Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).

a.	Suppose that today you buy a bond with an annual coupon rate of 10 percent for $1,190. The bond has 18 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b-1.	Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b-2.	What is the HPY on your investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Part A:

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
0	$ -1,190.00	1.0000	$ -1,190.00	1.0000	$ -1,190.00
1	$     100.00	0.9346	$        93.46	0.9259	$        92.59
2	$     100.00	0.8734	$        87.34	0.8573	$        85.73
3	$     100.00	0.8163	$        81.63	0.7938	$        79.38
4	$     100.00	0.7629	$        76.29	0.7350	$        73.50
5	$     100.00	0.7130	$        71.30	0.6806	$        68.06
6	$     100.00	0.6663	$        66.63	0.6302	$        63.02
7	$     100.00	0.6227	$        62.27	0.5835	$        58.35
8	$     100.00	0.5820	$        58.20	0.5403	$        54.03
9	$     100.00	0.5439	$        54.39	0.5002	$        50.02
10	$     100.00	0.5083	$        50.83	0.4632	$        46.32
11	$     100.00	0.4751	$        47.51	0.4289	$        42.89
12	$     100.00	0.4440	$        44.40	0.3971	$        39.71
13	$     100.00	0.4150	$        41.50	0.3677	$        36.77
14	$     100.00	0.3878	$        38.78	0.3405	$        34.05
15	$     100.00	0.3624	$        36.24	0.3152	$        31.52
16	$     100.00	0.3387	$        33.87	0.2919	$        29.19
17	$     100.00	0.3166	$        31.66	0.2703	$        27.03
18	$     100.00	0.2959	$        29.59	0.2502	$        25.02
18	$ 1,000.00	0.2959	$     295.86	0.2502	$     250.25
NPV	$     111.77		$        -2.56

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

= 7% + [ 111.77 / 114.33 ] * 1 %

= 7% + [ 0.98 * 1% ]

= 7% + 0.98%

= 7.98%

Part b.1:

Price of Bond = PV of CFs from it.

Year	CF	PVF @6.98%	Disc CF
1	$     100.00	0.9348	$        93.48
2	$     100.00	0.8738	$        87.38
3	$     100.00	0.8168	$        81.68
4	$     100.00	0.7635	$        76.35
5	$     100.00	0.7137	$        71.37
6	$     100.00	0.6671	$        66.71
7	$     100.00	0.6236	$        62.36
8	$     100.00	0.5829	$        58.29
9	$     100.00	0.5448	$        54.48
10	$     100.00	0.5093	$        50.93
11	$     100.00	0.4761	$        47.61
12	$     100.00	0.4450	$        44.50
13	$     100.00	0.4160	$        41.60
14	$     100.00	0.3888	$        38.88
15	$     100.00	0.3635	$        36.35
16	$     100.00	0.3397	$        33.97
16	$ 1,000.00	0.3397	$     339.75
Price after 2 Yeasr	$ 1,285.67

Part b.2:

Year	CF	PVF @12%	Disc CF	PVF @13%	Disc CF
0	$ -1,190.00	1.0000	$ -1,190.00	1.0000	$ -1,190.00
1	$     100.00	0.8929	$        89.29	0.8850	$        88.50
2	$     100.00	0.7972	$        79.72	0.7831	$        78.31
2	$ 1,285.67	0.7972	$ 1,024.93	0.7831	$ 1,006.87
NPV	$          3.93		$      -16.32

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

= 12% + [ 3.93 / 20.25 ] * 1 %

= 12% + [ 0.19 * 1% ]

= 12% + 0.19%

= 12.19%

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