Documented engineering arithmetic
Constant Annual Cash-Flow Calculator
A transparent present-value model for a proposed predictive-maintenance programme or another investment. It calculates only from your documented incremental assumptions; it does not predict or prove savings.
Model results
Model and timing
For years t = 1 … N, the model places the constant annual gross benefit B and recurring incremental cost C at each year-end. Initial investment C₀ occurs at time 0. Residual value R occurs at the end of year N. With d = r/100:
PV(outlays) = C₀ + PV(C)
NPV = PV(B) + PV(R) − PV(outlays)
Discounted return on outlays = NPV / PV(outlays) × 100%
BCR = [PV(B) + PV(R)] / PV(outlays)
Simple payback = C₀/(B−C) years, only when B−C > 0
| Kiekis | Meaning and unit |
|---|---|
| C₀ | Incremental investment paid at time 0; currency units |
| B | Constant annual gross incremental benefit; currency units/year |
| C | Constant annual recurring incremental outlay; currency units/year |
| N | Appraisal horizon; whole years |
| r | Annual discount rate entered as percent/year |
| R | Residual value received at end of year N; currency units |
What “ROI” means on this page
“Discounted return on outlays” is deliberately labelled and defined as NPV divided by PV(outlays). ROI has multiple conventions; this result is not IRR, accounting ROI, or a guaranteed PdM return. BCR and NPV are shown separately so the denominator cannot be mistaken.
Source classification
This is general discounted cash-flow arithmetic, not a formula prescribed by ISO. HM Treasury’s Green Book (2026) is an official methodological reference for lifetime costs and benefits, discounting, NPV/BCR, uncertainty and sensitivity analysis. Its public-sector scope and prescribed rates are not imported as commercial PdM defaults. See also the official discounting guidance. Accessed 13 July 2026.
For C₀ = 100, B = 50/year, C = 10/year, N = 5, r = 0% and R = 0: PV(B) = 250, PV(outlays) = 150, NPV = 100, discounted return on outlays = 66.6667%, BCR = 1.6667, annual net cash flow = 40/year, and simple payback = 2.5 years. This is an arithmetic test case, not a typical plant claim.