Jiminy\'s Cricket Farm issued a 30-year, 7.4 percent semiannual bond 8 years ago
ID: 2754776 • Letter: J
Question
Jiminy's Cricket Farm issued a 30-year, 7.4 percent semiannual bond 8 years ago. The bond currently sells for 91 percent of its face value. The book value of this debt issue is $96 million. In addition, the company has a second debt issue, a zero coupon bond with 11 years left to maturity; the book value of this issue is $66 million, and it sells for 55.5 percent of par. The company’s tax rate is 34 percent What is the total book value of debt? What is the total market value of debt? What is the aftertax cost of debt?
Explanation / Answer
(a)
Total book value = $96 million + $66 million = $162 million
(b)
Total market value = $96 million x 0.91 + $66 million x 0.555 = $(87.36 + 36.63) million = $123.99 million
(c)
(i) 7.4% bond
Pre-tax cost of debt = Bond YTM = [C + (F - P) / n] / [(F + P) / 2]
C: Annual coupon payment = $96 million x 7.4 = $7.104 million
F: Face value = $96 million
P: Market price = $96 million x 0.91 = 87.36 million
n: Years left till maturity = 30 - 8 = 22
YTM = [7.104 + (96 - 87.36) / 22] / [(96 + 87.36) / 2]
= [7.104 + 0.393] / 91.68
= 7.497 / 91.68 = 0.0818
Post-tax cost of debt = 0.0818 x 0.66 = 0.054 Or, 5.4%
(ii) Zero coupon bond
Price = Maturity value / (1 + YTM)n
$36.63 million [See part (a)] = $66 million / (1 + YTM)11
(1 + YTM)11 = 66 / 36.63 = 1.8018
Taking 11th square root at both sides:
1 + YTM = 1.055
YTM = 1.055 - 1 = 0.055
Post-tax cost of zero-coupon bond = 0.055 x 0.66 = 0.0363, or 3.63%
(iii)
Proportion of coupon debt = 96 / (96 + 66) = 59.26%
Proportion of zero coupon debt = (100 - 59.26)% = 40.74%
Weighted average cost of debt (Weighed by book value)
= 59.26% x 5.4% + 40.74% x 3.63%
= 3.2% + 1.48%
= 4.68%
NOTE: Cost of debt can be computed using other methods also (Book value & Market value of debt method). If non-YTM measures are used, cost of debt value can be a little different than answer above.
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