Financial economist specializing in advanced corporate finance, valuation, and capital budgeting.
The **Present Value of Growing Annuity Calculator** determines the current worth of a stream of cash flows that increases at a constant growth rate. This is a critical tool for valuing real estate leases, growing dividends, and pension plans. Enter values for exactly four core parameters to solve for the missing one.
Present Value of Growing Annuity Calculator
Instructions: Enter values for exactly four core parameters to solve for the missing one.
Annuity Parameters
Present Value of Growing Annuity Formula
General Case (when $\mathbf{R} \ne \mathbf{G}$):
$$PV = PMT_1 \times \left[ \frac{1 – \left(\frac{1+G}{1+R}\right)^N}{R – G} \right]$$Special Case (when $\mathbf{R} = \mathbf{G}$):
$$PV = PMT_1 \times \frac{N}{1+R}$$ Formula Source: InvestopediaVariables Explained ($\mathbf{PMT_1}, \mathbf{PV}, \mathbf{R}, \mathbf{N}, \mathbf{G}$)
- $\mathbf{PMT_1}$ ($Q$): The amount of the first periodic payment (e.g., received at end of year 1).
- $\mathbf{PV}$ ($F$): The Present Value, or the total current worth of all future increasing payments.
- $\mathbf{R}$ (Discount Rate, $P$): The annual rate used to discount future cash flows back to the present (as a decimal).
- $\mathbf{G}$ (Growth Rate): The annual rate at which the periodic payment ($\mathbf{PMT}$) increases (as a decimal).
- $\mathbf{N}$ (Number of Years, $V$): The total number of years (periods) over which payments are received.
Related Valuation Calculators
Analyze the current worth of future income streams:
- Present Value of Ordinary Annuity Calculator
- Present Value of Growing Perpetuity Calculator
- Discount Rate Calculator
- Net Present Value Calculator
What is Present Value of a Growing Annuity?
The **Present Value of a Growing Annuity** is the amount of money that a sequence of cash flows, which are expected to grow at a constant rate, is worth today. This calculation is superior to the standard present value model when dealing with income streams that are likely to increase, such as rental income from property, salary, or dividend payments from a mature company. It discounts both the passage of time (via $R$) and the increasing size of the payments (via $G$).
For financial analysts, this tool is vital in valuing businesses or investment opportunities where cash flows are not static. It answers the question: “Given my required rate of return and the expected increase in income, how much should I pay for this stream of income today?”
How to Calculate Present Value of a Growing Annuity (Example)
An investment pays \$2,000 next year ($\mathbf{PMT_1}$), growing by 4% ($\mathbf{G}$) annually for 5 years ($\mathbf{N}$). The discount rate ($\mathbf{R}$) is 10%.
- Step 1: Calculate the Compounding Factor Base
$$\frac{1+G}{1+R} = \frac{1.04}{1.10} \approx \mathbf{0.94545}$$
- Step 2: Calculate the Annuity Factor Term
$$\text{Term} = \left(\frac{1+G}{1+R}\right)^N = (0.94545)^5 \approx \mathbf{0.758838}$$
- Step 3: Calculate the Annuity Factor
$$\text{Factor} = \frac{1 – \text{Term}}{R – G} = \frac{1 – 0.758838}{0.10 – 0.04} \approx \frac{0.241162}{0.06} \approx \mathbf{4.01937}$$
- Step 4: Calculate the Present Value
$$\mathbf{PV} = \mathbf{PMT_1} \times \text{Factor} = \$2,000 \times 4.01937 \approx \mathbf{\$8,038.74}$$
The Present Value of the growing annuity is $\mathbf{\$8,038.74}$.
Frequently Asked Questions (FAQ)
Use it whenever the income stream you are valuing is expected to increase over the period. Common applications include: valuing commercial real estate leases with fixed annual escalators, valuing businesses with predictable cash flow growth, or calculating the present cost of future rising liabilities.
If $R < G$, the formula will yield an infinitely large or negative present value, suggesting that the cash flows are growing faster than the cost of capital. This scenario is mathematically unstable and typically signals an unrealistic growth rate assumption for the long term.
This standard formula assumes payments occur at the end of each period (ordinary annuity). For payments at the start of the period (annuity due), an extra multiplicative factor of $(1+R)$ is needed.
Yes. If $\mathbf{PV}$ is known (e.g., the price paid for an asset), the calculator can use iterative methods to solve for the constant growth rate ($G$) implied by the other variables.