Investment specialist and expert in intrinsic valuation using perpetuity and annuity models.
The **Present Value of Perpetuity Calculator** determines the current worth of an asset that promises to pay a fixed stream of cash flows forever. This is a fundamental concept in advanced valuation. Enter any three of the core parameters to solve for the missing one.
Present Value of Perpetuity Calculator
Instructions: Enter values for any three of the four core parameters to solve for the missing one.
Perpetuity Metrics
Perpetuity Present Value Formula
The Present Value of a standard perpetuity (starting in Year 1):
$$PV = \frac{C}{R}$$The Present Value of a deferred perpetuity (starting after Year $t$):
$$PV_{\text{deferred}} = \frac{C}{R} \times \frac{1}{(1+R)^{t-1}}$$ Formula Source: InvestopediaVariables Explained (Q, F, P, V – Parameters)
- $C$ (Cash Flow, $Q$): The fixed, periodic payment received each period.
- $R$ (Discount Rate, $F$): The required rate of return or interest rate (expressed as a decimal).
- $PV$ (Present Value, $P$): The current worth of the infinite future cash flows.
- $t$ (Starting Year, $V$): The year in which the first cash flow is received.
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What is a Perpetuity?
A **perpetuity** is a financial concept that refers to a stream of equal periodic cash flows that is assumed to continue forever. The most common example is a dividend payment from a preferred stock that has no maturity date. In valuation, the perpetuity concept is often used to calculate the terminal value of a company in a Discounted Cash Flow (DCF) model, assuming the company will continue to generate cash flows indefinitely.
The present value of a perpetuity is finite because of the time value of money: cash flows received further in the future are heavily discounted, making their contribution to the present value increasingly negligible. It is only possible to calculate the present value, as the future value of a perpetuity is infinite.
How to Calculate Perpetuity PV (Example)
Assume an investment promises to pay \$1,000 every year forever, and the required discount rate is 5% (0.05).
- Step 1: Identify Cash Flow ($C$) and Rate ($R$)
$C = \$1,000$ and $R = 0.05$.
- Step 2: Apply the Standard Perpetuity Formula
$$PV = \frac{C}{R}$$
- Step 3: Calculate the Result
$$PV = \frac{\$1,000}{0.05} = \mathbf{\$20,000}$$
The Present Value of this Perpetuity is $\mathbf{\$20,000}$.
Frequently Asked Questions (FAQ)
An **annuity** is a stream of equal payments that lasts for a specific, defined number of periods. A **perpetuity** is a stream of equal payments that theoretically lasts forever (an infinite number of periods).
A deferred perpetuity is one where the fixed payments do not begin immediately (at the end of Year 1), but rather start at some point in the future (e.g., Year 5). The formula adjusts the standard $PV$ by discounting it back to the present from the year before the payments start.
Yes. The Present Value changes whenever the Periodic Cash Flow ($C$) changes or, more commonly, whenever the Discount Rate ($R$) changes. Since $PV$ and $R$ are inversely related, if the discount rate goes up, the present value goes down.
The Gordon Growth Model (GGM) for stock valuation is essentially a growing perpetuity model. It assumes dividends grow at a constant rate ($g$) forever, modifying the formula to $P_0 = D_1 / (R – g)$.