Bond J has a coupon rate of 4.2 percent. Bond S has a coupon rate of 14.2 percen
ID: 2714881 • Letter: B
Question
Bond J has a coupon rate of 4.2 percent. Bond S has a coupon rate of 14.2 percent. Both bonds have ten years to maturity, make semiannual payments, and have a YTM of 9.4 percent.
If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).)
If interest rates suddenly fall by 2 percent instead, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)
Bond J has a coupon rate of 4.2 percent. Bond S has a coupon rate of 14.2 percent. Both bonds have ten years to maturity, make semiannual payments, and have a YTM of 9.4 percent.
Explanation / Answer
Assume face value of bonds =$100 Bond J Period Cash Flow Discount factor @9.4% PV cash floW Time period*Cash flow PV of time adjusted cash flow 1 2.1 0.91 1.92 2.1 1.92 2 2.1 0.84 1.75 4.2 3.51 3 2.1 0.76 1.60 6.3 4.81 4 2.1 0.70 1.47 8.4 5.86 5 2.1 0.64 1.34 10.5 6.70 6 2.1 0.58 1.22 12.6 7.35 7 2.1 0.53 1.12 14.7 7.84 8 2.1 0.49 1.02 16.8 8.19 9 2.1 0.45 0.94 18.9 8.42 10 2.1 0.41 0.86 21 8.55 11 2.1 0.37 0.78 23.1 8.60 12 2.1 0.34 0.71 25.2 8.57 13 2.1 0.31 0.65 27.3 8.49 14 2.1 0.28 0.60 29.4 8.36 15 2.1 0.26 0.55 31.5 8.19 16 2.1 0.24 0.50 33.6 7.98 17 2.1 0.22 0.46 35.7 7.75 18 2.1 0.20 0.42 37.8 7.50 19 2.1 0.18 0.38 39.9 7.24 20 102.1 0.17 16.93 2042 338.62 Bond price 35.22 0 474.45 Macaulay duration = 13.472 years Modified duration = 12.31 years Bond S Period Cash Flow Discount factor @9.4% PV cash floW Time period*Cash flow PV of time adjusted cash flow 1 7.1 0.91 6.49 7.1 6.49 2 7.1 0.84 5.93 14.2 11.86 3 7.1 0.76 5.42 21.3 16.27 4 7.1 0.70 4.96 28.4 19.83 5 7.1 0.64 4.53 35.5 22.65 6 7.1 0.58 4.14 42.6 24.85 7 7.1 0.53 3.79 49.7 26.50 8 7.1 0.49 3.46 56.8 27.68 9 7.1 0.45 3.16 63.9 28.47 10 7.1 0.41 2.89 71 28.91 11 7.1 0.37 2.64 78.1 29.07 12 7.1 0.34 2.42 85.2 28.99 13 7.1 0.31 2.21 92.3 28.71 14 7.1 0.28 2.02 99.4 28.26 15 7.1 0.26 1.85 106.5 27.68 16 7.1 0.24 1.69 113.6 26.98 17 7.1 0.22 1.54 120.7 26.21 18 7.1 0.20 1.41 127.8 25.36 19 7.1 0.18 1.29 134.9 24.47 20 107.1 0.17 17.76 2142 355.20 Bond price 79.59 0 814.44 Macaulay duration = 10.233 years Modified duration = 9.35 years % Change in Price = - Modified duration *%interest change 1 when interest rate rises by 2% Modified Duration years % change in Bond price Bond J 12.31 -24.63% Bond S 9.35 -18.71% 2 when interest rate falls by 2% Modified Duration years % change in Bond price Bond J 12.31 24.63% Bond S 9.35 18.71% Assume face value of bonds =$100 Bond J Period Cash Flow Discount factor @2.1% semi annually PV cash floW Time period*Cash flow PV of time adjusted cash flow 1 2.1 1 2.06 2.1 2.06 2 2.1 1 2.01 4.2 4.03 3 2.1 1 1.97 6.3 5.92 4 2.1 1 1.93 8.4 7.73 5 2.1 1 1.89 10.5 9.46 6 2.1 1 1.85 12.6 11.12 7 2.1 1 1.82 14.7 12.71 8 2.1 1 1.78 16.8 14.23 9 2.1 1 1.74 18.9 15.68 10 2.1 1 1.71 21 17.06 11 2.1 1 1.67 23.1 18.38 12 2.1 1 1.64 25.2 19.64 13 2.1 1 1.60 27.3 20.84 14 2.1 1 1.57 29.4 21.98 15 2.1 1 1.54 31.5 23.06 16 2.1 1 1.51 33.6 24.10 17 2.1 1 1.47 35.7 25.07 18 2.1 1 1.44 37.8 26.00 19 2.1 1 1.41 39.9 26.88 20 102.1 1 67.38 2042 1,347.54 Bond price 100.00 0 1,653.48 Macaulay duration = 17 years Modified duration = 15.11 years Bond S Period Cash Flow Discount factor @7.1% semi annually PV cash floW Time period*Cash flow PV of time adjusted cash flow 1 7.1 1 6.63 7.1 6.63 2 7.1 1 6.19 14.2 12.38 3 7.1 1 5.78 21.3 17.34 4 7.1 1 5.40 28.4 21.59 5 7.1 1 5.04 35.5 25.19 6 7.1 1 4.70 42.6 28.23 7 7.1 1 4.39 49.7 30.75 8 7.1 1 4.10 56.8 32.81 9 7.1 1 3.83 63.9 34.47 10 7.1 1 3.58 71 35.76 11 7.1 0 3.34 78.1 36.73 12 7.1 0 3.12 85.2 37.41 13 7.1 0 2.91 92.3 37.84 14 7.1 0 2.72 99.4 38.05 15 7.1 0 2.54 106.5 38.06 16 7.1 0 2.37 113.6 37.91 17 7.1 0 2.21 120.7 37.61 18 7.1 0 2.07 127.8 37.18 19 7.1 0 1.93 134.9 36.64 20 107.1 0 27.16 2142 543.29 Bond price 100.00 0 1,125.85 Macaulay duration = 11 years Modified duration = 10.29 years % Change in Price = - Modified duration *%interest change 1 when interest rate rises by 2% Modified Duration years % change in Bond price Bond J 15.11 -30% Bond S 10.29 -21% 2 when interest rate falls by 2% Modified Duration years % change in Bond price Bond J 15.11 30% Bond S 10.29 21%