Problem 7-7 Interest rate sensitivity An investor purchased the following 5 bond
ID: 2769286 • Letter: P
Question
Problem 7-7
Interest rate sensitivity
An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 10% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell and each then had a new YTM of 7%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table. Round your answers to the nearest cent or to two decimal places.
Price @ 10% Price @ Percentage Change
10-year, 10% annual coupon $ $ %
10-year zero
5-year zero
30-year zero
100 perpetuity
Explanation / Answer
Bond Price Calculation At 10% YTM 10% 10 Year Bond Zero Coupon 10 Year Bond Zero Coupon 5 Year Bond Zero Coupon 30 Year Bond $100 Perpetuity Period PV Factor @10% Interest+Maturity PV Of Cash Flows Interest+Maturity PV Of Cash Flows Interest+Maturity PV Of Cash Flows Interest+Maturity PV Of Cash Flows Year 1 0.909 100 90.91 - - - - - - =100/10% Year 2 0.826 100 82.64 - - - - - - Year 3 0.751 100 75.13 - - - - - - Year 4 0.683 100 68.30 - - - - - - Year 5 0.621 100 62.09 - - 1,000 620.92 - - Year 6 0.564 100 56.45 - - - - Year 7 0.513 100 51.32 - - - - Year 8 0.467 100 46.65 - - - - Year 9 0.424 100 42.41 - - - - Year 10 0.386 1,100 424.10 1,000 385.54 - - Year 11 0.350 - - Year 12 0.319 - - Year 13 0.290 - - Year 14 0.263 - - Year 15 0.239 - - Year 16 0.218 - - Year 17 0.198 - - Year 18 0.180 - - Year 19 0.164 - - Year 20 0.149 - - Year 21 0.135 - - Year 22 0.123 - - Year 23 0.112 - - Year 24 0.102 - - Year 25 0.092 - - Year 26 0.084 - - Year 27 0.076 - - Year 28 0.069 - - Year 29 0.063 - - Year 30 0.057 1,000 57.31 Total 1,000.0 385.5 620.9 57.3 1,000 Bond Price Calculation At 7% YTM 10% 10 Year Bond Zero Coupon 10 Year Bond Zero Coupon 5 Year Bond Zero Coupon 30 Year Bond $100 Perpetuity Period PV Factor @7% Interest+Maturity PV Of Cash Flows Interest+Maturity PV Of Cash Flows Interest+Maturity PV Of Cash Flows Interest+Maturity PV Of Cash Flows Year 1 0.935 100 93.46 - - - - - - =100/7% Year 2 0.873 100 87.34 - - - - - - Year 3 0.816 100 81.63 - - - - - - Year 4 0.763 100 76.29 - - - - - - Year 5 0.713 100 71.30 - - 1,000 712.99 - - Year 6 0.666 100 66.63 - - - - Year 7 0.623 100 62.27 - - - - Year 8 0.582 100 58.20 - - - - Year 9 0.544 100 54.39 - - - - Year 10 0.508 1,100 559.18 1,000 508.35 - - Year 11 0.475 - - Year 12 0.444 - - Year 13 0.415 - - Year 14 0.388 - - Year 15 0.362 - - Year 16 0.339 - - Year 17 0.317 - - Year 18 0.296 - - Year 19 0.277 - - Year 20 0.258 - - Year 21 0.242 - - Year 22 0.226 - - Year 23 0.211 - - Year 24 0.197 - - Year 25 0.184 - - Year 26 0.172 - - Year 27 0.161 - - Year 28 0.150 - - Year 29 0.141 - - Year 30 0.131 1,000 131.37 Total 1,210.7 508.3 713.0 131.4 1,429 Bonds Price @10% Price @7% % Change 10Yr 10% Bond 1,000.00 1,210.71 21.1% 10Yr 0 coupon bond 385.54 508.35 31.9% 5Yr 0 Coupon Bond 620.92 712.99 14.8% 30Yr 0 Coupon Bond 57.31 131.37 129.2% $100 perpetuity 1,000.00 1,428.57 42.9%