Question

How do you calculate the average cost of capital (by hand) for the following bond issue?

$3,000,000 bond

30-year maturity

Sold at 95% of face value

11% coupon rate

2% of face value would be charged as an underwriting commission

Answer 1

Average Cost of Capital =(C+((FV-PV)/t))/((FV+PV)/2)

C=Annual Coupon Payment =11%*$3 million=$330,000

FV=Maturity Payment =$3,000,000

PV=Present Value of amount received at issuance =($3,000,000*95%)-(2%*$3,000,000)=$2,850,000-$60,000=$2,790,000

t= time period in years =30

(C+((FV-PV)/t))=330,000+((3,000,000-2,790,000)/30)=$330,000+$7,000=$337,000

((FV+PV)/2)=(3,000,000+2,790,000)/2=$2,895,000

Average Cost of Capital=$337,000/$2,895,000=0.12

Average Cost of Capital=12%