Question

a. A newly issued bond has a maturity of 10 years and pays a 7% coupon rate (with coupon payments coming once annually). The bond sells at par value. What is the duration of the bond?

b. Find the actual price of the bond assuming that its yield to maturity immediately increases from 7% to 8% (with maturity still 10 years)

Answer 1

Part A:

Duartion = Sum [Weight * Year ]

Year	CF	PVF @7%	Disc CF	Weight	Wt * Year
1	$      70.00	0.9346	$   65.42	0.0654	0.07
2	$      70.00	0.8734	$   61.14	0.0611	0.12
3	$      70.00	0.8163	$   57.14	0.0571	0.17
4	$      70.00	0.7629	$   53.40	0.0534	0.21
5	$      70.00	0.7130	$   49.91	0.0499	0.25
6	$      70.00	0.6663	$   46.64	0.0466	0.28
7	$      70.00	0.6227	$   43.59	0.0436	0.31
8	$      70.00	0.5820	$   40.74	0.0407	0.33
9	$      70.00	0.5439	$   38.08	0.0381	0.34
10	$ 1,070.00	0.5083	$ 543.93	0.5439	5.44
Duration					7.52

Part B:

Price of Bond = PV of Cfs from it.

Year	CF	PVF @8%	Disc CF
1	$      70.00	0.9259	$      64.81
2	$      70.00	0.8573	$      60.01
3	$      70.00	0.7938	$      55.57
4	$      70.00	0.7350	$      51.45
5	$      70.00	0.6806	$      47.64
6	$      70.00	0.6302	$      44.11
7	$      70.00	0.5835	$      40.84
8	$      70.00	0.5403	$      37.82
9	$      70.00	0.5002	$      35.02
10	$ 1,070.00	0.4632	$    495.62
price of Bond			$    932.90