Question

Jiminy’s Cricket Farm issued a bond with 15 years to maturity and a semiannual coupon rate of 4 percent 2 years ago. The bond currently sells for 91 percent of its face value. The company’s tax rate is 21 percent. The book value of the debt issue is $30 million. 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 $20 million, and the bonds sell for 73 percent of par.

a.	What is the company’s total book value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.)
b.	What is the company’s total market value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.)
c.	What is your best estimate of the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer of Part a:
Total Book Value of Debt = $30,000,000 + $20,000,000
Total Book Value of Debt = $50,000,000

Answer of Part b:
Market Value of Debt 1 = $30,000,000 * 91%
Market Value of Debt 1 = $27,300,000

Market Value of Debt 2 = $20,000,000 * 73%
Market Value of Debt 2 = $14,600,000

Total Market Value of Debt = $27,300,000 + $14,600,000
Total Market Value of Debt = $41,900,000

Answer of Part c:
Debt 1:
Face Value = $30,000,0000
Current Price = 91% * $30,000,000 = $27,300,000

Annual Coupon Rate = 4%
Semiannual Coupon Rate = 2%
Semiannual Coupon = 2% * $30,000,000 = $600,000

Time to Maturity = 13 years
Semiannual Period to Maturity = 26

Let semiannual YTM be i%

$27,300,000 = $600,000 * PVIFA(i%, 26) + $30,000,000 * PVIF(i%, 26)

Using financial calculator:
N = 26
PV = -27300000
PMT = 600000
FV = 30000000

I = 2.47%

Semiannual YTM = 2.47%
Annual YTM = 2 * 2.47%
Annual YTM = 4.94%

Before-tax Cost of Debt = 4.94%
After-tax Cost of Debt = 4.94% * (1 - 0.21)
After-tax Cost of Debt = 3.90%

Debt 2:
Face Value = $20,000,0000
Current Price = 73% * $20,000,000 = $14,600,000

Time to Maturity = 7 years
Semiannual Period = 14

Let Semiannual YTM be i%

$14,600,000 = $20,000,000 * PVIF(i%, 14)

Using financial calculator:
N = 14
PV = -14600000
PMT = 0
FV = 20000000

I = 2.27%

Semiannual YTM = 2.27%
Annual YTM = 2 * 2.27%
Annual YTM = 4.54%

Before-tax Cost of Debt = 4.54%
After-tax Cost of Debt = 4.54% * (1 - 0.21)
After-tax Cost of Debt = 3.59%

Market Value of Debt 1 = $30,000,000 * 91%
Market Value of Debt 1 = $27,300,000

Market Value of Debt 2 = $20,000,000 * 73%
Market Value of Debt 2 = $14,600,000

Total Market Value of Debt = $27,300,000 + $14,600,000
Total Market Value of Debt = $41,900,000

Weight of 1st Issue of Debt = $27,300,000/$41,900,000
Weight of 1st Issue of Debt = 0.6516

Weight of 2nd Issue of Debt = $14,600,000/$41,900,000
Weight of 2nd Issue of Debt = 0.3484

Estimated After-tax Cost of Debt = 0.6516 * 3.90% + 0.3484 * 3.59%
Estimated After-tax Cost of Debt = 3.79%