40. Calculate the modified duration of a 10-year 7% semi-annual coupon bond priced at 97.50.
a. 7.316
b. 7.06
c. 6.88
d. 3.53
e. 3.67
Period | Cash flow | Period x Cash flow | PV of $1 at 3.6788% | Present value of cash flow | First we have to calculate bonds yield | ||||
1 | 3.5 | 3.5 | 0.9645 | 3.38 | PV | 97.5 | |||
2 | 3.5 | 7 | 0.9303 | 6.51 | FV | 100 | |||
3 | 3.5 | 10.5 | 0.8973 | 9.42 | PMT | 3.5 | (100 x 7%/2) | ||
4 | 3.5 | 14 | 0.8654 | 12.12 | NPER | 20 | (10 x 2) | ||
5 | 3.5 | 17.5 | 0.8347 | 14.61 | Rate(yield) | 3.6788% | per semi annual period | ||
6 | 3.5 | 21 | 0.8051 | 16.91 | =RATE(20,3.5,-97.5,100) | ||||
7 | 3.5 | 24.5 | 0.7766 | 19.03 | |||||
8 | 3.5 | 28 | 0.7490 | 20.97 | |||||
9 | 3.5 | 31.5 | 0.7224 | 22.76 | |||||
10 | 3.5 | 35 | 0.6968 | 24.39 | |||||
11 | 3.5 | 38.5 | 0.6721 | 25.87 | |||||
12 | 3.5 | 42 | 0.6482 | 27.23 | |||||
13 | 3.5 | 45.5 | 0.6252 | 28.45 | |||||
14 | 3.5 | 49 | 0.6030 | 29.55 | |||||
15 | 3.5 | 52.5 | 0.5816 | 30.54 | |||||
16 | 3.5 | 56 | 0.5610 | 31.42 | |||||
17 | 3.5 | 59.5 | 0.5411 | 32.19 | |||||
18 | 3.5 | 63 | 0.5219 | 32.88 | |||||
19 | 3.5 | 66.5 | 0.5034 | 33.47 | |||||
20 | 103.5 | 2070 | 0.4855 | 1,005.01 | |||||
Total | 1,426.69 | ||||||||
÷ | 97.5 | ||||||||
Maculay Duration | 14.6327 | period | |||||||
Modified duration = Maculay duration / (1+yield) | |||||||||
=14.6327/1.036788 | |||||||||
14.11349 | semi annual periods | ||||||||
Or | (14.11349/2) | 7.06 | Annual | Option B is right | |||||
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