Perpetuity investments are designed to produce a stream of regular payments that continue forever -- a theoretically infinite amount of money. People set up perpetuities to guarantee a source of income for their families over the generations, as well as to ensure that there will be money to meet certain expenses indefinitely, such as property or gravesite maintenance. To calculate a perpetuity, you need three pieces of information. First is how often you want the perpetuity to pay out. Second is how much you want each payment to be. Third is the average annual rate of return you believe the money invested in the perpetuity will earn. Plugging these figures into a formula gives you the "present value" of the perpetuity -- how much you need to have invested right now, at your assumed rate of return, to guarantee the payments. As it turns out, an infinite amount of money has a very finite value.
Convert your assumed average annual rate of return to a decimal by dividing by 100. For example, if you believe that your perpetuity investments will earn an average of 6 percent a year, the decimal equivalent is 6/100, or 0.06.
Divide your assumed average annual rate of return by the number of payments you want per year. For example, for monthly payments, divide by 12. With a 6 percent return, the calculation would be: 0.06 / 12 = 0.005. This is your periodic rate.
Divide your desired payment amount by the periodic rate. Say you want a perpetuity payment of $1,000 a month. Divide $1,000 by 0.005. The result is $200,000. This is the present value of the perpetuity. You would need $200,000 invested at a 6 percent annual return to guarantee an unending stream of $1,000 monthly payments.
- Written out, the formula for the present value of a perpetuity looks like this: PV = P/i. "PV" is the present value, "P" is the dollar amount you want each payment to be, and "i" is the periodic rate -- the annual rate divided by the number of payments per year.
- When setting up a perpetuity with a financial planner, make sure to take into account any management fees or commissions that must be paid. If maintaining the perpetuity will cost, say, 1 percent of the balance each year, then you must raise your assumed rate of return by 1 percent a year.
- The payments can only be guaranteed if the investments in the perpetuity, on average, meet or exceed the assumed rate of return. If they fall short, the perpetuity will run out of money and the payments will end.
- Wake Forest University: Present Value of a Perpetuity
- Financial Accounting for MBAs, Fourth Edition; Peter Easton, et al; 2010