Jiminy\'s Cricket Farm issued a 30-year, 8 percent semi-annual bond 7 years ago.
ID: 2619649 • Letter: J
Question
Jiminy's Cricket Farm issued a 30-year, 8 percent semi-annual bond 7 years ago. The bond currently sells for 87 percent of its face value. The book value of the debt issue is $25 million. The company's tax rate is 34 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 $77 million and the bonds sell for 74 percent of par.
What is the company's total market value of debt? (Do not round your intermediate calculations.)
What is your best estimate of the aftertax cost of debt? (Do not round your intermediate calculations.)
Jiminy's Cricket Farm issued a 30-year, 8 percent semi-annual bond 7 years ago. The bond currently sells for 87 percent of its face value. The book value of the debt issue is $25 million. The company's tax rate is 34 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 $77 million and the bonds sell for 74 percent of par.
Explanation / Answer
1st Issue of Bond:
Face Value = $25,000,000
Market Value = $25,000,000 * 87%
Market Value = $21,750,000
Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $25,000,000
Semiannual Coupon = $1,000,000
Time to Maturity = 30 years
Semiannual Period to Maturity = 60
Let semiannual YTM be i%
$21,750,000 = $1,000,000 * PVIFA(i%, 60) + $25,000,000 * PVIF(i%, 60)
Using financial calculator:
N = 60
PV = -21750000
PMT = 1000000
FV = 25000000
I = 4.65%
Semiannual YTM = 4.65%
Annual YTM = 2 * 4.65%
Annual YTM = 9.30%
2nd Issue of Bond:
Face Value = $77,000,000
Market Value = $77,000,000 * 74%
Market Value = $56,980,000
Time to Maturity = 7 years
Semiannual Period to Maturity = 14
Let semiannual YTM be i%
$56,980,000 = $77,000,000 * PVIF(i%, 14)
Using financial calculator:
N = 14
PV = -56980000
PMT = 0
FV = 77000000
I = 2.174%
Semiannual YTM = 2.174%
Annual YTM = 2 * 2.174%
Annual YTM = 4.35%
Answer a.
Total Book Value of Debt = Face Value of 1st Issue of Bond + Face Value of 2nd Issue of Bond
Total Book Value of Debt = $25,000,000 + $77,000,000
Total Book Value of Debt = $102,000,000
Answer b.
Total Market Value of Debt = Market Value of 1st Issue of Bond + Market Value of 2nd Issue of Bond
Total Market Value of Debt = $21,750,000 + $56,980,000
Total Market Value of Debt = $78,730,000
Answer c.
Weight of 1st Issue of Bond = Market Value of 1st Issue of Bond / Total Market Value of Debt
Weight of 1st Issue of Bond = $21,750,000 / $78,730,000
Weight of 1st Issue of Bond = 0.2763
Weight of 2nd Issue of Bond = Market Value of 2nd Issue of Bond / Total Market Value of Debt
Weight of 2nd Issue of Bond = $56,980,000 / $78,730,000
Weight of 2nd Issue of Bond = 0.7237
Before-tax Cost of Debt = Weight of 1st Issue of Bond*Annual YTM + Weight of 2nd Issue of Bond*Annual YTM
Before-tax Cost of Debt = 0.2763*9.30% + 0.7237*4.35%
Before-tax Cost of Debt = 5.718%
After-tax Cost of Debt = 5.718% * (1 - 0.34)
After-tax Cost of Debt = 3.79%
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