Question

Great Lakes Packing has two bond issues outstanding. The first issue has a coupon rate of 3.46 percent, a par value of $1,000 per bond, matures in 6 years, has a total face value of $3.4 million, and is quoted at 107 percent of face value. The second issue has a coupon rate of 5.78 percent, a par value of $2,000 per bond, matures in 19 years, has a total face value of $7.7 million, and is quoted at 93 percent of face value. Both bonds pay interest semiannually. The company's tax rate is 35 percent. What is the firm's weighted average aftertax cost of debt?

a. 4.13%

b. 5.00%

c. 3.03%

d. 2.81%

e. 3.20%

Answer 1

Bond 1:

To calculate the before tax cost of debt, we need to use RATE function in EXCEL

=RATE(nper,pmt,pv,fv,type)

Since, the payments are semi-annual

nper=number of periods=6*2=12

pmt=semi-annual coupon payment=(3.46%*$1000)/2=$17.3

pv=$1000*1.07=$1070

fv=1000

=RATE(12,17.3,-1070,1000,0)=1.1%

RATE=Semi-annual yield=1.1%

Annual yield=before tax cost of debt=2*1.1%=2.21%

After tax cost of debt=2.21%*(1-tax rate)=2.21%*(1-35%)=1.4%

Bond 2:

nper=number of periods=19*2=38

pmt=semi-annual coupon payment=(5.78%*$2000)/2=$57.8

pv=($2000*0.93)=1860

fv=2000

=RATE(38,57.8,-1860,2000,0)=3.21%

RATE=Semi-annual yield=3.21%

Annual yield=before tax cost of debt=2*3.21%=6.4%

After tax cost of debt=6.42%*(1-tax rate)=6.42%*(1-35%)=4.1%

==> Weights of each bonds are as below

Bond1=market value of bond1/total value

Market value of bond1=3,400,000*1.07=$3638000

Market value of bond2=7700000*0.93=$7161000

Weight of bond1=3638000/10799000=33.7%

Weight of bond2=66.3%

Weighted average after tax cost of debt=(33.7%*1.4%)+(66.3%*4.1%)=3.2%

Option e is correct