What is Perpetuity?
A perpetuity is an investment asset that provides a stream of cash flows with no end date. Unlike other financial instruments that have a finite duration, perpetuities continue indefinitely.
Key Takeaways:
- A perpetuity is an investment paying unending streams of identical amounts.
- Present value of perpetuity is calculated by dividing regular cash flows by the discount rate.
- Growing perpetuities increase cash flows for each period.
- Although rare today, perpetuities remain essential in financial theories.
Understanding Perpetuities
In simple terms, an annuity is a sequence of cash flows. Perpetuities take this one step further by having no termination date for the cash flows.
Historical Example of Perpetuity
The British consoles issued by the Bank of England are a historical example. These bonds paid annual interest forever. Though discontinued in 2015, for over 250 years they represented endless cash flows.
The Finite Value of Infinite Cash Flow
It might seem counterintuitive, but an infinite series of cash flows can have finite present value because subsequent payments are worth less due to the time value of money.
To find this value, the perpetuity formula plays a key role in financial models, especially when calculating a company’s terminal value.
Perpetuity Present Value Formula
The formula for computing the present value (PV) of a perpetuity is:[ PV = \frac{C}{r} ]
Where:
- PV = present value
- C = cash flow
- r = discount rate
For evaluating a company’s future terminal value, a variation of this formula is used.
Example of Perpetuity in Valuation
Imagine a company forecasts $100,000 cash flow in year 10, 8% cost of capital, and growth rate at 3%. The perpetuity value is: [ PV = \frac{CF_{year 10} imes (1 + g)}{r - g} \lambda = \frac{100000 imes 1.03}{0.08 - 0.03} = \frac{103,000}{0.05} \proportion-up = 2.06 million ] Thus, a $100,000 perpetuity, growing at 3%, is worth $2.06 million in 10 years.
Growing Perpetuities
Over time, inflation reduces the present value of fixed payments. Growing perpetuities increase with each period’s assumed consistent growth rate. Hence, the PV of a growing perpetuity is higher than a non-growing one. The formula:[ PV = \frac{C}{r-g} ]
How Perpetuity Works in Investing
Perpetuities, like certain government bonds or preferred stocks, offer indefinite cash flows without preset maturity dates.
Perpetuity vs. Annuity
While both provide fixed cash flows, annuities have specific end dates, whereas perpetuities do not. Both can be valued using the discounted cash flow (DCF) analysis method.
Perpetuities in Summary
Perpetuities are financial instruments offering endless cash flows, fundamental for many financial theories despite their rarity in modern products. Financial analysts frequently employ perpetuity valuation techniques to determine long-term asset value.
Related Terms: annuity, discounted cash flow, dividend discount model, present value.
References
- Federal Reserve Bank of St. Louis. “Consols: The Never-Ending Bonds”.
