Jiminy\'s Cricket Farm issued a 15-year, 6 percent semiannual bond 2 years ago.

Question

Jiminy's Cricket Farm issued a 15-year, 6 percent semiannual bond 2 years ago. The bond currently sells for 95 percent of its face value. The company's tax rate is 40 percent. Suppose the book value of the debt issue is $60 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 15 years left to maturity; the book value of this issue is $35 million, and the bonds sell for 51 percent of par. What is the company's total book value of debt? What is the company's total market value of debt? What is your best estimate of the aftertax cost of debt?

Explanation / Answer

(1) Total book value = $(60 + 35) million = $95 million = $95,000,000

(2)

Market value of first debt = $60 million x 95% = $57 million

Market value of second debt = $35 million x 51% = $17.85 million

Total market value = $(57 + 17.85) million = $74.85 million = $74,850,000

(3)

Bond YTM = Pre-tax cost of debt = [C + (F - P) / N] / [(F + P) / 2]

C: Annual coupon = $60 million x 6% = $3.6 million

F: Face value = $60 million

P: Market price = $57 million

N: Years to maturity = 15 - 2 = 13

YTM = [3.6 + (60 - 57) / 13] / [(60 + 57) / 2] = [3.6 + (3/13)] / [117 / 2] = (3.6 + 0.23) / 58.5 = 3.83 / 58.5

= 0.0655 = 6.55%

So, post-tax cost of debt = 6.55% x (1 - 0.4) = 6.55% x 0.6 = 3.93%

Proportion of this debt = $57 million / $74.85 million = 0.7615

For zero coupon bond, if YTM be R, then

$17.85 million x (1 + R)15 = $35 million

(1 + R)15 = 1.9608

1 + R = 1.0459

R = 0.0459 = 4.59%

Since this is a zero-coupon bond, this YTM is tax-free.

Proportion of this debt = 1 - 0.7615 = 0.2385

Therefore

After-tax cost of debt = 0.7615 x 3.93% + 0.2385 x 4.59% = 2.99% + 1.09% = 4.98%

NOTE: This cost of debt is computed using market value method. Answer will differ if book value method is used.

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