A 30-year maturity bond making annual coupon payments with a coupon rate of 14.3
ID: 2709532 • Letter: A
Question
A 30-year maturity bond making annual coupon payments with a coupon rate of 14.3% has duration of 11.34 years and convexity of 185.7. The bond currently sells at a yield to maturity of 8%. a. 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.) 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.) c. 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.)Explanation / Answer
Bond duration =11.34 years
Current Price = 1709.47
Yield =8%
Modified duration= 11.34/1.08=10.50 years
% change in bond price = - Modified Duration times the change in yield to maturity
YTM = 7% , then % change in YTM = -1%
So Bond price change = -10.5*(-0.01)= 10.5%
So Bond price when YTM=7 %= 1709.47*1.105=$1,888.96
When YTM =9%
Change in YTM =1%
So Bond price change = -10.5*(0.01)= -10.5%
So Bond price when YTM=9%
= 1709.47*89.5%=$1,529.97
Ans b.
For demand with convexity rule
% Price = - Modified Duration × y + 1/2× Convexity × (y)^2
Convexity=185.7
So , for YTM 7%
% price change = -10.5*(-0.01) +1/2*185.7*(-.01)^2
=0.105 + 0.009285=0.114285=11.4285%
So bond price =1709.47*1.1143=$1904.86
For YTM = 9%
% price change = -10.5*(-0.01) +1/2*185.7*(0.01)^2
=-0.105+0.009285=-0.095715=-9.57%
So bond price =1709.47*90.43%=$1545.87
YTM
Bond Price $ as per duration rule
Bond Price $ as per duration –convexity rule
7%
$1,888.96
$1904.86
9%
$1,529.97
$1545.87
% error
Ans c.
YTM
Bond Price $
Bond Price $ as per duration rule
Bond Price $ as per duration –convexity rule
% Error duration rule
% error duration convexity rule
7%
2,029.50
$1,888.96
$1,904.86
7%
6%
9%
1,451.61
$1,529.97
$1,545.87
-5%
-6%
period cash flow cash flow*period dicount factor @8% PV of cash flow dicount factor @7% PV of cash flow dicount factor @9% PV of cash flow 1 143 143 0.925925926 132.41 0.934579 133.64 0.917431 131.19 2 143 286 0.857 245.20 0.873 249.80 0.84168 240.72 3 143 429 0.794 340.55 0.816 350.19 0.772183 331.27 4 143 572 0.735 420.44 0.763 436.38 0.708425 405.22 5 143 715 0.681 486.62 0.713 509.79 0.649931 464.70 6 143 858 0.630 540.69 0.666 571.72 0.596267 511.60 7 143 1,001 0.583 584.07 0.623 623.37 0.547034 547.58 8 143 1,144 0.540 618.07 0.582 665.82 0.501866 574.14 9 143 1,287 0.500 643.82 0.544 700.04 0.460428 592.57 10 143 1,430 0.463 662.37 0.508 726.94 0.422411 604.05 11 143 1,573 0.429 674.63 0.475 747.32 0.387533 609.59 12 143 1,716 0.397 681.45 0.444 761.92 0.355535 610.10 13 143 1,859 0.368 683.55 0.415 771.42 0.326179 606.37 14 143 2,002 0.340 681.60 0.388 776.41 0.299246 599.09 15 143 2,145 0.315 676.19 0.362 777.45 0.274538 588.88 16 143 2,288 0.292 667.85 0.339 775.02 0.25187 576.28 17 143 2,431 0.270 657.02 0.317 769.59 0.231073 561.74 18 143 2,574 0.250 644.14 0.296 761.55 0.211994 545.67 19 143 2,717 0.232 629.56 0.277 751.27 0.19449 528.43 20 143 2,860 0.215 613.61 0.258 739.08 0.178431 510.31 21 143 3,003 0.199 596.56 0.242 725.26 0.163698 491.59 22 143 3,146 0.184 578.68 0.226 710.09 0.150182 472.47 23 143 3,289 0.170 560.17 0.211 693.80 0.137781 453.16 24 143 3,432 0.158 541.22 0.197 676.61 0.126405 433.82 25 143 3,575 0.146 522.01 0.184 658.69 0.115968 414.59 26 143 3,718 0.135 502.68 0.172 640.22 0.106393 395.57 27 143 3,861 0.125 483.35 0.161 621.35 0.097608 376.86 28 143 4,004 0.116 464.12 0.150 602.21 0.089548 358.55 29 143 4,147 0.107 445.09 0.141 582.91 0.082155 340.69 30 1143 34,290 0.099 3,407.65 0.131 4,504.58 0.075371 2,584.48 Total 19,385.36 23,014.48 16,461.27 Duration =11.34 Current price 1,709.47 2,029.50 1,451.61 Ans a. YTM Bond Price $ 7% 2,029.50 9% 1,451.61Related Questions
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