How to Calculate The Present Value of a Perpetuity

Perpetuities have no maturity date.

A perpetuity is a stream of equal payments that continue forever. Some investments, such as preferred stock and some bonds, are in essence perpetuities, and to transfer these assets from investor to investor they must have a present value (PV). There are two present value formulas that apply to perpetuities: the PV of a perpetuity and the PV of a growing perpetuity.

Things You'll Need

• Calculator
• Pen or pencil
• Paper
• Your perpetuity payment rate, interest rate and growth rate

Instructions

PV of a Perpetuity

1. Determine the annual payment of your perpetuity and the interest rate.

2. Plug the appropriate numbers into the following formula:

   PV of a perpetuity = P / i

   In this formula "P" represents your annual payment and "i" represents your interest or discount rate.

3. Calculate the present value of your perpetuity using the given formula.

4. Apply the following example as a point of reference to crosscheck your own calculations. A bond pays the bond holder $50 per year forever at an interest rate of 10 percent. To determine what is the bond worth today, you would apply the following formula:

   PV of the bond = $50 / $0.10

   As a result, the bond is worth $500 today.

5. Examine at your perpetuity's paperwork to ensure that it is not a growing perpetuity. If it is a growing perpetuity, use the growing perpetuity calculation steps instead.

PV of a Growing Perpetuity

1. Determine the annual payment, interest rate and growth rate of your perpetuity.

2. Plug the appropriate numbers into the following formula:

   PV of a growing perpetuity = P / (i - g)

   In this formula "P" represents your annual payment, "i" represents your interest or discount rate and "g" represents the growth rate.

3. Calculate the present value of your growing perpetuity using the given formula.

4. Apply the following example as a point of reference to crosscheck your own calculations. A share of preferred stock in company XYZ pays dividends of $100 per year forever at a fixed interest rate of 5 percent and a growth rate of 1 percent. To determine what a share of company XYZ's preferred stock is worth today, you would apply the following formula, show as a progression of calculations:

   PV of preferred stock in XYZ = $100 / ($0.05 - $0.01)

   PV of preferred stock in XYZ = $100 / .04

   PV of preferred stock in XYZ = $2,500

   As a result, the present value of a share of company XYZ's preferred stock would be $2,500.

Tips & Warnings

• Double check your calculations to ensure accuracy.

• Do not leave bank paperwork that contains your personal information in conspicuous locations.

References

• Net MBA: Perpetuities