Bond J is a 4 percent coupon bond. Bond K is a 10 percent coupon bond. Both bond
ID: 2784159 • Letter: B
Question
Bond J is a 4 percent coupon bond. Bond K is a 10 percent coupon bond. Both bonds have 7 years to maturity, make semiannual payments, and have a YTM of 8 percent.
Requirement 1:
(a) If interest rates suddenly rise by 4 percent, what is the percentage price change of Bond J?
Answer Options: -20.35, -18.35, -20.33, 26.80, -19.35
(b) If interest rates suddenly rise by 4 percent, what is the percentage price change of Bond K?
Answer Options: 23.31, -15.96, -17.94, -17.96, 26.64
Requirement 2:
(a) If interest rates suddenly fall by 4 percent, what is the percentage price change of Bond J?
Answer Options: 1.00, -20.37, -37.18, 26.78, 26.76
(b) If interest rates suddenly fall by 4 percent, what is the percentage price change of Bond K?
Answer Options: -17.98, 23.17, -36.32, -8.29, 23.39
Explanation / Answer
Based on the analysis
the answers are as follows
Requirement 1)
a) -20.35%
b) -17.96%
Requirement 2)
a) 26.78%
b) 23.29%
Bond J Present Value = Future value/[(1+(r/m))^mt] r is the interest rate that is 8% t is the year m is the compounding period coupon rate = 4% When YTM = 8% mt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cash flow 20 20 20 20 20 20 20 20 20 20 20 20 20 1020 present value 19.23 18.49 17.78 17.10 16.44 15.81 15.20 14.61 14.05 13.51 12.99 12.49 12.01 589.02 price 789 When YTM = 12% mt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cash flow 20 20 20 20 20 20 20 20 20 20 20 20 20 1020 present value 18.87 17.80 16.79 15.84 14.95 14.10 13.30 12.55 11.84 11.17 10.54 9.94 9.38 451.15 price 628 % price change -20.35% When YTM = 4% mt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cash flow 20 20 20 20 20 20 20 20 20 20 20 20 20 1020 present value 19.61 19.22 18.85 18.48 18.11 17.76 17.41 17.07 16.74 16.41 16.09 15.77 15.46 773.03 price 1000 % price change 26.78% Bond K Present Value = Future value/[(1+(r/m))^mt] r is the interest rate that is 8% t is the year m is the compounding period coupon rate = 10% When YTM = 8% mt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cash flow 50 50 50 50 50 50 50 50 50 50 50 50 50 1050 present value 48.08 46.23 44.45 42.74 41.10 39.52 38.00 36.53 35.13 33.78 32.48 31.23 30.03 606.35 price 1106 When YTM = 12% mt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cash flow 50 50 50 50 50 50 50 50 50 50 50 50 50 1050 present value 47.17 44.50 41.98 39.60 37.36 35.25 33.25 31.37 29.59 27.92 26.34 24.85 23.44 464.42 price 907 % price change -17.96% When YTM = 4% mt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cash flow 50 50 50 50 50 50 50 50 50 50 50 50 50 1050 present value 49.02 48.06 47.12 46.19 45.29 44.40 43.53 42.67 41.84 41.02 40.21 39.42 38.65 795.77 price 1363 % price change 23.29%