Jiminy\'s Cricket Farm issued a 30-year, 7.4 percent semiannual bond 8 years ago

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. Required 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).) Total book value of debt $ 162000000 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).) Total market value $ 123990000 What is the aftertax cost of the 7.4 percent coupon bond? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Aftertax cost of debt % What is the aftertax cost of the zero coupon bond? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Aftertax cost of debt % 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).) Aftertax cost of debt %

Whats in bold is what I need i got the wrong answers.

Explanation / Answer

1) 30-year, 7.4 percent semiannual bond issued 8 years ago. The bond currently sells for 91 percent of its face value. The book value of this debt issue is $96 million.

after tax cost of 7.4% coupon bond can be found out by solving the following equation by trial and error.

91 = 100*pvif(i,44) + 3.7*(1-0.34)*pvifa(i,44)

The after tax cost of debt is that discount rate which equals the PV of the incremental cash inflows to the current price of the bond. It is the IRR of the cash flows associated with the bond.

The i which equates the values can be found out by trial and error. The value of i is the half yearly rate.

Starting with 3%

PV = 100*0.2724 + 2.442*24..2543 = 27.24 + 59.23 = 86.47

discounting with 2%

PV = 100*0.4184 + 2.442*29.0800 = 41.84 + 71.01 = 112.85

The exact value of i will lie between 2% and 3%, which can be interpolated as follows:

i = 2 + (112.85-91)/(112.85-86.47) = 2 + 21.85/26.38 = 2.8283%

Annualised rate = 2.8283*2=5.66%

So after tax cost of the bond = 5.66%.

2) 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 before tax cost of this bond is given by solving for i from the following equation:

100 = 55.5*(1+i)^22

i = [(1.8182)^1/22] - 1 = 0.027547 = 2.7547%

After tax cost of the bond = 2.7547*0.66 = 1.82%.

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