Question

A bond has a yield to maturity of 5 percent. It matures in 13 years. Its coupon rate is 5 percent. What is its modified duration?  The bond pays coupons twice a year.

(Do not round intermediate calculations. Enter your answers rounded to 2 decimal places.)

Answer 1

Step-1, Calculation of Macaulay Duration of the Bond

Semi-annual Period (1)	Cash Flow (2)	Present Value Factor T 2.50% (3)	Present Value (4) = (3) x (2)	Weight to total (5)	Duration (6) = (1) x (5)
0.50	25	0.97561	24.39	0.0244	0.0122
1.00	25	0.95181	23.80	0.0238	0.0238
1.50	25	0.92860	23.21	0.0232	0.0348
2.00	25	0.90595	22.65	0.0226	0.0453
2.50	25	0.88385	22.10	0.0221	0.0552
3.00	25	0.86230	21.56	0.0216	0.0647
3.50	25	0.84127	21.03	0.0210	0.0736
4.00	25	0.82075	20.52	0.0205	0.0821
4.50	25	0.80073	20.02	0.0200	0.0901
5.00	25	0.78120	19.53	0.0195	0.0976
5.50	25	0.76214	19.05	0.0191	0.1048
6.00	25	0.74356	18.59	0.0186	0.1115
6.50	25	0.72542	18.14	0.0181	0.1179
7.00	25	0.70773	17.69	0.0177	0.1239
7.50	25	0.69047	17.26	0.0173	0.1295
8.00	25	0.67362	16.84	0.0168	0.1347
8.50	25	0.65720	16.43	0.0164	0.1397
9.00	25	0.64117	16.03	0.0160	0.1443
9.50	25	0.62553	15.64	0.0156	0.1486
10.00	25	0.61027	15.26	0.0153	0.1526
10.50	25	0.59539	14.88	0.0149	0.1563
11.00	25	0.58086	14.52	0.0145	0.1597
11.50	25	0.56670	14.17	0.0142	0.1629
12.00	25	0.55288	13.82	0.0138	0.1659
12.50	25	0.53939	13.48	0.0135	0.1686
13.00	1,025	0.52623	539.39	0.5394	7.0121
TOTAL			$1,000		9.7122 Years

Macaulay Duration = 9.7122 Years

Step-2, Calculation of Modified Duration of the Bond

Modified Duration of the Bond = Macaulay Duration / [1 + (YTM / Number of coupon payments per year)]

= 9.7122 Years / [1 + (0.05/2)]

= 9.7122 Years / 1.025

= 9.48 Years

“Therefore, the Modified Duration of the Bond will be 9.48 Years”