Garcia Company issues 900 15year bonds with a par value of 2

Garcia Company issues 9.00%, 15-year bonds with a par value of $200,000 and semiannual interest payments. On the issue date, the annual market rate for these bonds is 8.00%, which implies a selling price of 108 3/5. Confirm that the bonds’ selling price is approximately correct. Use present value Table B.1 and Table B.3 in Appendix B. (Round all table values to 4 decimal places, and use the rounded table values in calculations. Round your other final answers to nearest whole dollar amount.)

Solution

bond selling price = [present value of annuity factor ]* (semi annual interest payments) + [present value factor * face value of bonds]

here,

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

here,

r= 8% per annum =>4% for six months.

n = number of interest payment periods =>15 year *2 =>30 months.

now,

present value of annuity factor = [1 -(1.04)^(-30)]/0.04

=> 17.2920.

interest payment = $200,000 *9%*1/2 =>$9,000.

present value factor = 1/ (1.04)^(30)

=>0.3083.

face value = $200,000.

now,

bond value = [17.2920 * $9,000] + [200,000*0.3083]

=>155,628 + 61,660

=>217,288.

this value is approximately 108 3/5 => 200,000 * 108.60%............(3/5 =>0.60)

=>$217,200.

so the present value of bond (217,288) is approximately equal to selling price of bond (217,200).