The formulas
- Growing annuity PV = P / (r - g) x [1 - ((1 + g) / (1 + r))^n]
- If r = g: PV = P x n / (1 + r)
- Growing perpetuity PV = P / (r - g), needs r > g
- Start-of-year payments: multiply by (1 + r)
How it works
Many payment streams grow: rent with annual escalators, salaries, dividends, royalties. A growing annuity discounts a payment that rises by a fixed percent each year for a set term. A growing perpetuity runs forever and only has a finite value when the discount rate is above the growth rate.
P is the first payment, made one year from today for end-of-year timing. For start-of-year timing the first payment is today. The future value row compounds the present value to the end of the term.
Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
Why does the perpetuity fail when growth equals the rate?
Each payment then has the same present value and the sum never stops growing.
How does this relate to the Gordon growth model?
The Gordon model is a growing perpetuity applied to next year dividend.
Can growth be negative?
Yes. Enter a negative growth rate for a declining stream.
Formulas on this page are the standard definitions.
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