Question

A bond has a $1,000 par value, 20 years to maturity, and an 8% annual coupon and sells for $1,110.

1. What is its yield to maturity (YTM)? Round your answer to two decimal places.

       %

2. Assume that the yield to maturity remains constant for the next four years. What will the price be 4 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 @6%	Disc CF	PVF @7%	Disc CF
1	$      80.00	0.9434	$      75.47	0.9346	$      74.77
2	$      80.00	0.8900	$      71.20	0.8734	$      69.88
3	$      80.00	0.8396	$      67.17	0.8163	$      65.30
4	$      80.00	0.7921	$      63.37	0.7629	$      61.03
5	$      80.00	0.7473	$      59.78	0.7130	$      57.04
6	$      80.00	0.7050	$      56.40	0.6663	$      53.31
7	$      80.00	0.6651	$      53.20	0.6227	$      49.82
8	$      80.00	0.6274	$      50.19	0.5820	$      46.56
9	$      80.00	0.5919	$      47.35	0.5439	$      43.51
10	$      80.00	0.5584	$      44.67	0.5083	$      40.67
11	$      80.00	0.5268	$      42.14	0.4751	$      38.01
12	$      80.00	0.4970	$      39.76	0.4440	$      35.52
13	$      80.00	0.4688	$      37.51	0.4150	$      33.20
14	$      80.00	0.4423	$      35.38	0.3878	$      31.03
15	$      80.00	0.4173	$      33.38	0.3624	$      29.00
16	$      80.00	0.3936	$      31.49	0.3387	$      27.10
17	$      80.00	0.3714	$      29.71	0.3166	$      25.33
18	$      80.00	0.3503	$      28.03	0.2959	$      23.67
19	$      80.00	0.3305	$      26.44	0.2765	$      22.12
20	$      80.00	0.3118	$      24.94	0.2584	$      20.67
20	$ 1,000.00	0.3118	$    311.80	0.2584	$    258.42
PV of Cash Inflows'			$ 1,229.40		$ 1,105.94
Bond Price			$ 1,110.00		$ 1,110.00
NPV			$    119.40		$       -4.06

YTM = rate at which least +ve NPV+ [ NPV at that Rate / Change in NPV due to 1% inc in Disc Rate ] * 1%

= 6% + [ 119.40 / 123.46 ] * 1%

= 6% + 0.97%

= 6.97%

Part B:

Price after 4 Years: PV of Future CFs.

Year	CF	PVF @6.94%	Disc CF
1	$      80.00	0.9351	$      74.81
2	$      80.00	0.8744	$      69.95
3	$      80.00	0.8177	$      65.41
4	$      80.00	0.7646	$      61.17
5	$      80.00	0.7150	$      57.20
6	$      80.00	0.6686	$      53.49
7	$      80.00	0.6252	$      50.02
8	$      80.00	0.5846	$      46.77
9	$      80.00	0.5467	$      43.73
10	$      80.00	0.5112	$      40.90
11	$      80.00	0.4780	$      38.24
12	$      80.00	0.4470	$      35.76
13	$      80.00	0.4180	$      33.44
14	$      80.00	0.3909	$      31.27
15	$      80.00	0.3655	$      29.24
16	$      80.00	0.3418	$      27.34
16	$ 1,000.00	0.3418	$    341.79
Bond Price			$ 1,100.53