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Chap10_solution - Suggested Solutions to Chap 10 Exercises...

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Suggested Solutions to Chap 10 Exercises Fin 367 Spring 2008 Professor Bing Han Chapter 10: 1. The percentage bond price change is: – Duration × 0327 . 0 10 . 1 0050 . 0 194 . 7 y 1 y - = × - = + or a 3.27% decline 2. Computation of duration: a. YTM = 6% (1) (2) (3) (4) (5) Time until Payment (Years) Payment Payment Discounted at 6% Weight Column (1) x Column (4) 1 60 56.60 0.0566 0.0566 2 60 53.40 0.0534 0.1068 3 1060 890.00 0.8900 2.6700 Column Sum: 1000.00 1.0000 2.8334 Duration = 2.833 years b. YTM = 10% (1) (2) (3) (4) (5) Time until Payment (Years) Payment Payment Discounted at 10% Weight Column (1) x Column (4) 1 60 54.55 0.0606 0.0606 2 60 49.59 0.0551 0.1101 3 1060 796.39 0.8844 2.6531 Column Sum: 900.53 1.0000 2.8238 Duration = 2.824 years, which is less than the duration at the YTM of 6%.
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7. C: Highest maturity, zero coupon D: Highest maturity, next-lowest coupon A: Highest maturity, same coupon as remaining bonds B: Lower yield to maturity than bond E E: Highest coupon, shortest maturity, highest yield of all bonds. 11. a. The duration of the perpetuity is: (1.05/0.05) = 21 years. Let w be the weight of the zero-coupon bond, so that we find w by solving: (w × 5) + [(1 – w) × 21] = 10 w = 11/16 = 0.6875
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