Jiminy\'s Cricket Farm issued a 30-year, 8 percent semi-annual bond 8 years ago.

Question

Jiminy's Cricket Farm issued a 30-year, 8 percent semi-annual bond 8 years ago. The bond currently sells for 80 percent of its face value. The book value of the debt issue is $23 million. The company's tax rate is 32 percent, and the bond has a YTM of 10.31%.

In addition, the company has a second debt issue on the market, a zero coupon bond with 8 years left to maturity; the book value of this issue is $66 million, the face value (also called par value) is $81 million, and the bonds sell for 75 percent of par.

Required: What is your best estimate of the aftertax cost of debt (leave as an APR)? (Do not round your intermediate calculations.)

Note: This is going to be a yield, not a dollar amount. It is the weighted average YTM adjusted for taxes. You can get the YTM for the zero coupon bond using the present value equation for a single cash flow: PV = FV(1+r)-T. Since the YTM for the coupon bond is an APR, you should calculate the YTM for the zero as an APR with semi-annual compounding so that both bond yields are on the same compounding frequency:
zero-coupon price = CF(1+YTM/2)-2T.

Explanation / Answer

YTM = Interest(I) + Market value - face value/life

                   Market value+Face value/2

10.31% = I+80-100/8 /80+100/2

   I (before tax)= 9.28+2.5 = 11.78%

Interest after tax = 11.78(1-0.32) = 8.01%

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