A 30-year maturity bond making annual coupon payments with a coupon rate of 15.3
ID: 2759849 • Letter: A
Question
A 30-year maturity bond making annual coupon payments with a coupon rate of 15.3% has duration of 10.59 years and convexity of 163.0. The bond currently sells at a yield to maturity of 9%. a. Find the price of the bond if its yield to maturity falls to 8% or rises to 10%. {Do not round intermediate calculations. Round your answers to 2 decimal places.) b. What prices for the bond at these new yields would be predicted by the duration rule and the duration-with-convexity rule? {Do not round intermediate calculations. Round your answers to 2 decimal places.) YTM Duration Rule Duration-with-Convexity RuleExplanation / Answer
Par Value 1,000 Annual Interest 153.00 YTM 9% Maturity 30 Year Bond Price calculation Year Interest+Maturity Pv Factor @9% PV of Cash flows @YTM 9% Pv Factor @8% PV of Cash flows @YTM 8% Pv Factor @10% PV of Cash flows @YTM 10% 1 153 0.9174 140.37 0.926 141.67 0.909 139.09 2 153 0.8417 128.78 0.857 131.17 0.826 126.45 3 153 0.7722 118.14 0.794 121.46 0.751 114.95 4 153 0.7084 108.39 0.735 112.46 0.683 104.50 5 153 0.6499 99.44 0.681 104.13 0.621 95.00 6 153 0.5963 91.23 0.630 96.42 0.564 86.36 7 153 0.5470 83.70 0.583 89.27 0.513 78.51 8 153 0.5019 76.79 0.540 82.66 0.467 71.38 9 153 0.4604 70.45 0.500 76.54 0.424 64.89 10 153 0.4224 64.63 0.463 70.87 0.386 58.99 11 153 0.3875 59.29 0.429 65.62 0.350 53.63 12 153 0.3555 54.40 0.397 60.76 0.319 48.75 13 153 0.3262 49.91 0.368 56.26 0.290 44.32 14 153 0.2992 45.78 0.340 52.09 0.263 40.29 15 153 0.2745 42.00 0.315 48.23 0.239 36.63 16 153 0.2519 38.54 0.292 44.66 0.218 33.30 17 153 0.2311 35.35 0.270 41.35 0.198 30.27 18 153 0.2120 32.44 0.250 38.29 0.180 27.52 19 153 0.1945 29.76 0.232 35.45 0.164 25.02 20 153 0.1784 27.30 0.215 32.83 0.149 22.74 21 153 0.1637 25.05 0.199 30.39 0.135 20.67 22 153 0.1502 22.98 0.184 28.14 0.123 18.80 23 153 0.1378 21.08 0.170 26.06 0.112 17.09 24 153 0.1264 19.34 0.158 24.13 0.102 15.53 25 153 0.1160 17.74 0.146 22.34 0.092 14.12 26 153 0.1064 16.28 0.135 20.69 0.084 12.84 27 153 0.0976 14.93 0.125 19.15 0.076 11.67 28 153 0.0895 13.70 0.116 17.73 0.069 10.61 29 153 0.0822 12.57 0.107 16.42 0.063 9.65 30 1,153 0.0754 86.90 0.099 114.58 0.057 66.08 Total $ 1,647.24 $ 1,821.82 $ 1,499.63 a YTM Bond Price 8% $ 1,821.82 10% $ 1,499.63 b Duration Rule Price change =-Modified duration*% change in interets Duration with convesxity Rule= -Normal duration*% change in interets +1/2*Convexity*Interest cahneg ^2 Given Duration = 10.59 years Modified Duration = 10.58/1.09= 9.72 Years Convexity 163.00 Current Price 1,647.24 Duration rule Duration with Convexity YTM % Change in Price Changed Price % Change in Price Changed Price 8% 9.72% $ 1,807.4 10.54% $ 1,820.9 10% -9.72% $ 1,487.1 -8.91% $ 1,500.5 c Percent Error YTM Duration rule Duration with Convexity 8% 0.79% 0.05% 10% 0.83% -0.06% d The duration with convexity rule provides more accurate approximation to the Actual change in price.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.