Question

An investment offers $5,500 per year for 15 years, with the first payment occurring one year from now. If the required return is 6%, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

Answer 1

To calculate the value of the investment, we can use the formula for the present value of an ordinary annuity. For the first scenario, where the payments occur for 15 years, the value of the investment is $57,778.78. For the second scenario, where the payments occur for 40 years, the value is $28,638.99. For the third scenario, where the payments occur for 75 years, the value is $14,899.08. Finally, for the scenario where the payments occur forever, the value is $91,666.67.

Step-by-step explanation:

To calculate the value of the investment, we can use the formula for the present value of an ordinary annuity:

Present Value = Payment / (1 + Required Return)Number of Years

For the first scenario, where the payments occur for 15 years:

Present Value = $5,500 / (1 + 0.06)15 = $57,778.78

For the second scenario, where the payments occur for 40 years:

Present Value = $5,500 / (1 + 0.06)40 = $28,638.99

For the third scenario, where the payments occur for 75 years:

Present Value = $5,500 / (1 + 0.06)75 = $14,899.08

For the final scenario, where the payments occur forever:

The value of the investment can be calculated using the perpetuity formula:

Present Value = Payment / Required Return = $5,500 / 0.06 = $91,666.67