Question

If Wild Widgets, Inc., were an all-equity company, it would have a beta of .90. The company has a target debt-equity ratio of .45. The expected return on the market portfolio is 11 percent and Treasury bills currently yield 2.9 percent. The company has one bond issue outstanding that matures in 20 years, a par value of $1,000, and a coupon rate of 5.9 percent. The bond currently sells for $1,045. The corporate tax rate is 22 percent. a. What is the company’s cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the company’s cost of equity? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c. What is the company’s weighted average cost of capital? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Cost of Equity = Risk free Ret + Beta [ Market ret - Risk free Ret ]

= 2.9% + 0.90 ( 11% - 2.9% )

= 2.9% + 0.9 ( 8.1% )

= 2.9% + 7.29%

= 10.19%

Cost of Debt: it is nothing but YTM of Bond.

Year	CF	PVF @5%	Disc CF	PVF @6%	Disc CF
1	$      59.00	0.9524	$      56.19	0.9434	$      55.66
2	$      59.00	0.9070	$      53.51	0.8900	$      52.51
3	$      59.00	0.8638	$      50.97	0.8396	$      49.54
4	$      59.00	0.8227	$      48.54	0.7921	$      46.73
5	$      59.00	0.7835	$      46.23	0.7473	$      44.09
6	$      59.00	0.7462	$      44.03	0.7050	$      41.59
7	$      59.00	0.7107	$      41.93	0.6651	$      39.24
8	$      59.00	0.6768	$      39.93	0.6274	$      37.02
9	$      59.00	0.6446	$      38.03	0.5919	$      34.92
10	$      59.00	0.6139	$      36.22	0.5584	$      32.95
11	$      59.00	0.5847	$      34.50	0.5268	$      31.08
12	$      59.00	0.5568	$      32.85	0.4970	$      29.32
13	$      59.00	0.5303	$      31.29	0.4688	$      27.66
14	$      59.00	0.5051	$      29.80	0.4423	$      26.10
15	$      59.00	0.4810	$      28.38	0.4173	$      24.62
16	$      59.00	0.4581	$      27.03	0.3936	$      23.23
17	$      59.00	0.4363	$      25.74	0.3714	$      21.91
18	$      59.00	0.4155	$      24.52	0.3503	$      20.67
19	$      59.00	0.3957	$      23.35	0.3305	$      19.50
20	$      59.00	0.3769	$      22.24	0.3118	$      18.40
20	$ 1,000.00	0.3769	$    376.89	0.3118	$    311.80
PV of Cash Inflows	$ 1,112.16		$    988.53
Bind Price	$ 1,045.00		$ 1,045.00
NPV	$      67.16		$     -56.47

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

= 5% + [ 67.16 / 123.63 ] * 1 %

= 5% + [ 0.54 * 1% ]

= 5.54%

After Tax cost of Debt = YTM * ( 1 - Tax rate )

= 5.54% ( 1 -0.22)

= 5.54% * 0.78

= 4.32%

WACC = Weight avg cost of sources in capital structure.

Source	Weight	Cost	Wtd Cost
Debt	0.3103	4.32%	1.34%
Equity	0.6897	10.19%	7.03%
WACC	8.37%

Debt Weight = 0.45 / ( 1 + 0.45 )

= 0.45 / 1.45

= 0.3103

Equity Weight = 1 - Debt Weight

= 1 - 0.3103

= 0.6897