Question

The duration of an 11-year, $1,000 Treasury bond paying a 10 percent annual coupon and selling at par has been estimated at 6.763 years. What will be the new price of the bond if interest rates increase 0.10 percent (10 basis points)?

Answer 1

Let YTM be 13%

Thus duration of bond

Year	Interest	Redemption value	Total cash flow	PVIF @ 13%	PV	Weight	Duration
A						B	C = A x B
1	100		100	0.8850	88.50	0.107	0.107
2	100		100	0.7831	78.31	0.094	0.189
3	100		100	0.6931	69.31	0.084	0.251
4	100		100	0.6133	61.33	0.074	0.296
5	100		100	0.5428	54.28	0.065	0.327
6	100		100	0.4803	48.03	0.058	0.347
7	100		100	0.4251	42.51	0.051	0.359
8	100		100	0.3762	37.62	0.045	0.363
9	100		100	0.3329	33.29	0.040	0.361
10	100		100	0.2946	29.46	0.036	0.355
11	100	1000	1100	0.2607	286.77	0.346	3.803
					829.39		6.758

Now assume YTM = 12%

Year	Interest	Redemption value	Total cash flow	PVIF @ 12%	PV	Weight	Duration
A						B	C = A x B
1	100		100	0.8929	89.29	0.101	0.101
2	100		100	0.7972	79.72	0.090	0.181
3	100		100	0.7118	71.18	0.081	0.242
4	100		100	0.6355	63.55	0.072	0.288
5	100		100	0.5674	56.74	0.064	0.322
6	100		100	0.5066	50.66	0.057	0.345
7	100		100	0.4523	45.23	0.051	0.359
8	100		100	0.4039	40.39	0.046	0.367
9	100		100	0.3606	36.06	0.041	0.368
10	100		100	0.3220	32.20	0.037	0.365
11	100	1000	1100	0.2875	316.22	0.359	3.947
					881.25		6.887

Now using interpolation we can find YTM

YTM	Duration
12%	6.887
13%	6.758
1%	-0.129
?	-0.124

=0.124/0.129

=0.96%

Thus YTM = 12%+0.96%

=12.96%

If YTM raises by 0.1%, then New YTM = 12.96%+0.1% = 13.06%

Thus price of bond

Year	Interest	Redemption value	Total cash flow	PVIF @ 13.06%	PV
A
1	100		100	0.8845	88.45
2	100		100	0.7823	78.23
3	100		100	0.6919	69.19
4	100		100	0.6120	61.20
5	100		100	0.5413	54.13
6	100		100	0.4788	47.88
7	100		100	0.4235	42.35
8	100		100	0.3746	37.46
9	100		100	0.3313	33.13
10	100		100	0.2930	29.30
11	100	1000	1100	0.2592	285.10
					826.42

Price of bond is nothing but present value of future cash flow

Thus Price of bond = $826.42