The issuance price of bonds is determined by the present value of future cash flows, which include both the periodic interest payments and the repayment of the principal at maturity. In this case, Williams Company plans to issue bonds with a face value of $606,000, a coupon rate of 8 percent, and a maturity period of 10 years with semiannual interest payments.
The annual market rate of interest is 8 percent, but since interest is paid semiannually, the semiannual market rate is 4 percent (8 percent divided by 2). The periodic interest payment can be calculated as the face value multiplied by half of the annual coupon rate, resulting in an annual interest payment of $48,480 ($606,000 * 0.08 * 0.5).
To determine the issuance price, the present value of both the semiannual interest payments and the face value at maturity needs to be calculated using the semiannual market rate. This involves discounting each future cash flow back to its present value. The formula for present value is given by PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of periods.
Once the present values of all cash flows are determined, they are added to find the total present value, which represents the issuance price of the bonds. In this case, with a face value of $606,000, semiannual interest payments, and a semiannual market rate of 4 percent, the issuance price of the bonds can be calculated using these principles.