Question

Find the duration of a bond with settlement date June 6, 2016, and maturity date December 5, 2025. The coupon rate of the bond is 9%, and the bond pays coupons semiannually. The bond is selling at a yield to maturity of 10%. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Macaulay duration
Modified duration

Answer 1

Macaulay Duration

Assume that Bond's Face value is $1000 and Interest paid on 30th june and 31st December every year.

Period	Cash Flow	Period * Cash flow	PV @ 4.5%	PV of Cash flow
1	45	45	0.957	43.062
2	45	90	0.916	82.416
3	45	135	0.876	118.300
4	45	180	0.839	150.941
5	45	225	0.802	180.551
6	45	270	0.768	207.332
7	45	315	0.735	231.471
8	45	360	0.703	253.147
9	45	405	0.673	272.526
10	45	450	0.644	289.767
11	45	495	0.616	305.018
12	45	540	0.590	318.418
13	45	585	0.564	330.099
14	45	630	0.540	340.183
15	45	675	0.517	348.786
16	45	720	0.494	356.018
17	45	765	0.473	361.980
18	45	810	0.453	366.768
19	1045	19855	0.433	8603.207
			Total	13159.992

Macaulay Duration = Total PV of cash flow / current bond price

We are assuming that current bond price is $1000

Macaulay Duration = 13159.992 / 1000 = 13.16 years

Modified Duration

Modified Duration = Macaulay Duration / [1 + (YTM / n)]

n = 9 years and 6 months = 9.5 years

Modified Duration = 13.16 / [1 + (0.10 / 9.5)] = 13.023 years