Question

A bond has a yield to maturity of 8 percent. It matures in 10 years. Its coupon rate is 8 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

Period (1)	Cash Flow (2)	Present Value Factor T 4.00% (3)	Present Value (4) = (3) x (2)	Weight to total (5)	Duration (6) = (1) x (5)
0.50	40	0.96154	38.46	0.0385	0.02
1.00	40	0.92456	36.98	0.0370	0.04
1.50	40	0.88900	35.56	0.0356	0.05
2.00	40	0.85480	34.19	0.0342	0.07
2.50	40	0.82193	32.88	0.0329	0.08
3.00	40	0.79031	31.61	0.0316	0.09
3.50	40	0.75992	30.40	0.0304	0.11
4.00	40	0.73069	29.23	0.0292	0.12
4.50	40	0.70259	28.10	0.0281	0.13
5.00	40	0.67556	27.02	0.0270	0.14
5.50	40	0.64958	25.98	0.0260	0.14
6.00	40	0.62460	24.98	0.0250	0.15
6.50	40	0.60057	24.02	0.0240	0.16
7.00	40	0.57748	23.10	0.0231	0.16
7.50	40	0.55526	22.21	0.0222	0.17
8.00	40	0.53391	21.36	0.0214	0.17
8.50	40	0.51337	20.53	0.0205	0.17
9.00	40	0.49363	19.75	0.0197	0.18
9.50	40	0.47464	18.99	0.0190	0.18
10.00	1,040	0.45639	474.64	0.4746	4.75
TOTAL			$1,000		7.07 Years

Macaulay Duration = 7.07 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)]

= 7.07 Years / [1 + (0.08/2)]

= 7.07 Years / 1.04

= 6.80 Years.

“Therefore, The Modified Duration of the Bond = 6.80 Years”