Jiminy\'s Cricket Farm issued a 30-year, 7 percent semi-annual bond 9 years ago.

Question

Jiminy's Cricket Farm issued a 30-year, 7 percent semi-annual bond 9 years ago. The bond currently sells for 92 percent of its face value. The book value of the debt issue is $23 million. The company's tax rate is 34 percent, and the bond has a YTM of 7.78%.

In addition, the company has a second debt issue on the market, a zero coupon bond with 9 years left to maturity; the book value of this issue is $69 million, the face value (also called par value) is $84 million, and the bonds sell for 76 percent of par.

1. What is your best estimate of the aftertax cost of debt (leave as an APR)?

a.   3.53%

b.   3.71%

c.   2.8%

d.   2.66%

e.   2.12%

Best answer awarded on correctness and at least some explanation, not on speed.

Explanation / Answer

Hi,

Please find the answer as follows:

Cost of Second Debt:

PMT = 0 (indicates interest payment)

PV = 84*76% = 63.84 (indicates present value)

FV = 84 (indicates FV)

Nper = 9 (indicates the period)

Rate (YTM) = Rate(Nper,PMT,PV,FV) = Rate(9,0,-63.84,84) = 3.10%

After Tax Cost of Debt = Weight of First Bond*YTM of First Bond*(1-Tax Rate) + Weight of Second Bond*YTM of Second Bond*(1-Tax Rate)

After Tax Cost of Debt = 23/(23 + 69)*7.78*(1-.34) + 69/(23 + 69)*3.10*(1-.34) = 2.8%

Answer is 2.8%

Notes:

Weight of First Bond = Current Sales Value of First Bond/(Current Sales Value of First Bond + Current Sales Value of Second Bond)

Weight of Second Bond = Current Sales Value of Second Bond/(Current Sales Value of First Bond + Current Sales Value of Second Bond)

Thanks.

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