Question

Shaky Hands Insurance issues $900,000 of 8% bonds with semiannual coupon payments and that mature in 10 years. Compute the bond issue price assuming that the prevailing market rate of interest is 7% per year compounded semiannually.

Answer 1

bond price = [present value of annuity* interest payment] + [present value factor * face value]

here,

present value of annuity = [1- (1+r)^(-n)] / r

here,

r=7% per annum

=> 7%*6/12 =>3.5% for semi annual periods =>0.035.

n = 10 years *2 periods =>20

=>[1-(1.035)^(-0.035)] / 0.035

=>0.54974341/0.035

=>14.2124029.

interest payment

(assume $1000 to be default value of the bond).

=>$1,000*8%*6/12=>$40.

present value factor =1/(1+r)^n

=>1/(1.035)^20

=>0.50256588.

face value = 1,000.

now,

value of the bond = [14.2124029*40]+[0.50256588*1000]

=>568.496116+502.56588

=>$1,071.06.

issue price of each bond =$1,071.06.

(total amount raised from issue = 900,000 *(107.106)%=>963.955.80)