Question

Calculate the Macaulay duration of a 10%, $1,000 par bond that matures in three years if the bond's YTM is 12% and interest is paid semiannually.

1. Calculate this bond's modified duration (years). Do not round intermediate calculations. Round your answer to two decimal places.

2. Assuming the bond's YTM goes from 12% to 10.5%, calculate an estimate of the price change. Do not round intermediate calculations. Round your answer to three decimal places (in %). Use a minus sign to enter negative value, if any.

Problem 13-01 Calculate the Macaulay duration of a 10%, $1,000 par bond that matures in three years if the bond's YTM is 12% and interest is paid semiannually. You may use Appendix C to answer the questions. a. Calculate this bond's modified duration. Do not round intermediate calculations. Round your answer to two decimal places. years b. Assuming the bond's YTM goes from 12% to 10.5%, calculate an estimate of the price change. Do not round intermediate calculations. Round your answer to three decimal places. Use a minus sign to enter negative value, if any. %

Answer 1

Il Duration of a bond Duration = 1+y - (1+y) + t (C-7) va y C[ltyst - I]ty Il where ... y = YTM in decimals we C= Coupon rate in decimals t = total life of the Bond. Given y = 1.2% = 0.12 C = LOT = 0.10 t: 3 yeares . Duration: /1+0.12 -(1+0:12)+360.10.0.12) (0.12. 10.10.[C1 +0:12)2-1] +0:12 Des 1:12 - [1.12+0.30-0.36) sty 0.12 0.1605 1 = 9.33 – 6.60 1 - Duration = 2.73 yeares, @ Bonds modified duration in i modified duration = Duration It YTM = 2.73 - 2:44 yeared 2.73 - 2.44 112

Computation estinated change in bond price due to change in YTM. (1) Computution of price of bona if yTM = 12%. year I Cash flows PVF@YTM=127 Present value of Cf 1000X10% = $100 0.8928_I _$ 89:28 2 $100 L0.7972 | $79.72. 3_ $100 L0.3118_ $71.18 | 3 | Maturity- $ 1000 0.7118 ] $711.80 Price of bond woon when yTM 3124 $951.98. (1) Computation of price of bond if e/TM=10.5% year cash flowl Pv FC YTM=10.54. Prof Cf. I! $100 0.9050 $90.50 ||2|$100 0.81901) 1$ 81.90 $100 0.7412 $074.12 || 3 ) $1000___0.7412 $741120 Price of the __ bond when I $987.72 Y IM => 10:57. The estimated Price Change due to I drop of yTM from 127. to 10.5%. = $987.72 - $99198 skills a $ 35.74 P P .
a. Modified duration of the given bond is 2.44 years

b. If ther is a change in YTM of the given bond then the it was expected to ther was a rise of $35.74 in bond price

I.e from $951.98 (the bond price at YTM is 12%)

to $987.74 (the bond price at YTM is 10.5%)