A 30-year maturity bond making annual coupon payments with a coupon rate of 15.5
ID: 2759744 • Letter: A
Question
A 30-year maturity bond making annual coupon payments with a coupon rate of 15.5% has duration of 11.25 years and convexity of 182.9. The bond currently sells at a yield to maturity of 8%.
Find the price of the bond if its yield to maturity falls to 7% or rises to 9%. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
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.)
What is the percent error for each rule? (Do not round intermediate calculations. Round "Duration Rule" to 2 decimal places and "Duration-with-Convexity Rule" to 3 decimal places.)
Percent Error
A 30-year maturity bond making annual coupon payments with a coupon rate of 15.5% has duration of 11.25 years and convexity of 182.9. The bond currently sells at a yield to maturity of 8%.
Explanation / Answer
Par Value 1,000 Annual Interest 155.00 YTM 8% Maturity 30 Year Bond Price calculation Year Interest+Maturity Pv Factor @7% PV of Cash flows @YTM 7% Pv Factor @8% PV of Cash flows @YTM 8% Pv Factor @9% PV of Cash flows @YTM 10% 1 155 0.9346 144.86 0.926 143.52 0.917 142.20 2 155 0.8734 135.38 0.857 132.89 0.842 130.46 3 155 0.8163 126.53 0.794 123.04 0.772 119.69 4 155 0.7629 118.25 0.735 113.93 0.708 109.81 5 155 0.7130 110.51 0.681 105.49 0.650 100.74 6 155 0.6663 103.28 0.630 97.68 0.596 92.42 7 155 0.6227 96.53 0.583 90.44 0.547 84.79 8 155 0.5820 90.21 0.540 83.74 0.502 77.79 9 155 0.5439 84.31 0.500 77.54 0.460 71.37 10 155 0.5083 78.79 0.463 71.79 0.422 65.47 11 155 0.4751 73.64 0.429 66.48 0.388 60.07 12 155 0.4440 68.82 0.397 61.55 0.356 55.11 13 155 0.4150 64.32 0.368 56.99 0.326 50.56 14 155 0.3878 60.11 0.340 52.77 0.299 46.38 15 155 0.3624 56.18 0.315 48.86 0.275 42.55 16 155 0.3387 52.50 0.292 45.24 0.252 39.04 17 155 0.3166 49.07 0.270 41.89 0.231 35.82 18 155 0.2959 45.86 0.250 38.79 0.212 32.86 19 155 0.2765 42.86 0.232 35.92 0.194 30.15 20 155 0.2584 40.05 0.215 33.25 0.178 27.66 21 155 0.2415 37.43 0.199 30.79 0.164 25.37 22 155 0.2257 34.99 0.184 28.51 0.150 23.28 23 155 0.2109 32.70 0.170 26.40 0.138 21.36 24 155 0.1971 30.56 0.158 24.44 0.126 19.59 25 155 0.1842 28.56 0.146 22.63 0.116 17.98 26 155 0.1722 26.69 0.135 20.96 0.106 16.49 27 155 0.1609 24.94 0.125 19.40 0.098 15.13 28 155 0.1504 23.31 0.116 17.97 0.090 13.88 29 155 0.1406 21.79 0.107 16.64 0.082 12.73 30 1,155 0.1314 151.73 0.099 114.78 0.075 87.05 Total $ 2,054.77 $ 1,844.33 $ 1,667.79 a YTM Bond Price 7% $ 2,054.77 9% $ 1,667.79 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 = 11.25 years Modified Duration = 11.25/1.08 10.42 Years Convexity 182.90 Current Price 1,844.33 Duration rule Duration with Convexity YTM % Change in Price Changed Price % Change in Price Changed Price 7% 10.42% $ 2,036.5 11.33% $ 2,053.3 9% -10.42% $ 1,652.2 -9.51% $ 1,668.9 c Percent Error YTM Duration rule Duration with Convexity 8% 0.89% 0.07% 10% 0.94% -0.07% d The duration with convexity rule provides more accurate approximation to the Actual change in price.
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