Question

Mayfawny owns an 8 year bond with a par value of 1,000. The bond matures for par and pays semi-annual coupons at a rate of 6% convertible semi-annually.

Calculate the Modified duration of this bond at an annual effective interest rate of 9.2025%.

Answer 1

First let us calculate the macaulay duration of the bond

Cash flow per period = 6% of 1000 / 2 =30

semi annual yield =4.6%

year(t)	CF	PV factor	CF*pv factor	[(CF*pv factor)/ total ]* t
0.5	30	0.956023	28.68068834	0.017455204
1	30	0.91398	27.41939612	0.033375152
1.5	30	0.873786	26.21357181	0.047861117
2	30	0.835359	25.06077611	0.061008434
2.5	30	0.798623	23.95867697	0.072906828
3	30	0.763501	22.9050449	0.083640721
3.5	30	0.729925	21.89774847	0.093289523
4	30	0.697825	20.93474998	0.101927914
4.5	30	0.667137	20.01410132	0.109626102
5	30	0.637798	19.13394007	0.116450077
5.5	30	0.60975	18.29248573	0.12246184
6	30	0.582935	17.48803607	0.127719631
6.5	30	0.557299	16.71896374	0.13227814
7	30	0.53279	15.98371294	0.136188701
7.5	30	0.50936	15.28079631	0.139499489
8	1030	0.48696	501.5685214	4.884112118
Total	821.5512103	6.27980099

Modified duration = Macaulay duration / ( 1+ ytm/2) = 6.27980099/ 1.046 = 6.0036 years