Question

Great Lakes Packing has two bond issues outstanding. The first issue has a coupon rate of 3.42 percent, a par value of $1,000 per bond, matures in 4 years, has a total face value of $3.2 million, and is quoted at 105 percent of face value. The second issue has a coupon rate of 5.62 percent, a par value of $2,000 per bond, matures in 17 years, has a total face value of $7.5 million, and is quoted at 91 percent of face value. Both bonds pay interest semiannually. The company's tax rate is 39 percent. What is the firm's weighted average aftertax cost of debt?

Answer 1

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

MV of Bond1=1000*3200*1.05

=3360000

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

MV of Bond2=2000*3750*0.91

=6825000

Cost of debt

Bond1

K = Nx2

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

k=1

K =4x2

1050 =∑ [(3.42*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^4x2

k=1

YTM1 = 2.1099317081

Bond2

K = Nx2

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

k=1

K =17x2

1820 =∑ [(5.62*2000/200)/(1 + YTM/200)^k]     +   2000/(1 + YTM/200)^17x2

k=1

YTM2 = 6.5

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

Firm cost of debt=2.1099317081*(3360000)/(3360000+6825000)+6.5*(3360000)/(3360000+6825000)

Firm cost of debt=5.05%

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

After tax cost of debt = 5.05*(1-0.39)

= 3.08