A company issued 8%, 15-year bonds with a face amount of $100 million. The market yield for bonds of similar risk and maturity is 6%. Interest is paid semiannually. At what price did the bonds sell

$119.60 million

Explanation:

The bond price formula provided below is very useful in determining the amount of money received from the bond investors when the bond were issued:

Bond price=face value/(1+r)^n+semiannual coupon*(1-(1+r)^-n/r

face value=$100 million

r=semiannual yield=6%*6/12=3%

n=number of semiannual coupon payments in 15 years=15*2=30

semiannual coupon=face value*coupon rate*6/12=$100million*8%*6/12=$4 million

bond price=$100/(1+3%)^30+$4*(1-(1+3%)^-30/3%

bond price=$100/(1.03)^30+$4*(1-(1.03)^-30/0.03

bond price=$100/2.42726247+$4*(1-0.41198676)/0.03

bond price=$100/2.42726247+$4*0.58801324/0.03

bond price=$41.20+$ 78.40=$119.60 million

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