ON 13 Consider a bond with 30 years remaining to maturity t

ON 13. Consider a bond with 30 years remaining to maturity t face value. The yield to maturity of the bonds 7%. Calculate the first) hat pays an 8% annual coupon payment and has a$1,000 duration of the bond. (Hint: compute bond price

Solution

13 Years

Working:

Step-1:Calculation of price of bond
Price of bond is the present value of cash flow from bond.
a. Present Value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
				=	(1-(1+0.07)^-30)/0.07		i	7%
				=	12.40904			n	30
b. Present Value of 1		=	(1+i)^-n
				=	(1+0.07)^-30
				=	0.13137
c.	Annual Coupon	=	Face Value x Annual coupon rate
			=	$         1,000	x	8%
			=	$               80
d.	Present Value of annual coupon	$          80	x	12.40904	=	$     992.72
	Present Value of face Value		$    1,000	x	0.13137	=	$     131.37
	Current Price of bond						$ 1,124.09
Step-2:Calculation of Present Value of weighted cash flow
Year	Cash flow	Year*Cash flow	Discount factor	Present Value
a	b	c=a*b		d=1.07^-a		e=c*d
1	$           80	$            80		0.9346		$         74.77
2	80	160		0.8734		139.75
3	80	240		0.8163		195.91
4	80	320		0.7629		244.13
5	80	400		0.7130		285.19
6	80	480		0.6663		319.84
7	80	560		0.6227		348.74
8	80	640		0.5820		372.49
9	80	720		0.5439		391.63
10	80	800		0.5083		406.68
11	80	880		0.4751		418.08
12	80	960		0.4440		426.25
13	80	1,040		0.4150		431.56
14	80	1,120		0.3878		434.36
15	80	1,200		0.3624		434.94
16	80	1,280		0.3387		433.58
17	80	1,360		0.3166		430.54
18	80	1,440		0.2959		426.04
19	80	1,520		0.2765		420.29
20	80	1,600		0.2584		413.47
21	80	1,680		0.2415		405.74
22	80	1,760		0.2257		397.26
23	80	1,840		0.2109		388.14
24	80	1,920		0.1971		378.52
25	80	2,000		0.1842		368.50
26	80	2,080		0.1722		358.17
27	80	2,160		0.1609		347.61
28	80	2,240		0.1504		336.90
29	80	2,320		0.1406		326.11
30	1,080	32,400		0.1314		4,256.29
		Total				$ 14,611.48
Step-3:Calculation of duration of bond
	Duration of bond	=	Present Value of weighted cash/Current Price of bond
			=	$ 14,611.48	/	$   1,124.09
			=	13
Thus, duration of bond is 13 years