Question

Avicorp has a $12.5 million debt issue outstanding, with a 6.1% coupon rate. The debt has semi-annual coupons, the next coupon is due in six months, and the debt matures in five years. It is currently priced at 95% of par value. a. What is Avicorp's pre-tax cost of debt? Note: Compute the effective annual return. b. If Avicorp faces a 40% tax rate, what is its after-tax cost of debt? Note: Assume that the firm will always be able to utilize its full interest tax shield.

Answer 1

Assume Par Value is $ 1000 per bond

COst of Debt is YTM

YTM is the rate at which PV of Cash Inflows are equal to PV of Cash outflows

Period	CF	PVF @3.5%	Disc CF	PVF @4%	Disc CF
0	$ -950.00	1.0000	$ -950.00	1.0000	$ -950.00
1	$      30.50	0.9662	$    29.47	0.9615	$    29.33
2	$      30.50	0.9335	$    28.47	0.9246	$    28.20
3	$      30.50	0.9019	$    27.51	0.8890	$    27.11
4	$      30.50	0.8714	$    26.58	0.8548	$    26.07
5	$      30.50	0.8420	$    25.68	0.8219	$    25.07
6	$      30.50	0.8135	$    24.81	0.7903	$    24.10
7	$      30.50	0.7860	$    23.97	0.7599	$    23.18
8	$      30.50	0.7594	$    23.16	0.7307	$    22.29
9	$      30.50	0.7337	$    22.38	0.7026	$    21.43
10	$      30.50	0.7089	$    21.62	0.6756	$    20.60
10	$ 1,000.00	0.7089	$ 708.92	0.6756	$ 675.56
NPV			$    12.58		$   -27.05

YTM per Six Months = rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 0.5% inc in disc Rate ] * 0.5%

= 3.5% + [ 12.58 / 39.63 ] *0.5%

= 3.5% + [ 0.32 * 0.5% ]

= 3.5% + 0.16%

= 3.66%

YTM per anum = YTM per six months * 12 / 6

= 3.66% * 2

= 7.32%

Part B:

After Tax cost of Debt = Cost of debt * [ 1 - Tax rate ]

= 7.32% * [ 1 - 0.4 ]

= 7.32% * 0.6

= 4.39%