Question

Four years ago, your firm issued $1,000 par, 25-year bonds, with a 7 percent coupon rate and a 10 percent call premium.

b. If these bonds are now called, what is the actual yield to call for investors who originally purchased them at par?

c. If current interest rate on the bond is 5 percent and the bonds were not callable, at what price would each bond sell?

Answer 1

YTM is the Rate at which PV of cash Inflows are equal to PV of Cash Outflows

Year	CF	PVF @9%	Disc CF	PVF @10%	Disc CF
0	$ -1,000.00	1.0000	$ -1,000.00	1.0000	$ -1,000.00
1	$        70.00	0.9174	$        64.22	0.9091	$        63.64
2	$        70.00	0.8417	$        58.92	0.8264	$        57.85
3	$        70.00	0.7722	$        54.05	0.7513	$        52.59
4	$        70.00	0.7084	$        49.59	0.6830	$        47.81
4	$ 1,100.00	0.7084	$     779.27	0.6830	$     751.31
NPV			$          6.05		$      -26.79

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

= 9% + [ 6.05 / 32.84 ] * 1%

= 9% + 0.18%

= 9.18%

Part C:

Bond Price is PV of CFs from it.

Year	CF	PVF @5%	Disc CF
1	$      70.00	0.9524	$      66.67
2	$      70.00	0.9070	$      63.49
3	$      70.00	0.8638	$      60.47
4	$      70.00	0.8227	$      57.59
5	$      70.00	0.7835	$      54.85
6	$      70.00	0.7462	$      52.24
7	$      70.00	0.7107	$      49.75
8	$      70.00	0.6768	$      47.38
9	$      70.00	0.6446	$      45.12
10	$      70.00	0.6139	$      42.97
11	$      70.00	0.5847	$      40.93
12	$      70.00	0.5568	$      38.98
13	$      70.00	0.5303	$      37.12
14	$      70.00	0.5051	$      35.35
15	$      70.00	0.4810	$      33.67
16	$      70.00	0.4581	$      32.07
17	$      70.00	0.4363	$      30.54
18	$      70.00	0.4155	$      29.09
19	$      70.00	0.3957	$      27.70
20	$      70.00	0.3769	$      26.38
21	$      70.00	0.3589	$      25.13
21	$ 1,000.00	0.3589	$    358.94
Price of Bond			$1,256.42

Pls comment, if any further assistance is required