Question

A bond that makes annual payments is initially selling at $1,000. It has a 6% coupon rate and 6% YTM. The maturity is 10 years and face value is $1,000. If the YTM falls to 5%, what is the percentage change in the price? Enter as a whole percentage to two decimals with no symbols (e.g if the change is 9.52% enter 9.52).

Numeric Response

Answer 1

Duration:
Duaration = Sum [ Weight * Year ]

Year	Cash Flow	PVF@ 6 %	Disc CF	Weight	Wt * Year
1	$                60.00	0.9434	$      56.60	0.0566	0.0566
2	$                60.00	0.8900	$      53.40	0.0534	0.1068
3	$                60.00	0.8396	$      50.38	0.0504	0.1511
4	$                60.00	0.7921	$      47.53	0.0475	0.1901
5	$                60.00	0.7473	$      44.84	0.0448	0.2242
6	$                60.00	0.7050	$      42.30	0.0423	0.2538
7	$                60.00	0.6651	$      39.90	0.0399	0.2793
8	$                60.00	0.6274	$      37.64	0.0376	0.3012
9	$                60.00	0.5919	$      35.51	0.0355	0.3196
10	$                60.00	0.5584	$      33.50	0.0335	0.3350
10	$           1,000.00	0.5584	$    558.39	0.5584	5.5839
Duration in Years					7.8017

Modified duaration :
Modified duration = Duration / [ 1 + YTM ]
It specifies% change in Price in opposite direction due to 1% change in YTM.

Particulars	Values
Duration	7.8017
YTM	6.0000%

Modified Duration = Duration / [ 1 + YTM ]
= 7.8017 / [ 1 + 0.06 ]
= 7.8017 / [ 1.06 ]
= 7.3601 %

I.e 1% decrease in Disc rate ( 6% to 5%) will leads to 7.36% inc in Bond Price.

Answer is 7.36