Question

An investment offers $6,125 per year for 15 years, with the first payment occurring one year from now. Assume the required return is 8 percent. a. What is the value of the investment today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What would the value be if the payments occurred for 40 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What would the value be if the payments occurred for 75 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your

Answer 1

The present value of an investment offering $6,125 per year at an 8 percent return is $55,570.20 for 15 years, $79,935.68 for 40 years, $88,513.29 for 75 years, and $76,562.50 for an indefinite number of years. These values are calculated using the present value formulas for annuities and perpetuities.

Step-by-step explanation:

To calculate the present value of an investment that offers $6,125 per year, we need to discount these payments back to their value today at the required return of 8 percent.

1. For 15 years, the present value (PV) is calculated using the formula PV = PMT × ((1 - (1 + r)^{-n}) / r), where PMT is the annual payment, r is the annual discount rate, and n is the number of years. Therefore, the PV is $6,125 × ((1 - (1 + 0.08)^{-15}) / 0.08), which equals $55,570.20.
2. For 40 years, the present value is $6,125 × ((1 - (1 + 0.08)^{-40}) / 0.08), which equals $79,935.68.
3. For 75 years, the present value is $6,125 × ((1 - (1 + 0.08)^{-75}) / 0.08), which equals $88,513.29.
4. To calculate the present value when the payments occur forever, we use the formula for a perpetuity: PV = PMT / r. Thus, the present value is $6,125 / 0.08, which equals $76,562.50.