Result
Discounted payback period
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This calculation is for informational purposes only and does not replace advice from a qualified professional. Formulas and rates may not fit your exact situation — double-check the figures before making decisions.
How it is calculated
With a constant annual flow, the accumulated present value over t years = flow × (1 − (1 + rate)^−t) ÷ rate. The discounted payback period is the t at which this equals the investment: t = −ln(1 − investment × rate ÷ flow) ÷ ln(1 + rate). At a zero rate the formula reduces to the simple payback period.
The discounted payback is always greater than or equal to the simple (non-discounted) payback at the same positive rate — because cash received later is discounted more heavily and contributes less toward covering the investment. The gap between the two shows how much the time value of money stretches out the real recovery period.
If investment × discount rate exceeds the annual flow, discounted income never adds up to enough to cover the investment even over an infinite horizon — the project doesn't pay back in discounted terms, even if it formally pays back on a simple basis.