Payback Period Calculator mechanism

Model scope

The underlying concepts are standard, but the specification is not implementation-complete. Exact ambiguities requiring resolution are: cash-flow timing, discount-rate compounding and units, fractional-period interpolation, no-payback output, multiple-crossing behavior, and treatment of zero or negative initial cost.

• The simple-payback formula is only described as cumulative cash flow crossing zero; it does not specify whether the initial cost is treated as a negative time-zero cash flow and whether fractional-period interpolation is used.
• The discounted-payback formula does not explicitly define PV_t = CF_t/(1+r)^t, the cash-flow timing convention, or whether the discount rate is effective per period.
• The specification does not define behavior when cumulative cash flow never reaches zero, reaches zero exactly, crosses zero more than once, or becomes negative again after payback.
• The chart's breakeven point is not defined for no-payback cases, multiple crossings, or fractional-period interpolation.

Units and conventions

• Initial cost and every cash flow use the same currency units; initial cost is a positive amount representing a time-zero outflow.
• Cash flows are equally spaced and occur at the end of each stated period.
• For discounted payback, r is a decimal effective discount rate per cash-flow period, and PV_t = CF_t/(1+r)^t.
• Unless a vector explicitly uses months, annual cash flows and annual discount rates are assumed; monthly data require a monthly rate if discounting is performed.
• Payback is linearly interpolated within the period containing the crossing: prior completed periods plus unrecovered balance divided by the next period's relevant cash flow or discounted cash flow.
• A payback period of zero is valid when the initial cost is zero; no-payback cases should be represented explicitly rather than as an arbitrary large number.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "mode": "simple",
    "initial_cost": 10000,
    "cash_flow_series": [
      2500,
      3500,
      4000,
      3000
    ],
    "cash_flow_period": "annual"
  },
  "expected_outputs": {
    "payback_period_years": 3,
    "payback_period_months": 36,
    "breakeven_point_years": 3
  },
  "working": "Start cumulative cash flow = -10000. After year 1: -10000 + 2500 = -7500. After year 2: -7500 + 3500 = -4000. After year 3: -4000 + 4000 = 0. Therefore payback occurs exactly at 3 years = 36 months; the chart breakeven point is year 3."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The input discount_rate = -1 makes every discounted cash-flow denominator (1 + discount_rate)^t equal zero, so the discounted result is undefined. The instrument specification does not state that this invalid rate is rejected. A second robustness risk is the undocumented sign convention for initial cost and cash flows, which can change the meaning of the result.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json