Great Lakes Packing has two bond issues outstanding. The first issue has a coupon rate of 3.54 percent, a par value of $1,000 per bond, matures in 4 years, has a total face value of $3.8 million, and is quoted at 103 percent of face value. The second issue has a coupon rate of 6.10 percent, a par value of $2,000 per bond, matures in 23 years, has a total face value of $8.1 million, and is quoted at 95 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

3.20%

Explanation:

The firm's weighted average aftertax cost of debt can be determined by first of all determining the before-tax cost of each debt.

Using a financial calculator, the before-tax costs of debt are ascertained as follows:

Bond 1:

N=8(number of semiannual coupons in 4 years)

PMT=17.70  (semiannual coupon=face value*coupon rate/2=$1,000*3.54%/2=$17.70)

PV=-1030(current price=$1000*103%=$1030)

FV=1000(the face value is $1000)

CPT

I/Y=1.37%(the semannual yield, annual yield=1.37%*2=2.74%)

after-tax cost of first debt=2.74%*(1-39%)=1.67%

Bond 2:

N=46(number of semiannual coupons in 23  years)

PMT=30.50 (semiannual coupon=face value*coupon rate/2=$1,000*6.10%/2=$30.50)

PV=-950(current price=$1000*95%=$950)

FV=1000(the face value is $1000)

CPT

I/Y=3.26%%(the semannual yield, annual yield=3.26%%*2=6.52%)

after-tax cost of second debt=6.52%*(1-39%)=3.98%

market value of first debt=$3.8 million*103%=$3,914,000

market value of second debt=$8.1 million*95%=$7,695,000

total market value of debts=$3,914,000+$7,695,000=$11,609,000

firm's weighted average aftertax cost of debt=(1.67%*$3,914,000/$11,609,000)+(3.98%*$7,695,000/$11,609,000)

firm's weighted average aftertax cost of debt=3.20%

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