Question

You are analyzing the after-tax cost of debt for a firm. You know that the firm’s 12-year maturity, 11.50 percent semiannual coupon bonds are selling at a price of $1,222.96. These bonds are the only debt outstanding for the firm.

What is the current YTM of the bonds and after-tax cost of debt for this firm if the bonds are selling

YTM ________ %

After-tax cost of debt __________ %

Answer 1

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

Period	CF	PVF @4%	Disc CF	PVF @4.5%	Disc CF
0	$ -1,222.96	1	$ -1,222.96	1	$ -1,222.96
1	$        57.50	0.961538	$        55.29	0.956938	$        55.02
2	$        57.50	0.924556	$        53.16	0.91573	$        52.65
3	$        57.50	0.888996	$        51.12	0.876297	$        50.39
4	$        57.50	0.854804	$        49.15	0.838561	$        48.22
5	$        57.50	0.821927	$        47.26	0.802451	$        46.14
6	$        57.50	0.790315	$        45.44	0.767896	$        44.15
7	$        57.50	0.759918	$        43.70	0.734828	$        42.25
8	$        57.50	0.73069	$        42.01	0.703185	$        40.43
9	$        57.50	0.702587	$        40.40	0.672904	$        38.69
10	$        57.50	0.675564	$        38.84	0.643928	$        37.03
11	$        57.50	0.649581	$        37.35	0.616199	$        35.43
12	$        57.50	0.624597	$        35.91	0.589664	$        33.91
13	$        57.50	0.600574	$        34.53	0.564272	$        32.45
14	$        57.50	0.577475	$        33.20	0.539973	$        31.05
15	$        57.50	0.555265	$        31.93	0.51672	$        29.71
16	$        57.50	0.533908	$        30.70	0.494469	$        28.43
17	$        57.50	0.513373	$        29.52	0.473176	$        27.21
18	$        57.50	0.493628	$        28.38	0.4528	$        26.04
19	$        57.50	0.474642	$        27.29	0.433302	$        24.91
20	$        57.50	0.456387	$        26.24	0.414643	$        23.84
21	$        57.50	0.438834	$        25.23	0.396787	$        22.82
22	$        57.50	0.421955	$        24.26	0.379701	$        21.83
23	$        57.50	0.405726	$        23.33	0.36335	$        20.89
24	$        57.50	0.390121	$        22.43	0.347703	$        19.99
24	$ 1,000.00	0.390121	$     390.12	0.347703	$     347.70
NPV			$        43.86		$      -41.77

YTM per 6 months = Rate at which Least +ve NPV + [ NPV at that Rate / Change in NPV due to 0.5% inc in Disc rate ] * 0.5%

= 4% + [ ( 43.86 / 85.63 ) * 0.5% ]

= 4% + [ 0.51 * 0.5% ]

= 4% + 0.26%

= 4.26%

YTM per anum = YTM per six months * 2

= 4.26% * 2

= 8.52%

YTM is 8.52%

After Tax cost of debt = YTM (1 - Tax Rate)

= 8.52% ( 1 - Tax Rate )

Tax Rate is missed in Problem...

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