Question

A.What is the value of the bond now?

B. Calculate the Duration of the Bond.. Show Formula for both

C. If Interest rates are 6%. What is the Duration of a perpetuity?

A bond makes semiannual payments.

The coupon is $60.

Par is $1,000.

The bond has 16 years left to maturity. Interest rates are now 4.7% per year.

Answer 1

A.  The bond price is the NPV of all the future cash flows discounted at the market yield

where is the cash-flow at time t

r is the yield per period = 0.047/2 = 0.0235

n is the total number of periods = 16*2=32

	Interest rate (r)	0.0235
Period	Cash flows	PV of cash-flows = Cashflow/(1+Interest rate)^Period	Time (t)	PV of cash-flows*t
1	30	29.3111871	0.5	14.65559355
2	30	28.63818965	1	28.63818965
3	30	27.9806445	1.5	41.97096675
4	30	27.33819687	2	54.67639375
5	30	26.71050012	2.5	66.7762503
6	30	26.09721556	3	78.29164667
7	30	25.49801227	3.5	89.24304294
8	30	24.91256694	4	99.65026778
9	30	24.3405637	4.5	109.5325366
10	30	23.78169389	5	118.9084695
11	30	23.23565598	5.5	127.7961079
12	30	22.70215533	6	136.212932
13	30	22.18090408	6.5	144.1758765
14	30	21.67162099	7	151.7013469
15	30	21.17403125	7.5	158.8052344
16	30	20.68786639	8	165.5029311
17	30	20.21286409	8.5	171.8093447
18	30	19.74876804	9	177.7389123
19	30	19.29532783	9.5	183.3056144
20	30	18.85229881	10	188.5229881
21	30	18.41944193	10.5	193.4041402
22	30	17.99652362	11	197.9617598
23	30	17.5833157	11.5	202.2081306
24	30	17.17959521	12	206.1551426
25	30	16.78514432	12.5	209.814304
26	30	16.39975019	13	213.1967525
27	30	16.02320488	13.5	216.3132659
28	30	15.65530521	14	219.1742729
29	30	15.29585267	14.5	221.7898637
30	30	14.94465332	15	224.1697997
31	30	14.60151765	15.5	226.3235236
32	1030	489.8082781	16	7836.93245
		1145.062846		12475.35805
			Duration	10.89491122

Bond price = $1145.06

B.)

Duration = (PV of cash-flows*t) / (PV of all cash-flows)

where is the cash-flow at time t

r is the yield per period = 0.047/2 = 0.0235

n is the total number of periods = 16*2=32

( Calculation included in part a table)

Duration of the bond = (PV of cash-flows * t) / PV of cash-flows

Duration of the bond = 10.894

C)

Duration of a perpetual bond is given by =

r is the yield per period = 0.047/2 = 0.0235

Hence duration of a perpetual bond = (1+0.0235)/0.0235

Duration of a perpetual bond= 43.553