Final answer:
The value of Flora Co.'s bond that pays semiannual interest is calculated by discounting the semiannual interest payments and the face value at maturity using the required rate of return. If interest were paid annually instead, the calculation would involve a single annual discount rate with fewer compounding periods, which would result in a lower bond value.
Step-by-step explanation:
When calculating the value of Flora Co.'s bond that pays semiannual interest, we need to first determine the individual payments and then discount them to their present value using the required rate of return. Let's break it down step-by-step:
- The bond pays 5 percent interest annually on a $1,000 face value, so the semiannual interest payment is 2.5 percent, or $25.
- Since the bond matures in 19 years and interest is paid semiannually, there will be 38 payments.
- Using the formula for the present value of an annuity and the present value of a single sum for the maturity amount, we can calculate the bond's current value for a required return of 14 percent, which is also semiannual (7 percent per period).
If the interest were paid annually, the process would be similar, but we would use a single annual discount rate of 14 percent and 19 periods to calculate the present value.
Calculations:
- Semiannual interest payments (PV of annuity): PV = $25 * [1 - (1 + 0.07)^-38] / 0.07
- Face value payment at maturity (PV of single sum): PV = $1,000 / (1 + 0.07)^38
- Add both present values to find the bond's value.
The value of the bond would be lower if the interest were paid annually because interest would be compounded less frequently.