Jiminy\'s Cricket Farm issued a 30-year, 7 percent semi-annual bond 6 years ago.

Question

Jiminy's Cricket Farm issued a 30-year, 7 percent semi-annual bond 6 years ago. The bond currently sells for 80 percent of its face value. The book value of the debt issue is $20 million. The company's tax rate is 33 percent, and the bond has a YTM of 9.05%. In addition, the company has a second debt issue on the market, a zero coupon bond with 6 years left to maturity; the book value of this issue is $64 million, the face value (also called par value) is $79 million, and the bonds sell for 80 percent of par. Required: (a) What is the company's total book value of debt? Note: Book value represents the original value of the debt. For coupon bonds, the par value is the book value (coupon bonds are always originally sold at par). For zero-coupon bonds, the book value will be what the bonds are originally sold for plus any accrued interest (so the book value will equal par value only at maturity). In this problem, you are given the book value of the coupon and zero-coupon bonds. (b) What is the company's total market value of debt? (Do not round your intermediate calculations.) Note: Market value is what the bonds are worth today. This market price is often quoted as a percentage of the par value. So if a bond's par is $1,000 and the bond trades at 92% of par, the bond is worth $920. (c) 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

(a) What is the company's total book value of debt?. The book value of the debt issue is $20 million Zero oupon bond book value is $64million So Total BV of Debt = 20+64 = 84 Million (b) What is the company's total market value of debt? The bond currently sells for 80 percent of its face value. The book value of the debt issue is $20 million. So Mkt value = 80%*20m = 16Million For zero coupon, book value is $64 million and the bonds sell for 80 percent of par. So Mkt value = 80%*79m = $63.20 Milion So Mkt Value =16+ $63.20 = $79.20Million (c) What is your best estimate of the aftertax cost of debt (leave as an APR)? Bond Face value = 20M, Bond period = 30-6=24 yrs. Semiannual bond. So nper= 24*2=48 period. Current Bond price = 80%of FV = 16M Coupon = 7%. So PMT = 7%*20M/2 = $700,000 =0.7M So Semiannual Yield = Rate(nper,PMT,PV,FV) =Rate(48,0.7,16,20) = 4.53% So YTM = 2*Semiannual = 2*4.53% = 9.06% Zero Coupon: Bond Face value = 79M, Bond period = 6 yrs. Semiannual bond. So nper= 6*2=12 period. Current Bond price = 80%*79m = $63.20 Milion Coupon = 0%. So PMT = 0 SO Semiannual yield = Rate(nper,PMT,PV,FV) =Rate(12,0,63.2,79) = 1.88% So YTM = 2*Semiannual = 2*1.88% =3.75% So Total Yield = 9.06% *(20/79.20)+3.75%*(63.20/79.20) = 5.28% SO AFter Tax cost of Debt = 5.28%*(1-T) = 5.28%*(1-33%) = 3.54%

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