In: Finance
Find the duration of a bond with settlement date June 14, 2016,
and maturity date December 21, 2025. The coupon rate of the bond is
8%, and the bond pays coupons semiannually. The bond is selling at
a yield to maturity of 9%. (Do not round intermediate
calculations. Round your answers to 4 decimal
places.)
| Macaulay duration | |
| Modified duration | |
Number of Periods = 9.5* 2= 19
Coupon semiannual = 8%*1000 /2 = 40
Rate = 9%/2= 4.5
| Time(n) | Cash flow | PV of Cash flow=(Cash flow)/(1+4.5%)^n | PV*Time | ||
| 1 | 40 | 38.28 | 38.277512 | ||
| 2 | 40 | 36.63 | 73.2583961 | ||
| 3 | 40 | 35.05 | 105.155592 | ||
| 4 | 40 | 33.54 | 134.169815 | ||
| 5 | 40 | 32.10 | 160.490209 | ||
| 6 | 40 | 30.72 | 184.294977 | ||
| 7 | 40 | 29.39 | 205.751968 | ||
| 8 | 40 | 28.13 | 225.019241 | ||
| 9 | 40 | 26.92 | 242.245594 | ||
| 10 | 40 | 25.76 | 257.571073 | ||
| 11 | 40 | 24.65 | 271.127445 | ||
| 12 | 40 | 23.59 | 283.038655 | ||
| 13 | 40 | 22.57 | 293.421253 | ||
| 14 | 40 | 21.60 | 302.384803 | ||
| 15 | 40 | 20.67 | 310.032265 | ||
| 16 | 40 | 19.78 | 316.460367 | ||
| 17 | 40 | 18.93 | 321.759942 | ||
| 18 | 40 | 18.11 | 326.016266 | ||
| 19 | 1040 | 450.63 | 8562.04334 | ||
| Total | 937.0335 | 12612.5187 | |||
| Maculay Duration | 13.4601 | (=12612.5187/937.0335) | |||
| Modified Duration | 12.8804 | (=Maculay Duration/(1+YTM) | |||
So Maculay Duration in terms of years = 13.4601/2 = 6.7300
Modified duration = 12.8804/2 = 6.4402
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