Growing Perpetuity Formula
What Is the Growing Perpetuity Formula?
The growing perpetuity formula is used to calculate the present value of a cash flow stream that grows at a constant rate forever (Peter Moles et al., 2014). It is a fundamental tool in finance, often referred to as the Gordon model when applied to unlevered companies (Mario Massari et al., 2016). This model simplifies complex valuation problems by assuming a steady-state growth scenario, making it particularly useful for businesses expected to grow in line with the broader economy over the long term (Mario Massari et al., 2016).
Core Mechanism and Calculation
The formula is expressed as PV = CF1 / (i - g), where CF1 is the cash flow occurring at the end of the first period, i is the discount rate, and g is the constant growth rate (Robert Parrino et al., 2021). A common mistake in application is using the current period's cash flow (CF0) instead of the next period's (CF1) (Peter Moles et al., 2014). To find CF1, the current cash flow must be multiplied by (1 + g) (Peter Moles et al., 2014).
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Applications and Significance in Valuation
The growing perpetuity formula is widely used in the valuation of common stock and entire companies (Robert Parrino et al., 2021). It serves as a cornerstone for discounted cash flow (DCF) methods, providing a simplified way to analyze long-term business value (Pablo Fernandez et al., 2002). Mathematically, it is derived from the growing annuity formula by setting the number of periods to infinity, provided that the discount rate remains greater than the growth rate to ensure a valid result (Robert Parrino et al., 2021).
