Question

A bond has a $1,000 par value, 15 years to maturity, and a 8% annual coupon and sells for $1,080. What is its yield to maturity (YTM)? Round your answer to two decimal places. 7.12 % Assume that the yield to maturity remains constant for the next 2 years. What will the price be 2 years from today? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

YTM is the rate at which PV of Cash inflows are equal to Bond Price.

Year	CF	PVF @7%	Disc CF	PVF @8%	Disc CF
1	$      80.00	0.9346	$      74.77	0.9259	$      74.07
2	$      80.00	0.8734	$      69.88	0.8573	$      68.59
3	$      80.00	0.8163	$      65.30	0.7938	$      63.51
4	$      80.00	0.7629	$      61.03	0.7350	$      58.80
5	$      80.00	0.7130	$      57.04	0.6806	$      54.45
6	$      80.00	0.6663	$      53.31	0.6302	$      50.41
7	$      80.00	0.6227	$      49.82	0.5835	$      46.68
8	$      80.00	0.5820	$      46.56	0.5403	$      43.22
9	$      80.00	0.5439	$      43.51	0.5002	$      40.02
10	$      80.00	0.5083	$      40.67	0.4632	$      37.06
11	$      80.00	0.4751	$      38.01	0.4289	$      34.31
12	$      80.00	0.4440	$      35.52	0.3971	$      31.77
13	$      80.00	0.4150	$      33.20	0.3677	$      29.42
14	$      80.00	0.3878	$      31.03	0.3405	$      27.24
15	$      80.00	0.3624	$      29.00	0.3152	$      25.22
15	$ 1,000.00	0.3624	$    362.45	0.3152	$    315.24
PV of Cash Inflows			$ 1,091.08		$ 1,000.00
Bond Price			$ 1,080.00		$ 1,080.00
NPV			$      11.08		$     -80.00

YTM = Rate at which least +ve NPV + [ NPV at that Rate / CHange in NPV due to 1% nc in DIsc Rate ] * 1%

= 7% + [ 11.08 / 91.08 ] * 1%

= 7% + 0.12%

= 7.12%

Price after 2 Years:

PV of CFs for balance period.

Year	CF	PVF @7.12%	Disc CF
1	$      80.00	0.9335	$      74.68
2	$      80.00	0.8715	$      69.72
3	$      80.00	0.8136	$      65.08
4	$      80.00	0.7595	$      60.76
5	$      80.00	0.7090	$      56.72
6	$      80.00	0.6619	$      52.95
7	$      80.00	0.6179	$      49.43
8	$      80.00	0.5768	$      46.15
9	$      80.00	0.5385	$      43.08
10	$      80.00	0.5027	$      40.21
11	$      80.00	0.4693	$      37.54
12	$      80.00	0.4381	$      35.05
13	$      80.00	0.4090	$      32.72
13	$ 1,000.00	0.4090	$    408.96
Price of Bond			$ 1,073.05