Final answer:
The value of Flora Co.'s bond is calculated by finding the present value of 38 semiannual payments and the lump sum at maturity using a 14% annual discount rate, divided by two for the semiannual period. For annual payments, the value is based on 19 annual payments discounted at the 14% annual rate. The frequency of payments affects the bond's present value, with more frequent payments and higher discount rates leading to a lower present value.
Step-by-step explanation:
The value of Flora Co.'s bonds can be calculated by determining the present value of its future cash flows, which consist of interest payments and the principal amount at maturity. As the interest is paid semiannually, the bond will make a total of 19 * 2 = 38 payments of $25 each (since 5% of $1,000 is $50, divided by two for semiannual payments). Utilizing the present value of an annuity formula, along with the present value of a lump sum formula for the repayment of the principal at the end of 19 years, we calculate the bond's value when the required rate of return is 14% (7% per semiannual period).
If the interest were paid annually, the calculation changes slightly. Instead of 38 payments, there would be 19 payments of $50 each. Since the payments are less frequent, each payment needs to be discounted back to its present value using the 14% annual required rate of return. The formula for the present value of an annuity is used again, along with the present value of a lump sum for the repayment of the principal.
In both scenarios, the process of calculating the present value of future cash flows basis is similar. What changes between semiannual and annual payments is the frequency and the compounding period for the interest rate. This frequency has an impact on the current value of the bond. A higher discount rate or more frequent compounding (as in the case of semiannual interest payments) generally results in a lower present value.