Suspect Corp. issued a bond with a maturity of 30 years and a
semiannual coupon rate of 6 percent 3 years ago. The bond currently
sells for 92 percent of its face value. The book value of the debt
issue is $50 million. In addition, the company has a second debt
issue on the market, a zero coupon bond with 12 years left to
maturity; the book value of this issue is $50 million and the bonds
sell for 54 percent of par. The company’s tax rate is 40
percent.
What is the company’s total book value of debt? (Do not
round intermediate calculations. Enter your answer in dollars, not
millions of dollars, e.g., 1,234,567.)
Total book value
$
What is the company’s total market value of debt? (Do not
round intermediate calculations. Enter your answer in dollars, not
millions of dollars, e.g., 1,234,567.)
Total market value
$
What is your best estimate of the aftertax cost of debt?
(Do not round intermediate calculations. Enter your answer
as a percent rounded to 2 decimal places, e.g.,
32.16.)
Cost of debt
%
Answer:
1st Issue of Bonds:
Face Value = $50,000,000
Market Value = 92% * $50,000,000
Market Value = $46,000,000
Annual Coupon Rate = 6%
Semiannual Coupon Rate = 3%
Semiannual Coupon = 3% * $50,000,000
Semiannual Coupon = $1,500,000
Time to Maturity = 27 years
Semiannual Period to Maturity = 54
Let semiannual YTM be i%
$46,000,000 = $1,500,000 * PVIFA(i%, 54) + $50,000,000 * PVIF(i%, 54)
Using financial calculator:
N = 54
PV = -46,000,000
PMT = 1,500,000
FV = 50,000,000
I = 3.321%
Semiannual YTM = 3.321%
Annual YTM = 2 * 3.321%
Annual YTM = 6.642%
Before-tax Cost of Debt = 6.642%
After-tax Cost of Debt = 6.642% * (1 - 0.40)
After-tax Cost of Debt = 3.985%
2nd Issue of Bonds:
Face Value = $50,000,000
Market Value = 54% * $50,000,000
Market Value = $27,000,000
Time to Maturity = 12 years
Semiannual Period to Maturity = 24
Let semiannual YTM be i%
$27,000,000 = $50,000,000 * PVIF(i%, 24)
Using financial calculator:
N = 24
PV = -27000000
PMT = 0
FV = 50000000
I = 2.601%
Semiannual YTM = 2.601%
Annual YTM = 2 * 2.601%
Annual YTM = 5.202%
Before-tax Cost of Debt = 5.202%
After-tax Cost of Debt = 5.202% * (1 - 0.31)
After-tax Cost of Debt = 3.121%
Answer a.
Total Book Value of Debt = $50,000,000 + $50,000,000
Total Book Value of Debt = $100,000,000
Answer b.
Total Market Value of Debt = $46,000,000 + $27,000,000
Total Market Value of Debt = $73,000,000
Answer c.
Weight of 1st Issue of Debt = $46,000,000 /
$73,000,000
Weight of 1st Issue of Debt = 0.6301
Weight of 2nd Issue of Debt = $27,000,000 /
$73,000,000
Weight of 2nd Issue of Debt = 0.3699
Estimated After-tax Cost of Debt = 0.6301 * 3.985% + 0.3699 *
3.121%
Estimated After-tax Cost of Debt = 3.67%
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