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.)
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).
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