Question

Bill Mitselfik has purchased a bond that was issued by Acme Chemical. This bond has a face value of $1,000 and pays a dividend of 10% per​ year, compounded​ semi-annually. Bill bought the bond fiveyears ago at face value and there are six years remaining until the bond matures. Bill wishes to sell it now for a price that will result in Bill earning an annual yield of 12% compounded​ semi-annually. What price does Bill need to sell the bond for to earn his desired​ return?

The selling price of the bond should be ​$________. (Round to the nearest​ dollar.)

Answer 1

Purchase price of bond=P=$1000

Coupon payment=C=1000*10%/2=$50 per semi annual

Number of periods for which dividend earned=n=5*2=10 semi annual

Rate of return=i=12%/2=6% per semi annual

Let the selling price be F

So, Purchase price should be equal to PV of all cash inflows had during holding period

P=C*(P/A,6%,10)+F*(P/F,6%,10)

(P/F,6%,10)=1/(1+6%)^10=0.558395

1000=50*7.360087+F*0.558395

F=(1000-50*7.360087)/0.558395=$1131.81

Selling price should be $1131.81 or say $1132