 13.94 487.82 36 1025 0.244 249.76 8,991.38 36 1055 0.244 257.07 9,254.54 Total 716.38 15,579.91 Total 1,283.62 23,749.32 Bond Price $ 716.38 Bond Price $ 1,283.62 Macaulay's Duration =15579.91/716.38 Macaulay's Duration =23749.32/1283.62 = 21.75 years = 18.50 years Normal Duration = Macaulay's Duration/1+YTM/2 =21.75/1.04 =20.91Years Normal Duration = Macaulay's Duration/1+YTM/2 =18.5/1.04 =17.79 Years When interest rate rises by 2% Bond Nomal Duration years % change in price =-Modified duration*% proce change Bond J 20.91 -41.82% Bond K 17.79 -35.58% When interest rate falls by 2% Bond Nomal Duration years % change in price =-Modified duration*% proce change Bond J 20.91 41.82% Bond K 17.79 35.58%