Question

Jiminy’s Cricket Farm issued a bond with 30 years to maturity and a semiannual coupon rate of 7 percent 5 years ago. The bond currently sells for 95 percent of its face value. The company’s tax rate is 24 percent. The book value of the debt issue is $55 million. 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 $40 million, and the bonds sell for 64 percent of par.

a.	What is the company’s total book value of debt?

b.	What is the company’s total market value of debt?

c.	What is your best estimate of the aftertax cost of debt?

Answer 1

a. BV of company debt = BV of debt 1 + BV of debt 2 = 55+40 = 95m

B

MV of Bond1=Par value*bonds outstanding*%age of par

MV of Bond1=1000*55000*0.95

=52250000

MV of Bond2=Par value*bonds outstanding*%age of par

MV of Bond2=1000*40000*0.64

=25600000

MV of DEBT= MV of Bond1+ MV of Bond 2

=52250000+25600000

=77850000

c

Cost of debt

Bond1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =25x2

950 =∑ [(7*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^25x2

k=1

YTM1 = 7.443532608

Bond2

K = N

Bond Price   =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =9

640 =∑ [(0*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^9

k=1

YTM2 = 5.08

Firm cost of debt=YTM1*(MV bond1)/(MV bond1+MV bond2)+YTM2*(MV bond2)/(MV bond1+MV bond2)

Firm cost of debt=7.443532608*(52250000)/(52250000+25600000)+5.08*(52250000)/(52250000+25600000)

Firm cost of debt=6.67%

After tax cost of debt = cost of debt*(1-tax rate)

After tax cost of debt = 6.67*(1-0.24)

= 5.0692