Question

Great Lakes Packing has two bond issues outstanding. The first issue has a coupon rate of 3.84 percent, a par value of $1,000 per bond, matures in 7 years, has a total face value of $5.3 million, and is quoted at 102 percent of face value. The second issue has a coupon rate of 6.61 percent, a par value of $1,000 per bond, matures in 16 years, has a total face value of $9.6 million, and is quoted at 105 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?

3.06%

2.94%

3.17%

5.21%

4.19%

Answer 1

MV of Bond 1=Par value*bonds outstanding*%age of par

MV of Bond 1=1000*5300*1.02

=5406000

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

MV of Bond2=1000*9600*1.05

=10080000

MV of firm debt = MV of bond 1 + MV of bond 2

=5406000+10080000

=15486000

K = Nx2

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

k=1

K =7x2

1020 =∑ [(3.84*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^7x2

k=1

YTM = 3.5152

Bond2

K = Nx2

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

k=1

K =16x2

=∑ [(6.61*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^16x2

k=1

YTM2 = 6.1157

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

Firm cost of debt=3.5152*(5406000)/(5406000+10080000)+6.1157*(10080000)/(5406000+10080000)

Firm cost of debt=5.2079%

After tax rate = Cost of debt * (1-Tax rate)

After tax rate = 5.2079 * (1-0.39)

After tax rate = 3.17