Question

Seven Sons Farm issued a 30-year, 7 percent semi-annual bond 5 years ago. The bond currently sells for 92 percent of its face value. The book value of the debt issue is $21 million. Seven Sons' tax rate is 33 percent.

In addition, the company has a second debt issue on the market, a zero coupon bond with 5 years left to maturity; the book value of this issue is $81 million and the bonds sell for 74 percent of par.

  

Required:

  

(a)	What is the company's total book value of debt? (Do not round your intermediate calculations.)
	(Click to select)76,950,000126,240,00079,260,000102,000,000127,050,000

  

(b)	What is the company's total market value of debt? (Do not round your intermediate calculations.)
	(Click to select)79,260,00075,297,00082,430,400102,000,00083,223,000

  

(c)	What is your best estimate of the aftertax cost of debt? (Do not round your intermediate calculations.)

Answer 1

1^st Issue of Bonds:

Face Value = $21,000,000

Market Value = 92% * $21,000,000
Market Value = $19,320,000

Annual Coupon Rate = 7%
Semiannual Coupon Rate = 3.5%
Semiannual Coupon = 3.5% * $21,000,000
Semiannual Coupon = $735,000

Time to Maturity = 25 years
Semiannual Period to Maturity = 50

Let semiannual YTM be i%

$19,320,000 = $735,000 * PVIFA(i%, 50) + $21,000,000 * PVIF(i%, 50)

Using financial calculator:
N = 50
PV = -19320000
PMT = 735000
FV = 21000000

I = 3.864%

Semiannual YTM = 3.864%
Annual YTM = 2 * 3.864%
Annual YTM = 7.728%

Before-tax Cost of Debt = 7.728%
After-tax Cost of Debt = 7.728% * (1 - 0.33)
After-tax Cost of Debt = 5.178%

2^nd Issue of Bonds:

Face Value = $81,000,000

Market Value = 74% * $81,000,000
Market Value = $59,940,000

Time to Maturity = 5 years
Semiannual Period to Maturity = 10

Let semiannual YTM be i%

$59,940,000 = $81,000,000 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -59940000
PMT = 0
FV = 81000000

I = 3.057%

Semiannual YTM = 3.057%
Annual YTM = 2 * 3.057%
Annual YTM = 6.114%

Before-tax Cost of Debt = 6.114%
After-tax Cost of Debt = 6.114% * (1 - 0.33)
After-tax Cost of Debt = 4.096%

Answer a.

Total Book Value of Debt = $21,000,000 + $81,000,000
Total Book Value of Debt = $102,000,000

Answer b.

Total Market Value of Debt = $19,320,000 + $59,940,000
Total Market Value of Debt = $79,260,000

Answer c.

Weight of 1^st Issue of Debt = $19,320,000/$79,260,000
Weight of 1^st Issue of Debt = 0.2438

Weight of 2^nd Issue of Debt = $59,940,000/$79,260,000
Weight of 2^nd Issue of Debt = 0.7562

Estimated After-tax Cost of Debt = 0.2438 * 5.178% + 0.7562 * 4.096%
Estimated After-tax Cost of Debt = 4.36%