AW of a Permanent Investment

The annual worth equivalent of a very long-lived project is the AW value of its capitalized cost (CC), discussed in Section 4 chapter 4. The AW value of the first cost, P, or present worth, PW, of the alternative uses the same relation as Equation (4-2).

Cash flows that occur at regular intervals are converted to AW values over one life cycle of their occurrence. All other nonregular cash flows are first converted to a P value and then multiplied by i to obtain the AW value over infinity.

If you receive an inheritance of $10,000 today, how long do you have to invest it at 8% per year to be able to withdraw $2000 every year forever? Assume the 8% per year is a return that you can depend on forever.

Cash flow is detailed in Figure (5-4). Solving Equation (5-5) for PW indicates that it is necessary to have $25,000 accumulated at the time that the $2000 annual withdrawals start.

Comment: It is easy to use a spreadsheet to solve this problem. In any cell write the function = NPER(8%,,-10000,25000) to display the answer of 11.91 years. The financial calculator function n(8,0,-10000,25000) displays the same n value.

Figure (5-4): Diagram to determine n for a perpetual withdrawal, Example (5-4).