Growing perpetuity
A growing perpetuity is a stream of cash flows that increases at a constant rate g each period and never ends, with a present value of C / (r − g), valid only when the discount rate r exceeds the growth rate g.
FrameworkTime value of money
See it move
A business expects €200,000 of free cash flow next year, growing 3% every year forever, discounted at an 8% cost of capital. Its present value is €200,000 divided by (0.08 minus 0.03), or €4,000,000. The formula only works when the discount rate exceeds the growth rate; it is the engine behind the Gordon growth model and most DCF terminal values.
The formula
Variables
- Present value of all future cash flows
- Cash flow received at the end of period one
- Discount rate per period (must exceed g)
- Constant growth rate per period
Valid only when r > g; if g equals or exceeds r the series does not converge to a finite value. This is the engine of the Gordon growth model and the standard terminal value formula in DCF analysis.
Check yourself
A firm is expected to generate £180,000 in free cash flow at the end of the next year, growing at a constant 3% per year indefinitely. The cost of capital is 9%. What is the present value of this cash-flow stream?