Answer:
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%
