Jiminy\'s Cricket Farm issued a 30-year, 7.2 percent semiannual bond 5 years ago

Question

Jiminy's Cricket Farm issued a 30-year, 7.2 percent semiannual bond 5 years ago. The bond currently sells for 89.5 percent of its face value. The book value of this debt issue is $99 million. In addition, the company has a second debt issue, a zero coupon bond with 8 years left to maturity; the book value of this issue is $69 million, and it sells for 57 percent of par. The company’s tax rate is 40 percent.

What is the total book value of debt? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).)

What is the total market value of debt? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).)

What is the aftertax cost of debt? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

What is the total book value of debt? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).)

Explanation / Answer

1.The total book value of the 7.2% bond + Book Value of Zero coupon bond = 99 + 69 = $168 Million = 168,000,000

Hence the total book Value of debt is $168,000,000

2.

Market Value of 7.2% bond

We need to calculate the cost of debt which is the YTM (Yield to maturity). YTM = rate(5*2,36,-895,1000)*2 since we need the annual YTM. nper = 5*2, pmt = 0.072*1000/2, pv =895 and fv=100

Hence YTM = 9.9139% and the after tax cost of debt = 9.9139*(1-0.4) = 0.0594834 = 5.95%

Hence market value of this bond issue is 0.072*99000000*((1-1/1.0595^5)/0/0595) + 99000000/1.0595^5

Hence Market Value = 30,066,614.29 + 74,153,284.02 = $104,219,898.30

Market Value of Zero coupn bond:

We also need to calculate the yiled which is Face Value/ Current value)^(1/Years to maturity) - 1

=(69000000/39330000^(1/8)-1 =0.072792 and after tax rate is 0.072792*(1-0.4) = 4.37%

Hence Market Value of debt = Face value/(1+r)^t = 69000000/(1.0437)^8 = $49,005,364.41

Henc total market value of debt =$104,219,898.30 +$49,005,364.41= $153,225,262.70

3. After tax cost of debt

Market weight of 7.2% bond is 104,219,898.30/153225262.70 = 0.68

Market Weight of zero coupon bond 1-0.68 = 0.32

after tax cost of of 7.2% bond is 5.95% and that of zero copon bond is 4.37%

Hence after tax cost of debt will be 0.68*5.95 + 0.32*4.37 = 5.44%

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