Question

Jiminy's Cricket Farm issued a 30-year, 6 percent semi-annual bond 7 years ago. The bond currently sells for 93 percent of its face value. The book value of the debt issue is $21 million. The company's tax rate is 33 percent.

In addition, the company has a second debt issue on the market, a zero coupon bond with 7 years left to maturity; the book value of this issue is $82 million and the bonds sell for 76 percent of par.

  

Required:

  

(a)	What is the company's total book value of debt? (Do not round your intermediate calculations.)
	(Click to select)103,000,00081,850,00077,900,000128,100,000127,280,000

  

(b)	What is the company's total market value of debt? (Do not round your intermediate calculations.)
	(Click to select)77,757,500103,000,00085,124,00081,850,00085,942,500

  

(c)	What is your best estimate of the aftertax cost of debt? (Do not round your intermediate calculations.)
	(Click to select)3.58%2.29%3.41%2.92%3.07%

Answer 1

1^st Issue of Bonds:

Face Value = $21,000,000

Market Value = 93% * $21,000,000
Market Value = $19,530,000

Annual Coupon Rate = 6%
Semiannual Coupon Rate = 3%
Semiannual Coupon = 3% * $21,000,000
Semiannual Coupon = $630,000

Time to Maturity = 23 years
Semiannual Period to Maturity = 46

Let semiannual YTM be i%

$19,530,000 = $630,000 * PVIFA(i%, 46) + $21,000,000 * PVIF(i%, 46)

Using financial calculator:
N = 46
PV = -19530000
PMT = 630000
FV = 21000000

I = 3.30%

Semiannual YTM = 3.30%
Annual YTM = 2 * 3.30%
Annual YTM = 6.60%

Before-tax Cost of Debt = 6.60%
After-tax Cost of Debt = 6.60% * (1 - 0.33)
After-tax Cost of Debt = 4.422%

2^nd Issue of Bonds:

Face Value = $82,000,000

Market Value = 76% * $82,000,000
Market Value = $62,320,000

Time to Maturity = 7 years
Semiannual Period to Maturity = 14

Let semiannual YTM be i%

$62,320,000 = $82,000,000 * PVIF(i%, 14)

Using financial calculator:
N = 14
PV = -62320000
PMT = 0
FV = 82000000

I = 1.98%

Semiannual YTM = 1.98%
Annual YTM = 2 * 1.98%
Annual YTM = 3.96%

Before-tax Cost of Debt = 3.96%
After-tax Cost of Debt = 3.96% * (1 - 0.33)
After-tax Cost of Debt = 2.653%

Answer a.

Total Book Value of Debt = $21,000,000 + $82,000,000
Total Book Value of Debt = $103,000,000

Answer b.

Total Market Value of Debt = $19,530,000 + $62,320,000
Total Market Value of Debt = $81,850,000

Answer c.

Weight of 1^st Issue of Debt = $19,530,000/$81,850,000
Weight of 1^st Issue of Debt = 0.2386

Weight of 2^nd Issue of Debt = $62,320,000/$81,850,000
Weight of 2^nd Issue of Debt = 0.7614

Estimated After-tax Cost of Debt = 0.2386 * 4.422% + 0.7614 * 2.653%
Estimated After-tax Cost of Debt = 3.07%