Question

Use the following information to answer the question:

Coupon Rate = 6% Face Value = $1,000 Maturity = 10 years Yield to Maturity = 6.5%

Assuming semi-annual coupon payments, find the duration of this bond. By approximately how much would the price of the bond change if its yield to maturity decreased from 6.5% to 6%? What will happen to the bond’s duration?

Excel with formula explanation please

Answer 1

Using Excel function to calculate duration

Duration with YTM 6.5%

Time(n)	Cash flow=6%*1000/2 = 30	PV of Cash flow=(Cash flow)/(1+6.5%/2)^n	PV*Time
1	30	29.06	29.06
2	30	28.14	56.28
3	30	27.26	81.77
4	30	26.40	105.59
5	30	25.57	127.83
6	30	24.76	148.57
7	30	23.98	167.88
8	30	23.23	185.82
9	30	22.50	202.47
10	30	21.79	217.88
11	30	21.10	232.13
12	30	20.44	245.26
13	30	19.79	257.33
14	30	19.17	268.40
15	30	18.57	278.52
16	30	17.98	287.74
17	30	17.42	296.10
18	30	16.87	303.65
19	30	16.34	310.43
20	1030	543.30	10865.91
	Total	963.65	14668.61
	Maculay Duration	15.22	(=14668.61/963.65)

Price when YTM is  6.5% = 963.65
Price when YTM is 6% = 1000( Because coupon rate and YTM are same hence Price is at par value)
Percentage change in Price = (1000-963.65)/963.65 = 3.77%
Duration with YTM 6%

Time(n)	Cash flow=6%*1000/2 = 30	PV of Cash flow=(Cash flow)/(1+6%/2)^n	PV*Time
1	30	29.13	29.13
2	30	28.28	56.56
3	30	27.45	82.36
4	30	26.65	106.62
5	30	25.88	129.39
6	30	25.12	150.75
7	30	24.39	170.75
8	30	23.68	189.46
9	30	22.99	206.93
10	30	22.32	223.23
11	30	21.67	238.40
12	30	21.04	252.50
13	30	20.43	265.57
14	30	19.83	277.67
15	30	19.26	288.84
16	30	18.70	299.12
17	30	18.15	308.56
18	30	17.62	317.19
19	30	17.11	325.06
20	1030	570.29	11405.72
	Total	1000.00	15323.80
	Maculay Duration	15.32	(=15323.80/1000)

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