Perpetuity
A perpetuity is an infinite series of equal periodic cash flows, valued by dividing the cash flow by the discount rate (PV = C / r). The formula assumes the first payment arrives at the end of period one.
FrameworkTime value of money
See it move
A perpetuity that pays €500 every year forever is valued today at €500 ÷ 0.05 = €10,000. Each future payment is discounted further into the future, so the infinite series still converges to a finite sum. The formula assumes the first payment lands at the end of period one and that the discount rate never changes; preference shares are priced the same way.
The formula
Variables
- Present value of the perpetuity
- Constant cash flow received at the end of each period
- Discount rate per period (expressed as a decimal; must be greater than zero)
Assumes the first payment arrives at the end of period one and the discount rate is constant. Preference shares paying a fixed dividend with no maturity date are priced using this formula.
Check yourself
A charitable endowment promises to pay €4,000 per year forever, with the first payment arriving in exactly one year. The appropriate discount rate is 5% per annum. What is the present value of the endowment today?