Question

Jiminy’s Cricket Farm issued a bond with 25 years to maturity and a semiannual coupon rate of 4 percent 3 years ago. The bond currently sells for 108 percent of its face value. The company’s tax rate is 22 percent. The book value of the debt issue is $30 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 10 years left to maturity; the book value of this issue is $15 million, and the bonds sell for 73 percent of par.

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

Answer 1

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

MV of Bond1=1000*30000*1.08

=32400000

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

MV of Bond2=1000*15000*0.73

=10950000

Bond1

K = Nx2

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

k=1

K =22x2

1080 =∑ [(4*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^22x2

k=1

YTM1 = 3.4767326656

Bond2

K = N

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

k=1

K =10

730 =∑ [(0*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^10

k=1

YTM2 = 3.2

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

Firm cost of debt=3.4767326656*(32400000)/(32400000+10950000)+3.2*(32400000)/(32400000+10950000)

Firm cost of debt=3.41%

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

After tax cost of debt = 3.41*(1-0.22)

= 2.6598